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 - RPRT
T1 - A class of Hamiltonians for a three-particle fermionic system at unitarity
Y1 - 2015
A1 - Michele Correggi
A1 - Gianfausto Dell'Antonio
A1 - Domenico Finco
A1 - Alessandro Michelangeli
A1 - Alessandro Teta
AB - We consider a quantum mechanical three-particle system made of two identical fermions of mass one and a different particle of mass $m$, where each fermion interacts via a zero-range force with the different particle. In particular we study the unitary regime, i.e., the case of infinite two-body scattering length. The Hamiltonians describing the system are, by definition, self-adjoint extensions of the free Hamiltonian restricted on smooth functions vanishing at the two-body coincidence planes, i.e., where the positions of two interacting particles coincide. It is known that for $m$ larger than a critical value $m^* \simeq (13.607)^{-1}$ a self-adjoint and lower bounded Hamiltonian $H_0$ can be constructed, whose domain is characterized in terms of the standard point-interaction boundary condition at each coincidence plane. Here we prove that for $m\in(m^*,m^{**})$, where $m^{**}\simeq (8.62)^{-1}$, there is a further family of self-adjoint and lower bounded Hamiltonians $H_{0,\beta}$, $\beta \in \mathbb{R}$, describing the system. Using a quadratic form method, we give a rigorous construction of such Hamiltonians and we show that the elements of their domains satisfy a further boundary condition, characterizing the singular behavior when the positions of all the three particles coincide.
UR - http://urania.sissa.it/xmlui/handle/1963/34469
N1 - This SISSA preprint is composed of 29 pages and is recorded in PDF format
U1 - 34644
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions
JF - Rev. Math. Phys. 24 (2012), 1250017
Y1 - 2012
A1 - Michele Correggi
A1 - Gianfausto Dell'Antonio
A1 - Domenico Finco
A1 - Alessandro Michelangeli
A1 - Alessandro Teta
AB - We study the stability problem for a non-relativistic quantum system in\\r\\ndimension three composed by $ N \\\\geq 2 $ identical fermions, with unit mass,\\r\\ninteracting with a different particle, with mass $ m $, via a zero-range\\r\\ninteraction of strength $ \\\\alpha \\\\in \\\\R $. We construct the corresponding\\r\\nrenormalised quadratic (or energy) form $ \\\\form $ and the so-called\\r\\nSkornyakov-Ter-Martirosyan symmetric extension $ H_{\\\\alpha} $, which is the\\r\\nnatural candidate as Hamiltonian of the system. We find a value of the mass $\\r\\nm^*(N) $ such that for $ m > m^*(N)$ the form $ \\\\form $ is closed and bounded from below. As a consequence, $ \\\\form $ defines a unique self-adjoint and bounded from below extension of $ H_{\\\\alpha}$ and therefore the system is stable. On the other hand, we also show that the form $ \\\\form $ is unbounded from below for $ m < m^*(2)$. In analogy with the well-known bosonic case, this suggests that the system is unstable for $ m < m^*(2)$ and the so-called Thomas effect occurs.
PB - World Scientific
UR - http://hdl.handle.net/1963/6069
U1 - 5955
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -
TY - JOUR
T1 - Decay of a bound state under a time-periodic perturbation: a toy case
JF - J. Phys. A 38 (2005) 4769-4781
Y1 - 2005
A1 - Michele Correggi
A1 - Gianfausto Dell'Antonio
AB - We study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with ``strength\\\'\\\' (\\\\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\\\\alpha(t)), we prove complete ionization as (t \\\\to \\\\infty). We prove also that, under the same conditions, all the states of the system are scattering states.
UR - http://hdl.handle.net/1963/2298
U1 - 1718
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Ionization for Three Dimensional Time-dependent Point Interactions
JF - Comm. Math. Phys. 257 (2005) 169-192
Y1 - 2005
A1 - Michele Correggi
A1 - Gianfausto Dell'Antonio
A1 - Rodolfo Figari
A1 - Andrea Mantile
AB - We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the ``strength\\\'\\\' of the interaction (\\\\alpha(t)) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of (\\\\alpha(t)), we prove that there is complete ionization as (t \\\\to \\\\infty), starting from a bound state at time (t = 0). Moreover we prove also that, under the same conditions, all the states of the system are scattering states.
UR - http://hdl.handle.net/1963/2297
U1 - 1719
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Rotating Singular Perturbations of the Laplacian
JF - Ann. Henri Poincare 5 (2004) 773-808
Y1 - 2004
A1 - Michele Correggi
A1 - Gianfausto Dell'Antonio
AB - We study a system of a quantum particle interacting with a singular time-dependent uniformly rotating potential in 2 and 3 dimensions: in particular we consider an interaction with support on a point (rotating point interaction) and on a set of codimension 1 (rotating blade). We prove the existence of the Hamiltonians of such systems as suitable self-adjoint operators and we give an explicit expression for their unitary semigroups. Moreover we analyze the asymptotic limit of large angular velocity and we prove strong convergence of the time-dependent propagator to some one-parameter unitary group as (\\\\omega \\\\to \\\\infty).
PB - Springer
UR - http://hdl.handle.net/1963/2945
U1 - 1755
U2 - Mathematics
U3 - Mathematical Physics
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 - Quantum mechanics and stochastic mechanics for compatible observables at different times
JF - Ann.Physics 296 (2002), no.2, 371
Y1 - 2002
A1 - Michele Correggi
A1 - Giovanni Morchio
PB - SISSA Library
UR - http://hdl.handle.net/1963/1577
U1 - 2541
U2 - Mathematics
U3 - Mathematical Physics
ER -