In this paper we recover the non-perturbative partition function of 2D Yang–Mills theory from the perturbative path integral. To achieve this goal, we study the perturbative path integral quantization for 2D Yang–Mills theory on surfaces with boundaries and corners in the Batalin–Vilkovisky formalism (or, more precisely, in its adaptation to the setting with boundaries, compatible with gluing and cutting–-the BV-BFV formalism). We prove that cutting a surface (e.g. a closed one) into simple enough pieces–-building blocks–-and choosing a convenient gauge-fixing on the pieces, and assembling back the partition function on the surface, one recovers the known non-perturbative answers for 2D Yang–Mills theory.

UR - https://doi.org/10.1007/s00220-019-03392-w ER - TY - RPRT T1 - Transmission conditions obtained by homogenisation Y1 - 2018 A1 - Gianni Dal Maso A1 - Giovanni Franzina A1 - Davide Zucco AB - We study the asymptotic behaviour of solutions to variational problems in perforated domains with Neumann boundary conditions. We consider perforations that in the limit concentrate on a smooth manifold. We characterise the limits of the solutions and show that they solve a variational problem with a transmission condition across the manifold. This is expressed through a measure on the manifold, vanishing on sets of capacity zero. Then, we prove that every such measure can be obtained by homogenising suitable perforations. Eventually, we provide an asymptotic formula for this measure by using some auxiliary minimum problems. UR - http://preprints.sissa.it/handle/1963/35310 U1 - 35618 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - RPRT T1 - Truncation and convergence issues for bounded linear inverse problems in Hilbert space Y1 - 2018 A1 - Noe Caruso A1 - Alessandro Michelangeli A1 - Paolo Novati AB - We present a general discussion of the main features and issues that (bounded) inverse linear problems in Hilbert space exhibit when the dimension of the space is infinite. This includes the set-up of a consistent notation for inverse problems that are genuinely infinite-dimensional, the analysis of the finite-dimensional truncations, a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests. PB - SISSA UR - http://preprints.sissa.it/handle/1963/35326 U1 - 35637 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Time quasi-periodic gravity water waves in finite depth Y1 - 2017 A1 - P Baldi A1 - Massimiliano Berti A1 - Emanuele Haus A1 - Riccardo Montalto AB - We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments. UR - http://preprints.sissa.it/handle/1963/35296 U1 - 35602 U2 - Mathematics ER - TY - JOUR T1 - On the third critical speed for rotating Bose-Einstein condensates JF - Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901 Y1 - 2016 A1 - Daniele Dimonte A1 - Michele Correggi AB - We study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevskii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in Correggi et al. [J. Math. Phys. 53, 095203 (2012)] that such a transition occurs when the angular velocity is of order ε−4, with ε−2 denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and ε ≪ 1 (Thomas-Fermi regime). In this paper, we identify a finite value Ωc such that if Ω = Ω0/ε4 with Ω0 > Ωc, the condensate is in the giant vortex phase. Under the same condition, we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer. PB - AIP Publisher UR - http://urania.sissa.it/xmlui/handle/1963/35246 U1 - 35557 U2 - Mathematics ER - TY - JOUR T1 - Towards a gauge theory interpretation of the real topological string JF - Phys. Rev. D Y1 - 2016 A1 - Hayashi, Hirotaka A1 - Nicolò Piazzalunga A1 - Uranga, Angel M. AB -We consider the real topological string on certain noncompact toric Calabi-Yau three-folds $\mathbb{X}$, in its physical realization describing an orientifold of type IIA on $\mathbb{X}$ with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane Bogomol’nyi-Prasad-Sommerfield (BPS) states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.

PB - American Physical Society VL - 93 UR - https://link.aps.org/doi/10.1103/PhysRevD.93.066001 ER - TY - JOUR T1 - t-Structures are Normal Torsion Theories JF - Applied Categorical Structures Y1 - 2016 A1 - Domenico Fiorenza A1 - Fosco Loregian AB -We characterize $t$-structures in stable ∞-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathcal{t}$ on a stable $\infty$-category $\mathbb{C}$ is equivalent to a normal torsion theory $\mathbf{F}$ on $\mathbb{C}$, i.e. to a factorization system $\mathbf{F} = (\mathcal{\epsilon}, \mathcal{M})$ where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.

VL - 24 UR - https://doi.org/10.1007/s10485-015-9393-z ER - TY - THES T1 - t-structures on stable (infinity,1)-categories Y1 - 2016 A1 - Fosco Loregian KW - category theory, higher category theory, factorization system, torsion theory, homological algebra, higher algebra AB - The present work re-enacts the classical theory of t-structures reducing the classical definition coming from Algebraic Geometry to a rather primitive categorical gadget: suitable reflective factorization systems (defined in the work of Rosický, Tholen, and Cassidy-Hébert-Kelly), which we call "normal torsion theories" following. A relation between these two objects has previously been noticed by other authors, on the level of the triangulated homotopy categories of stable (infinity,1)-categories. The main achievement of the present thesis is to observe and prove that this relation exists genuinely when the definition is lifted to the higher-dimensional world where the notion of triangulated category comes from. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/35202 U1 - 35477 U2 - Mathematics U4 - 1 U5 - MAT/03 ER - TY - THES T1 - Two explorations in Dynamical Systems and Mechanics Y1 - 2016 A1 - Paolo Gidoni KW - Poincaré-Birkhoff Theorem AB - This thesis contains the work done by Paolo Gidoni during the doctorate programme in Matematical Analysis at SISSA, under the supervision of A. Fonda and A. DeSimone. The thesis is composed of two parts: "Avoiding cones conditions and higher dimensional twist" and "Directional friction in bio-inspired locomotion". PB - SISSA U1 - 35527 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Three-sphere low-Reynolds-number swimmer with a passive elastic arm Y1 - 2015 A1 - Alessandro Montino A1 - Antonio DeSimone AB - One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34530 U1 - 34735 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - A topological join construction and the Toda system on compact surfaces of arbitrary genus JF - Analysis & PDE Y1 - 2015 A1 - Aleks Jevnikar A1 - Kallel, Sadok A1 - Andrea Malchiodi PB - Mathematical Sciences Publishers VL - 8 ER - TY - RPRT T1 - Translation and adaptation of Birman's paper "On the theory of self-adjoint extensions of positive definite operators" (1956) Y1 - 2015 A1 - Mikhail Khotyakov A1 - Alessandro Michelangeli AB - This is an accurate translation from Russian and adaptation to the modern mathematical jargon of a classical paper by M. Sh. Birman published in 1956, which is still today central in the theory of self-adjoint extensions of semi-bounded operators, and for which yet no English version was available so far. PB - SISSA UR - http://urania.sissa.it/xmlui/handle/1963/34443 U1 - 34570 ER - TY - JOUR T1 - Topological Invariants of Eigenvalue Intersections and Decrease of Wannier Functions in Graphene JF - J. Stat. Phys 155 (2014) 1027-1071 Y1 - 2014 A1 - Domenico Monaco A1 - Gianluca Panati KW - Wannier functions, Bloch bundles, conical intersections, eigenspace vorticity, pseudospin winding number, graphene AB -We investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a geometric invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value n∈Z of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. With the help of these canonical models, we show that the single band Wannier function w satisfies |w(x)|≤const |x|^{−2} as |x|→∞, both in monolayer and bilayer graphene.

PB - Journal of Statistical Physics U1 - 7368 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - The topology of a subspace of the Legendrian curves on a closed contact 3-manifold Y1 - 2014 A1 - Ali Maalaoui A1 - Vittorio Martino AB - In this paper we study a subspace of the space of Legendrian loops and we show that the injection of this space into the full loop space is an S 1-equivariant homotopy equivalence. This space can be also seen as the space of zero Maslov index Legendrian loops and it shows up as a suitable space of variations in contact form geometry. PB - Advanced Nonlinear Studies UR - http://urania.sissa.it/xmlui/handle/1963/35016 U1 - 35262 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - THES T1 - Topology of moduli spaces of framed sheaves Y1 - 2013 A1 - Gharchia Abdellaoui KW - Moduli spaces, framed sheaves, instantons PB - SISSA UR - http://hdl.handle.net/1963/7152 U1 - 7158 U2 - Mathematics U4 - 1 U5 - MAT/03 GEOMETRIA ER - TY - RPRT T1 - On the tritronquée solutions of P$_I^2$ Y1 - 2013 A1 - Tamara Grava A1 - Andrey Kapaev A1 - Christian Klein AB -For equation P$_I^2$, the second member in the P$_I$ hierarchy, we prove existence of various degenerate solutions depending on the complex parameter $t$ and evaluate the asymptotics in the complex $x$ plane for $|x|\to\infty$ and $t=o(x^{2/3})$. Using this result, we identify the most degenerate solutions $u^{(m)}(x,t)$, $\hat u^{(m)}(x,t)$, $m=0,\dots,6$, called {\em tritronqu\'ee}, describe the quasi-linear Stokes phenomenon and find the large $n$ asymptotics of the coefficients in a formal expansion of these solutions. We supplement our findings by a numerical study of the tritronqu\'ee solutions.

PB - SISSA U1 - 7282 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Tabulation of Painlevé 6 transcendents JF - Nonlinearity, Volume 25, Issue 12, December 2012, Pages 3235-3276 Y1 - 2012 A1 - Davide Guzzetti AB - The critical and asymptotic behaviors of solutions of the sixth Painlev'e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated. PB - IOP Publishing UR - http://hdl.handle.net/1963/6520 N1 - 30 pages, 1 figure; this article was published in "Nonlinearity" in 2012 U1 - 6471 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Thermodynamic phase transitions and shock singularities JF - Proc. R. Soc. A 8 March 2012 vol. 468 no. 2139 701-719 Y1 - 2012 A1 - Giuseppe De Nittis A1 - Antonio Moro AB - We show that under rather general assumptions on the form of the entropy\\r\\nfunction, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of the characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of\\r\\nnon-hydrodynamic type such as the classical plasma and the ideal Bose gas are\\r\\nalso discussed. PB - The Royal Society UR - http://hdl.handle.net/1963/6090 U1 - 5978 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - RPRT T1 - Topological sensitivity analysis for high order elliptic operators Y1 - 2012 A1 - Samuel Amstutz A1 - Antonio André Novotny A1 - Nicolas Van Goethem KW - Topological derivative, Elliptic operators, Polarization tensor AB - The topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation. It has applications in many different fields such as shape and topology optimization, inverse problems, image processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. The topological derivative has been fully developed for a wide range of second order differential operators. In this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m, m>=1. The general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced. We provide full mathematical justifications for the derived formulas, including precise estimates of remainders. PB - SISSA UR - http://hdl.handle.net/1963/6343 U1 - 6272 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - RPRT T1 - Thin-walled beams with a cross-section of arbitrary geometry: derivation of linear theories starting from 3D nonlinear elasticity Y1 - 2011 A1 - Elisa Davoli AB -The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and δ_h, respectively, the diameter and the thickness of the cross-section, we analyse the case where the scaling factor of the elastic energy is of order ε_h^2, with ε_h/δ_h^2 \rightarrow l \in [0, +\infty). Different linearized models are deduced according to the relative order of magnitude of δ_h with respect to h.

ER - TY - JOUR T1 - The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity JF - Calculus of Variations and Partial Differential Equations 41 (2011) 241-259 Y1 - 2011 A1 - Helmut Abels A1 - Maria Giovanna Mora A1 - Stefan Müller AB - The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation. PB - Springer UR - http://hdl.handle.net/1963/3835 U1 - 492 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - The Transition between the Gap Probabilities from the Pearcey to the Airy Process–a Riemann-Hilbert Approach JF - International Mathematics Research Notices Y1 - 2011 A1 - Marco Bertola A1 - Mattia Cafasso VL - doi: 10.1093/imrn/rnr066 ER - TY - JOUR T1 - Taming open/closed string duality with a Losev trick JF - JHEP 06(2010)063 Y1 - 2010 A1 - Giulio Bonelli A1 - Andrea Prudenziati A1 - Alessandro Tanzini AB - A target space string field theory formulation for open and closed B-model is provided by giving a Batalin-Vilkovisky quantization of the holomorphic Chern-Simons theory with off-shell gravity background. The target space expression for the coefficients of the holomorphic anomaly equation for open strings are obtained. Furthermore, open/closed string duality is proved from a judicious integration over the open string fields. In particular, by restriction to the case of independence on continuous open moduli, the shift formulas of [7] are reproduced and shown therefore to encode the data of a closed string dual. UR - http://hdl.handle.net/1963/3855 U1 - 854 U2 - Physics U3 - Mathematical Physics ER - TY - JOUR T1 - A three-dimensional model for the dynamics and hydrodynamics of rowing boats JF - Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology Y1 - 2010 A1 - L. Formaggia A1 - Andrea Mola A1 - N Parolini A1 - M Pischiutta AB -This paper proposes a new model describing the dynamics of a rowing boat for general three-dimensional motions. The complex interaction between the different components of the rowers–-oars–-boat system is analysed and reduced to a set of ordinary differential equations governing the rigid motion along the six degrees of freedom. To treat the unstable nature of the physical problem, a rather simple (but effective) control model is included, which mimics the main active control techniques adopted by the rowers during their action.

VL - 224 UR - https://doi.org/10.1243/17543371jset46 ER - TY - JOUR T1 - A time-dependent perturbative analysis for a quantum particle in a cloud chamber JF - Annales Henri Poincare 11 (2010) 539-564 Y1 - 2010 A1 - Gianfausto Dell'Antonio A1 - Rodolfo Figari A1 - Alessandro Teta AB - We consider a simple model of a cloud chamber consisting of a test particle (the alpha-particle) interacting with two other particles (the atoms of the vapour) subject to attractive potentials centered in $a_1, a_2 \\\\in \\\\mathbb{R}^3$. At time zero the alpha-particle is described by an outgoing spherical wave centered in the origin and the atoms are in their ground state. We show that, under suitable assumptions on the physical parameters of the system and up to second order in perturbation theory, the probability that both atoms are ionized is negligible unless $a_2$ lies on the line joining the origin with $a_1$. The work is a fully time-dependent version of the original analysis proposed by Mott in 1929. PB - Springer UR - http://hdl.handle.net/1963/3969 U1 - 432 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Twisted Covariance as a Non Invariant Restriction of the Fully Covariant DFR Model JF - Comm. Math. Phys. 295 (2010) 701-729 Y1 - 2010 A1 - Gherardo Piacitelli AB - We discuss twisted covariance over the noncommutative spacetime algebra generated by the relations [q_theta^mu,q_theta^nu]=i theta^{mu nu}, where the matrix theta is treated as fixed (not a tensor), and we refrain from using the asymptotic Moyal expansion of the twists. We show that the tensor nature of theta is only hidden in the formalism: in particular if theta fulfils the DFR conditions, the twisted Lorentz covariant model of the flat quantum spacetime may be equivalently described in terms of the DFR model, if we agree to discard a huge non invariant set of localisation states; it is only this last step which, if taken as a basic assumption, severely breaks the relativity principle. We also will show that the above mentioned, relativity breaking, ad hoc rejection of localisation states is an independent, unnecessary assumption, as far as some popular approaches to quantum field theory on the quantum Minkowski spacetime are concerned. The above should raise some concerns about speculations on possible observable consequences of arbitrary choices of theta in arbitrarily selected privileged frames. UR - http://hdl.handle.net/1963/3605 U1 - 696 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Two-dimensional almost-Riemannian structures with tangency points JF - Ann. Inst. H. Poincare Anal. Non Lineaire Y1 - 2010 A1 - Andrei A. Agrachev A1 - Ugo Boscain A1 - Grégoire Charlot A1 - Roberta Ghezzi A1 - Mario Sigalotti AB -Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We study the relation between the topological invariants of an almost-Riemannian structure on a compact oriented surface and the rank-two vector bundle over the surface which defines the structure. We analyse the generic case including the presence of tangency points, i.e. points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a classification of oriented almost-Riemannian structures on compact oriented surfaces in terms of the Euler number of the vector bundle corresponding to the structure. Moreover, we present a Gauss-Bonnet formula for almost-Riemannian structures with tangency points.

PB - Elsevier VL - 27 UR - http://hdl.handle.net/1963/3870 U1 - 839 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II Y1 - 2009 A1 - Antonio DeSimone A1 - Luca Heltai A1 - Cataldo Manigrasso AB - The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations. UR - http://hdl.handle.net/1963/3700 U1 - 605 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Topological branes, p-algebras and generalized Nahm equations JF - Phys. Lett. B 672 (2009) 390-395 Y1 - 2009 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Maxim Zabzine AB - Inspired by the recent advances in multiple M2-brane theory, we consider the generalizations of Nahm equations for arbitrary p-algebras. We construct the topological p-algebra quantum mechanics associated to them and we show that this can be obtained as a truncation of the topological p-brane theory previously studied by the authors. The resulting topological p-algebra quantum mechanics is discussed in detail and the relation with the M2-M5 system is pointed out in the p=3 case, providing a geometrical argument for the emergence of the 3-algebra structure in the Bagger-Lambert-Gustavsson theory UR - http://hdl.handle.net/1963/2702 U1 - 1398 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Topological expansion for the Cauchy two-matrix model JF - J. Phys. A Y1 - 2009 A1 - Marco Bertola A1 - Ferrer, A. Prats VL - 42 UR - http://dx.doi.org/10.1088/1751-8113/42/33/335201 ER - TY - RPRT T1 - Twisted Covariance vs Weyl Quantisation Y1 - 2009 A1 - Gherardo Piacitelli AB - In this letter we wish to clarify in which sense the tensor nature of the commutation relations [x^mu,x^nu]=i theta ^{mu nu} underlying Minkowski spacetime quantisation cannot be suppressed even in the twisted approach to Lorentz covariance. We then address the vexata quaestio \\\"why theta\\\"? UR - http://hdl.handle.net/1963/3451 U1 - 885 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings JF - Adv. Theor. Math. Phys. 12 (2008) 1429-1446 Y1 - 2008 A1 - Giulio Bonelli A1 - Alessandro Tanzini AB - We study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants. UR - http://hdl.handle.net/1963/1992 U1 - 2204 U2 - Physics U3 - Elementary Particle Theory ER - TY - JOUR T1 - Topological methods for an elliptic equation with exponential nonlinearities JF - Discrete Contin. Dyn. Syst. 21 (2008) 277-294 Y1 - 2008 A1 - Andrea Malchiodi AB - We consider a class of variational equations with exponential nonlinearities on compact surfaces. From considerations involving the Moser-Trudinger inequality, we characterize some sublevels of the Euler-Lagrange functional in terms of the topology of the surface and of the data of the equation. This is used together with a min-max argument to obtain existence results. UR - http://hdl.handle.net/1963/2594 U1 - 1528 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Transition layer for the heterogeneous Allen-Cahn equation JF - Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008) 609-631 Y1 - 2008 A1 - Fethi Mahmoudi A1 - Andrea Malchiodi A1 - Juncheng Wei AB - We consider the equation $\\\\e^{2}\\\\Delta u=(u-a(x))(u^2-1)$ in $\\\\Omega$, $\\\\frac{\\\\partial u}{\\\\partial \\\\nu} =0$ on $\\\\partial \\\\Omega$, where $\\\\Omega$ is a smooth and bounded domain in $\\\\R^n$, $\\\\nu$ the outer unit normal to $\\\\pa\\\\Omega$, and $a$ a smooth function satisfying $-10} and {a<0}. Assuming $\\\\nabla a \\\\neq 0$ on $K$ and $a\\\\ne 0$ on $\\\\partial \\\\Omega$, we show that there exists a sequence $\\\\e_j \\\\to 0$ such that the above equation has a solution $u_{\\\\e_j}$ which converges uniformly to $\\\\pm 1$ on the compact sets of $\\\\O_{\\\\pm}$ as $j \\\\to + \\\\infty$. UR - http://hdl.handle.net/1963/2656 U1 - 1467 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Transport Rays and Applications to Hamilton–Jacobi Equations T2 - Nonlinear PDE’s and Applications : C.I.M.E. Summer School, Cetraro, Italy 2008 / Stefano Bianchini, Eric A. Carlen, Alexander Mielke, Cédric Villani. Eds. Luigi Ambrosio, Giuseppe Savaré. - Berlin : Springer, 2011. - (Lecture Notes in Mathematics ; 20 Y1 - 2008 A1 - Stefano Bianchini A1 - Matteo Gloyer AB - The aim of these notes is to introduce the readers to the use of the Disintegration Theorem for measures as an effective tool for reducing problems in transport equations to simpler ones. The basic idea is to partition Rd into one dimensional sets, on which the problem under consideration becomes one space dimensional (and thus much easier, hopefully). JF - Nonlinear PDE’s and Applications : C.I.M.E. Summer School, Cetraro, Italy 2008 / Stefano Bianchini, Eric A. Carlen, Alexander Mielke, Cédric Villani. Eds. Luigi Ambrosio, Giuseppe Savaré. - Berlin : Springer, 2011. - (Lecture Notes in Mathematics ; 20 PB - Springer SN - 978-3-642-21718-0 UR - http://hdl.handle.net/1963/5463 N1 - This volume collects the notes of the CIME course Nonlinear PDE’s and\\r\\napplications held in Cetraro (Italy) on June 23–28, 2008. The school consisted\\r\\nin 5 series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), Felix Otto (Bonn University), Cedric Villani (Ecole Normale Superieure de Lyon). U1 - 5298 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Time optimal swing-up of the planar pendulum JF - 46th IEEE Conference on Decision and Control (2007) 5389 - 5394 Y1 - 2007 A1 - Mireille E. Broucke A1 - Paolo Mason A1 - Benedetto Piccoli AB - This paper presents qualitative and numerical results on the global structure of the time optimal trajectories of the planar pendulum on a cart. UR - http://hdl.handle.net/1963/1867 U1 - 2355 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Time-dependent systems of generalized Young measures Y1 - 2007 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time. JF - Netw. Heterog. Media 2 (2007) 1-36 UR - http://hdl.handle.net/1963/1795 U1 - 2749 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Twisted noncommutative equivariant Y1 - 2007 A1 - Lucio Cirio AB - We propose Weil and Cartan models for the equivariant cohomology of covariant actions on toric deformation manifolds. The construction is based on the noncommutative Weil algebra of Alekseev and Meinrenken; we show that one can implement a Drinfeld twist of their models in order to take into account the noncommutativity of the spaces we are acting on. UR - http://hdl.handle.net/1963/1991 U1 - 2205 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Thomae type formulae for singular Z_N curves JF - Lett. Math. Phys. 76 (2006) 187-214 Y1 - 2006 A1 - Victor Z. Enolski A1 - Tamara Grava AB - We give an elementary and rigorous proof of the Thomae type formula for singular $Z_N$ curves. To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs. An important step of the proof is the use of the Szego kernel computed explicitly in algebraic form for non-singular 1/N-periods. The proof inherits principal points of Nakayashiki\\\'s proof [31], obtained for non-singular ZN curves. UR - http://hdl.handle.net/1963/2125 U1 - 2118 U2 - Mathematics U3 - Mathematical Physics ER - TY - RPRT T1 - Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic field Y1 - 2006 A1 - Ugo Boscain A1 - Paolo Mason AB - In this paper we consider the minimum time population transfer problem for the z-component\\nof the spin of a (spin 1/2) particle driven by a magnetic field, controlled along the x axis, with bounded amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. Let (-E,E) be the two energy levels, and |omega (t)| ≤ M the bound on the field amplitude. For each couple of values E and M, we determine the time optimal synthesis starting from the level -E and we provide the explicit expression of the time optimal trajectories steering the state one to the state two, in terms of a parameter that can be computed solving numerically a suitable equation. For M/E << 1, every time optimal trajectory is bang-bang and in particular the corresponding control is periodic with frequency of the order of the resonance frequency wR = 2E. On the other side, for M/E > 1, the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching. Fixed E we also prove that for M → ∞ the time needed to reach the state two tends to zero. In the case M/E > 1 there are time optimal trajectories containing a singular arc. Finally we compare these results with some known results of Khaneja, Brockett and Glaser and with those obtained by controlling the magnetic field both on the x and y directions (or with one external field, but in the rotating wave approximation). As byproduct we prove that the qualitative shape of the time optimal synthesis presents different patterns, that cyclically alternate as M/E → 0, giving a partial proof of a conjecture formulated in a previous paper. JF - Journal of Mathematical Physics 47, 062101 (2006) UR - http://hdl.handle.net/1963/1734 U1 - 2418 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - On topological M-theory Y1 - 2006 A1 - Giulio Bonelli A1 - Alessandro Tanzini A1 - Maxim Zabzine AB - We construct a gauge fixed action for topological membranes on G2-manifolds such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds. JF - Adv. Theor. Math. Phys. 10 (2006) 239-260 UR - http://hdl.handle.net/1963/1765 U1 - 2779 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Topological symmetry of forms, N=1 supersymmetry and S-duality on special manifolds JF - J. Geom. Phys. 56 (2006) 2379-2401 Y1 - 2006 A1 - Laurent Baulieu A1 - Alessandro Tanzini AB - We study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT\\\'s (Almost Topological Quantum Field Theories), that is, theories with observables that are invariant under changes of metrics belonging to restricted classes. For Kahler manifolds in four dimensions, our topological model is related to N=1 Super Yang-Mills theory. Extended supersymmetries are recovered by considering the coupling with chiral multiplets. We also analyse Calabi-Yau manifolds in six and eight dimensions, and seven dimensional G_2 manifolds of the kind recently discussed by Hitchin. We argue that the two-form field could play an interesting role for the study of the conjectured S-duality in topological string. We finally show that in the case of real forms in six dimensions the partition function of our topological model is related to the square of that of the holomorphic Chern-Simons theory, and we discuss the uplift to seven dimensions and its relation with the recent proposals for the topological M-theory. UR - http://hdl.handle.net/1963/2168 U1 - 2076 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Two-matrix model with semiclassical potentials and extended Whitham hierarchy JF - J. Phys. A Y1 - 2006 A1 - Marco Bertola VL - 39 ER - TY - RPRT T1 - Time minimal trajectories for two-level quantum systems with drift Y1 - 2005 A1 - Ugo Boscain A1 - Paolo Mason AB - On a two-level quantum system driven by an external field, we consider the population transfer problem from the first to the second level, minimizing the time of transfer, with bounded field amplitude. On the Bloch sphere (i.e. after a suitable Hopf projection), this problem can be attacked with techniques of optimal syntheses on 2-D manifolds. JF - Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC \\\'05. 44th IEEE Conference on UR - http://hdl.handle.net/1963/1688 U1 - 2445 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Time Optimal Synthesis for Left-Invariant Control Systems on SO(3) JF - SIAM J. Control Optim. 44 (2005) 111-139 Y1 - 2005 A1 - Ugo Boscain A1 - Yacine Chitour AB - Consider the control system given by $\\\\dot x=x(f+ug)$, where $x\\\\in SO(3)$, $|u|\\\\leq 1$ and $f,g\\\\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\\\\|f\\\\|=\\\\cos(\\\\al)$ and $\\\\|g\\\\|=\\\\sin(\\\\al)$, $\\\\al\\\\in ]0,\\\\pi/4[$. In this paper, we provide an upper bound and a lower bound for $N(\\\\alpha)$, the maximum number of switchings for time-optimal trajectories. More precisely, we show that $N_S(\\\\al)\\\\leq N(\\\\al)\\\\leq N_S(\\\\al)+4$, where $N_S(\\\\al)$ is a suitable integer function of $\\\\al$ which for $\\\\al\\\\to 0$ is of order $\\\\pi/(4\\\\alpha).$ The result is obtained by studying the time optimal synthesis of a projected control problem on $R P^2$, where the projection is defined by an appropriate Hopf fibration. Finally, we study the projected control problem on the unit sphere $S^2$. It exhibits interesting features which will be partly rigorously derived and partially described by numerical simulations. UR - http://hdl.handle.net/1963/2258 U1 - 1989 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Topological vector symmetry, topological gauge fixing of BRSTQFT and construction of maximal supersymmetry Y1 - 2005 A1 - Laurent Baulieu A1 - Guillaume Bossard A1 - Alessandro Tanzini AB - The scalar and vector topological Yang-Mills symmetries determine a closed and consistent sector of Yang-Mills supersymmetry. We provide a geometrical construction of these symmetries, based on a horizontality condition on reducible manifolds. This yields globally well-defined scalar and vector topological BRST operators. These operators generate a subalgebra of maximally supersymmetric Yang-Mills theory, which is small enough to be closed off-shell with a finite set of auxiliary fields and large enough to determine the Yang-Mills supersymmetric theory. Poincaré supersymmetry is reached in the limit of flat manifolds. The arbitrariness of the gauge functions in BRSTQFTs is thus removed by the requirement of scalar and vector topological symmetry, which also determines the complete supersymmetry transformations in a twisted way. Provided additional Killing vectors exist on the manifold, an equivariant extension of our geometrical framework is provided, and the resulting \\\"equivariant topological field theory\\\" corresponds to the twist of super Yang-Mills theory on omega backgrounds. JF - JHEP 0508 (2005) 037 UR - http://hdl.handle.net/1963/1741 U1 - 2411 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - Traffic flow on a road network JF - SIAM J. Math. Anal. 36 (2005) 1862-1886 Y1 - 2005 A1 - Giuseppe Maria Coclite A1 - Benedetto Piccoli A1 - Mauro Garavello AB - This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars,\\ndefined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence, uniqueness and stability of solutions to the Cauchy problem. Our method is based on wave front tracking approach, see [6], and works also for boundary data and time dependent coefficients of traffic distribution at junctions, so including traffic lights. PB - SISSA Library UR - http://hdl.handle.net/1963/1584 U1 - 2534 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Tensor of coherences parametrization of multiqubit density operators for entanglement characterization JF - Phys. Rev. A 69 (2004) 012311 Y1 - 2004 A1 - Claudio Altafini AB - For multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parameterization obtained by the juxtaposition of the affine Bloch vectors of each qubit. While it maintains the tensorial structure of the underlying space, it highlights the pattern of correlations, both classical and quantum, between the subsystems and, due to the affine parameterization, it contains in its components all reduced densities of all orders. The main purpose of our use of this formalism is to deal with entanglement. For example, the detection of bipartite entanglement is straightforward, as it is the synthesis of densities having positive partial transposes between desired qubits. In addition, finding explicit mixtures for families of separable states becomes a feasible issue for few qubit symmetric densities (we compute it for Werner states) and, more important, it provides some insight on the possible origin of entanglement for such densities. PB - American Physical Society UR - http://hdl.handle.net/1963/2845 U1 - 1855 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Time-dependent singular interactions Y1 - 2004 A1 - Michele Correggi KW - Rotating singular interactions PB - SISSA UR - http://hdl.handle.net/1963/5310 U1 - 5135 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - Three-Phase Solutions of the Kadomtsev - Petviashvili Equation JF - Studies in Applied Mathematics. Year : 1997 ; Volume: 99 ; Issue: 2 ; Pages: 137-203 Y1 - 1997 A1 - Boris Dubrovin A1 - Ron Flickinger A1 - Harvey Segur AB - The Kadomtsev]Petviashvili KP. equation is known to admit explicit periodic\\r\\nand quasiperiodic solutions with N independent phases, for any integer\\r\\nN, based on a Riemann theta-function of N variables. For Ns1 and 2,\\r\\nthese solutions have been used successfully in physical applications. This\\r\\narticle addresses mathematical problems that arise in the computation of\\r\\ntheta-functions of three variables and with the corresponding solutions of\\r\\nthe KP equation. We identify a set of parameters and their corresponding\\r\\nranges, such that e¨ery real-valued, smooth KP solution associated with a\\r\\nRiemann theta-function of three variables corresponds to exactly one choice\\r\\nof these parameters in the proper range. Our results are embodied in a\\r\\nprogram that computes these solutions efficiently and that is available to the\\r\\nreader. We also discuss some properties of three-phase solutions. PB - SISSA UR - http://hdl.handle.net/1963/6484 U1 - 6426 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - CHAP T1 - Topological conformal field theory from the point of view of integrable systems T2 - Integrable quantum field theories / edited by L. Bonora ... \et al.! - New York : Plenum Press, 1993. - page : 283 - 302. Y1 - 1993 A1 - Boris Dubrovin AB - Recent results on classification of massive topological conformal field theories (TCFT) in terms of monodromy data of auxiliary linear operators with rational coefficients are presented. Procedure of coupling of a TCFT to topological gravity is described (at tree-level approximation) via certain integrable hierarchies of hydrodynamic type and their tau-functions. It is explained how the calculation of the ground state metric on TCFT can be interpreted in terms of harmonic maps. Also a construction of some models via Coxeter groups is described. JF - Integrable quantum field theories / edited by L. Bonora ... \et al.! - New York : Plenum Press, 1993. - page : 283 - 302. PB - SISSA SN - 0306445344 UR - http://hdl.handle.net/1963/6479 N1 - NATO ASI series / B ;v. 310 U1 - 6431 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - JOUR T1 - Topological "observables" in semiclassical field theories JF - Phys. Lett. B 297 (1992) 82-88 Y1 - 1992 A1 - Margherita Nolasco A1 - Cesare Reina AB -We give a geometrical set up for the semiclassical approximation to euclidean field theories having families of minima (instantons) parametrized by suitable moduli spaces ${\mathcal{M}}$. The standard examples are of course Yang-Mills theory and non-linear $\sigma$-models. The relevant space here is a family of measure spaces $\tilde{\mathcal{N}} \rightarrow \mathcal{M}$, with standard fibre a distribution space, given by a suitable extension of the normal bundle to $\mathcal{M}$ in the space of smooth fields. Over $\tilde{\mathcal{N}}$ there is a probability measure $d\mu$ given by the twisted product of the (normalized) volume element on $\mathcal{M}$ and the family of gaussian measures with covariance given by the tree propagator $C_\phi$ in the background of an instanton $\phi \in \mathcal{M}$. The space of "observables", i.e. measurable functions on ($\tilde{\mathcal{N}},\, d\mu$), is studied and it is shown to contain a topological sector, corresponding to the intersection theory on $\mathcal{M}$. The expectation value of these topological "observables" does not depend on the covariance; it is therefore exact at all orders in perturbation theory and can moreover be computed in the topological regime by setting the covariance to zero.

PB - Elsevier UR - http://hdl.handle.net/1963/3541 U1 - 1160 U2 - Mathematics U3 - Mathematical Physics ER - TY - JOUR T1 - The two-point boundary value problem from the Cauchy problem JF - J. Differential Equations 60 (1985), no. 1, 1--20 Y1 - 1985 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/332 U1 - 3635 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Towards a theory for periodic solutions to first order ordinary differential equations. Y1 - 1983 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/295 U1 - 3672 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Three uniqueness theorems for strongly non-linear elliptic problems Y1 - 1982 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/167 U1 - 3800 U2 - Mathematics U3 - Functional Analysis and Applications ER -