01183nas a2200121 4500008004100000245007100041210006300112260001800175520077400193100002100967700002200988856005101010 2016 en d00aOn the third critical speed for rotating Bose-Einstein condensates0 athird critical speed for rotating BoseEinstein condensates bAIP Publisher3 aWe 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.1 aDimonte, Daniele1 aCorreggi, Michele uhttp://urania.sissa.it/xmlui/handle/1963/3524601837nas a2200145 4500008004100000245007900041210006900120520133000189100002201519700002901541700002001570700002901590700002101619856005101640 2015 en d00aA class of Hamiltonians for a three-particle fermionic system at unitarity0 aclass of Hamiltonians for a threeparticle fermionic system at un3 aWe 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.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://urania.sissa.it/xmlui/handle/1963/3446901607nas a2200157 4500008004100000245009600041210006900137260002100206520106500227100002201292700002901314700002001343700002901363700002101392856003601413 2012 en d00aStability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions0 aStability for a System of N Fermions Plus a Different Particle w bWorld Scientific3 aWe 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.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFinco, Domenico1 aMichelangeli, Alessandro1 aTeta, Alessandro uhttp://hdl.handle.net/1963/606900818nas a2200109 4500008004300000245007400043210006900117520043500186100002200621700002900643856003600672 2005 en_Ud 00aDecay of a bound state under a time-periodic perturbation: a toy case0 aDecay of a bound state under a timeperiodic perturbation a toy c3 aWe 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.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/229801006nas a2200133 4500008004300000245007100043210006900114520056200183100002200745700002900767700002000796700002000816856003600836 2005 en_Ud 00aIonization for Three Dimensional Time-dependent Point Interactions0 aIonization for Three Dimensional Timedependent Point Interaction3 aWe 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.1 aCorreggi, Michele1 aDell'Antonio, Gianfausto1 aFigari, Rodolfo1 aMantile, Andrea uhttp://hdl.handle.net/1963/229701012nas a2200121 4500008004300000245005300043210005300096260001300149520064100162100002200803700002900825856003600854 2004 en_Ud 00aRotating Singular Perturbations of the Laplacian0 aRotating Singular Perturbations of the Laplacian bSpringer3 aWe 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).1 aCorreggi, Michele1 aDell'Antonio, Gianfausto uhttp://hdl.handle.net/1963/294500335nas a2200109 4500008004100000245004100041210004000082260001000122653003500132100002200167856003600189 2004 en d00aTime-dependent singular interactions0 aTimedependent singular interactions bSISSA10aRotating singular interactions1 aCorreggi, Michele uhttp://hdl.handle.net/1963/531000411nas a2200109 4500008004100000245009300041210006900134260001800203100002200221700002200243856003600265 2002 en d00aQuantum mechanics and stochastic mechanics for compatible observables at different times0 aQuantum mechanics and stochastic mechanics for compatible observ bSISSA Library1 aCorreggi, Michele1 aMorchio, Giovanni uhttp://hdl.handle.net/1963/1577