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.Wed, 20 Nov 2019 10:51:09 GMT2019-11-20T10:51:09Z10731Stationary states for non linear one-dimensional Schrodinger equations with singular potentialhttp://hdl.handle.net/11380/305998Titolo: Stationary states for non linear one-dimensional Schrodinger equations with singular potential
Abstract: In this paper we consider the time-independent one-dimensional non linear Schrodinger equation (NLS) with pointwise singular potential. We prove that when the strength of the pointwise interaction is less than a critical value, depending on the nonlinearity power a, then a non linear real-valued bound state exists. Furthermore, we show that when or is larger than 2 a further new real-valued stationary state appears under some conditions.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11380/3059982006-01-01T00:00:00ZMolecular localization induced by collisionshttp://hdl.handle.net/11380/458438Titolo: Molecular localization induced by collisions
Abstract: We consider a periodically driven double well as a simplified dynamical model for molecular localizationinduced by collisions. If the frequency of the collisions is high enough, so that the instability of the states islarger than a critical value, then the states are localized and we have the redshift of the inversion line.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/11380/4584382000-01-01T00:00:00ZAbsence of the absolutely continuous spectrum for Stark-Bloch operators with strongly singular periodic potentialshttp://hdl.handle.net/11380/8622Titolo: Absence of the absolutely continuous spectrum for Stark-Bloch operators with strongly singular periodic potentials
Abstract: We correct here the proof of the boundedness of the coupling term X given by us in a previous paper (1995 J. Phys. A: Math. Gen. 28 1101-6).
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/11380/86221998-01-01T00:00:00ZUniversal Critical Power for Nonlinear Schrödinger Equations with a Symmetric Double Well Potentialhttp://hdl.handle.net/11380/626276Titolo: Universal Critical Power for Nonlinear Schrödinger Equations with a Symmetric Double Well Potential
Abstract: Here we consider stationary states for nonlinear Schrödinger equations in any spatial dimension n with symmetric double well potentials. These states may bifurcate as the strength of the nonlinear term increases and we observe two different pictures depending on the value of the nonlinearity power: a supercritical pitchfork bifurcation, and a subcritical pitchfork bifurcation with two asymmetric branches occurring as the result of saddle-node bifurcations. We show that in the semiclassical limit, or for a large barrier between the two wells, the first kind of bifurcation always occurs when the nonlinearity power is less than a critical value; in contrast, when the nonlinearity power is larger than such a critical value then we always observe the second scenario. The remarkable fact is that such a critical value is a universal constant in the sense that it does not depend on the shape of the double well potential and on the dimension n.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11380/6262762009-01-01T00:00:00ZWannier ladders and perturbation theoryhttp://hdl.handle.net/11380/11186Titolo: Wannier ladders and perturbation theory
Abstract: Following Avron we consider the Stark effect for Bloch electrons in the case of a finite number of gaps. We prove that the ladders of resonances are given by the Wannier decoupled-band approximation and the perturbation theory. The Fermi golden rule yields the width behaviour of Buslaev and Dmitrieva.
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/11380/111861993-01-01T00:00:00ZA nonlinear Schrodinger equation with two symmetric point interactions in one dimensionhttp://hdl.handle.net/11380/639320Titolo: A nonlinear Schrodinger equation with two symmetric point interactions in one dimension
Abstract: We consider a time-dependent one-dimensional nonlinear Schrodinger equation with a symmetric double-well potential represented by two Dirac’s δ. Among our results we give an explicit formula for the integral kernel of the unitarysemigroup associated with the linear part of the Hamiltonian. Then we establish the corresponding Strichartz-type estimate and we prove local existence and uniqueness of the solution to the original nonlinear problem.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11380/6393202010-01-01T00:00:00ZNonlinear Schrödinger equations with multiple-well potentialhttp://hdl.handle.net/11380/876289Titolo: Nonlinear Schrödinger equations with multiple-well potential
Abstract: We consider the stationary solutions for a class of Schrödinger equations with a N-well potential and
a nonlinear perturbation. By means of semiclassical techniques we prove that the dominant term of
the ground state solutions is described by a N-dimensional Hamiltonian system, where the coupling
term among the coordinates is a tridiagonal Toeplitz matrix. In particular, in the limit of large focusing
nonlinearity we prove that the ground state stationary solutions consist of N wavefunctions localized on
a single well. Furthermore, we consider in detail the case of N = 4 wells, where we show the occurrence
of spontaneous symmetry-breaking bifurcation effect.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/11380/8762892012-01-01T00:00:00ZHorn 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/11380/6132401991-01-01T00:00:00ZSTARK LADDERS OF RESONANCES - WANNIER LADDERS AND PERTURBATION-THEORYhttp://hdl.handle.net/11380/304811Titolo: STARK LADDERS OF RESONANCES - WANNIER LADDERS AND PERTURBATION-THEORY
Abstract: Let H-B be any fixed one-dimensional Bloch Hamiltonian with only the first m gaps open and H-F = H-B + Fx be the corresponding Stark Hamiltonian. For any positive F small enough H-F has only m ladders of sharp resonances given by the analytic translation method, the decoupled band approximation and the regular perturbation theory. This way, the Wannier conjecture becomes a definite regular perturbation theory for the Stark ladders as eigenvalues of the translated Hamiltonian.
Sat, 01 Jan 1994 00:00:00 GMThttp://hdl.handle.net/11380/3048111994-01-01T00:00:00ZAbsence 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/11380/6130611995-01-01T00:00:00Z