Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Mon, 22 Jul 2019 20:54:21 GMT2019-07-22T20:54:21Z10731Horn of singularities for the Stark-Wannier laddershttp://hdl.handle.net/11380/613240Titolo: Horn of singularities for the Stark-Wannier ladders
Abstract: We prove that the small field asymptotic behaviour of the Stark-Wannier ladders near the real direction is generically highly singular. This result is in agreement with the conjecture of a chaotic behaviour of the lifetime of the states because of infinitely many crossings.
Tue, 01 Jan 1991 00:00:00 GMThttp://hdl.handle.net/11380/6132401991-01-01T00:00:00ZAbsence of the absolutely continuous spectrum for Stark-Bloch operators with strongly singular periodic potentialshttp://hdl.handle.net/11380/613061Titolo: Absence of the absolutely continuous spectrum for Stark-Bloch operators with strongly singular periodic potentials
Abstract: We prove the absence of the absolutely continuous spectrum for the operator -d(2)/dx(2) + Sigma(j epsilon Z)alpha delta'(x - j) + fx, > 0 and alpha not equal 0, by means of the crystal momentum representation and the Howland's criterion for Floquet-type operators.
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/11380/6130611995-01-01T00:00:00ZSecond School and Workshop on "Mathematical Methods in Quantum Mechanics"http://hdl.handle.net/11380/616556Titolo: Second School and Workshop on "Mathematical Methods in Quantum Mechanics"
Abstract: Aim and topicsThe aim of the meeting is to present the state of the art in some challenging open problems in Quantum Mechanics from the point of view of Mathematical Physics. It is mainly addressed to young people interested in working on the subject. Among the topics covered: Derivation of macroscopic equations from microscopic quantum dynamics, coupled dynamics of particles and radiation fields, quantum information and entanglement, classical behaviour in quantum systems, scattering and spectral analysis for Schrödinger operators, quantum graphs.Three short courses will be given in a series of lectures scheduled in the morning of each day. Some invited talks will be given in the afternoon followed by short contributed talks given by participants.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11380/6165562007-01-01T00:00:00ZFirst School and Workshop "Mathematical Methods in Quantum Mechanics"http://hdl.handle.net/11380/616557Titolo: First School and Workshop "Mathematical Methods in Quantum Mechanics"
Abstract: The aim of the meeting is to present the state of the art in some challenging open problems in Quantum Mechanics from the point of view of Mathematical Physics. It is mainly addressed to young people interested in working on the subject.Among the topics covered: scattering for linear and nonlinear Schrödinger equation, many-body problems, derivation of macroscopic equations from quantum dynamics, Born-Oppenheimer approximation, classical behavior in quantum systems.Three short courses will be given in a series of lectures scheduled in the morning of each day. Some invited talks will be given in the afternoon followed by short contributed talks given by participants.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11380/6165572005-01-01T00:00:00ZStationary solutions to the
multi-dimensional Gross–Pitaevskii
equation with double-well potentialhttp://hdl.handle.net/11380/1046715Titolo: Stationary solutions to the
multi-dimensional Gross–Pitaevskii
equation with double-well potential
Abstract: In this paper we consider a nonlinear Schr ̈odinger equation with a cubic
nonlinearity and a multi-dimensional double well potential. In the semiclassical
limit the problem of the existence of stationary solutions simply reduces to the
analysis of a finite dimensional Hamiltonian system which exhibits different
behaviour depending on the dimension. In particular, in dimension 1 the
symmetric stationary solution shows a standard pitchfork bifurcation effect,
while in dimensions 2 and 3 new asymmetrical solutions associated with saddle
points occur. These last solutions are localized on a single well and this fact is
related to the phase transition effect observed in Bose–Einstein condensates in
periodical lattices.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11380/10467152014-01-01T00:00:00ZFirst principle explanation of phase transition for Bose-Einstein
condensates in optical latticeshttp://hdl.handle.net/11380/1046716Titolo: First principle explanation of phase transition for Bose-Einstein
condensates in optical lattices
Abstract: In this paper we consider Bose-Einstein condensates (BECs) in one-, two- and three-dimension
lattice potentials. The key argument for the explanation of the transition from Superfluidity phase to Mott-
Insulator phase is suggested to be the spontaneous symmetry breaking effect which occurs for critical values
of the ratio between the on-site interaction term and the hopping matrix element. Such an effect can be
directly seen in the Gross-Pitaevskii equation with double-well potentials and it also explains the different
behavior between one-dimensional models and two/three-dimensional models.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11380/10467162014-01-01T00:00:00ZSingular continuous spectrum in a class of random Schroedinger operatorshttp://hdl.handle.net/11380/612564Titolo: Singular continuous spectrum in a class of random Schroedinger operators
Abstract: For a class of random Schrodinger operators in L2(R(d)) H(omega) = -DELTA + SIGMA(j is-an-element-of Z(d)) q(j)(omega) f(x - j) where q(j) are continuous independent identically distributed bounded random variables and f has a power decay and defined sign, in any energy interval the singular continuous spectrum is either empty or with positive Lebesgue measure. As a consequence, the proof of localization for a class of random but deterministic one-dimensional operators is shifted to showing that the singular continuous spectrum has null Lebesgue measure.
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/11380/6125641993-01-01T00:00:00ZSpectral splitting method for nonlinear Schrodinger equations with singular potentialhttp://hdl.handle.net/11380/612613Titolo: Spectral splitting method for nonlinear Schrodinger equations with singular potential
Abstract: We consider the time-dependent one-dimensional nonlinear Schro¨dinger equation with pointwise singular potential. Bymeans of spectral splitting methods we prove that the evolution operator is approximated by the Lie evolution operator,where the kernel of the Lie evolution operator is explicitly written. This result yields a numerical procedure which is muchless computationally expensive than multi-grid methods previously used. Furthermore, we apply the Lie approximation inorder to make some numerical experiments concerning the splitting of a soliton, interaction among solitons and blow-upphenomenon.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11380/6126132007-01-01T00:00:00ZThird School and Workshop on "Mathematical Methods in Quantum Mechanics"http://hdl.handle.net/11380/616555Titolo: Third School and Workshop on "Mathematical Methods in Quantum Mechanics"
Abstract: The aim of the meeting is to present the state of the art in some challenging open problems in Quantum Mechanics from the point of view of Mathematical Physics. It is mainly addressed to young people interested in working on the subject.Among the topics covered: quantum systems with magnetic fields, quantum transport theory, quantum dechoerence and entanglement, classical behaviour in quantum systems, scattering and spectral analysis for Schroedinger operators, quantum chaos, adiabatic and semiclassical methods. non linear Schroedinger equations.Three courses will be given in a series of lectures scheduled in the morning of each day. Some invited talks will be given in the afternoon followed by short contributed talks given by participants.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11380/6165552009-01-01T00:00:00ZSolution to the double-well nonlinear Schrödinger equation with Stark-type external fieldhttp://hdl.handle.net/11380/1060123Titolo: Solution to the double-well nonlinear Schrödinger equation with Stark-type external field
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11380/10601232015-01-01T00:00:00Z