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218
An Adiabatic Theorem without a gap condition
 Commun. Math. Phys
, 1999
"... We prove an adiabatic theorem for the ground state of the Dicke model in a slowly rotating magnetic field and show that for weak electronphoton coupling, the adiabatic time scale is close to the time scale of the corresponding two level system–without the quantized radiation field. There is a corre ..."
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Cited by 41 (5 self)
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We prove an adiabatic theorem for the ground state of the Dicke model in a slowly rotating magnetic field and show that for weak electronphoton coupling, the adiabatic time scale is close to the time scale of the corresponding two level system–without the quantized radiation field. There is a correction to this time scale which is the Lamb shift of the model. The photon field affect the rate of approach to the adiabatic limit through a logarithmic correction originating from an infrared singularity characteristic of QED.
Wellposedness for the fene dumbbell model of polymeric flows
 2008. WELLPOSEDNESS FOR THE MICROSCOPIC FENE MODEL 15
"... interactions, wellposedness. ..."
Spectra of selfadjoint extensions and applications to solvable Schrödinger operators
, 2007
"... ..."
On a Model for Quantum Friction II  Fermi’s Golden Rule and Dynamics at Positive Temperature
 UNIVERSITE DEGENEVE SCHOLA GENEVENSIS MDLIX
, 1994
"... We investigate the dynamics of an Nlevel system linearly coupled to a field of massless bosons at positive temperature. Using complex deformation techniques, we develop timedependent perturbation theory and study spectral properties of the total ..."
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Cited by 30 (4 self)
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We investigate the dynamics of an Nlevel system linearly coupled to a field of massless bosons at positive temperature. Using complex deformation techniques, we develop timedependent perturbation theory and study spectral properties of the total
Scattering theory for systems with different spatial asymptotics to the left and right
 COMMUN.MATH.PHYS. 63
, 1978
"... We discuss the existence and completeness of scattering for onedimensional systems with different spatial asymptotics at ± oo, for example 2 4 V(x) where V(x) = 0 (resp. sin x) if x < 0 (resp. x> 0). We then extend our results to higher dimensional systems periodic, except for a localised impurit ..."
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Cited by 30 (12 self)
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We discuss the existence and completeness of scattering for onedimensional systems with different spatial asymptotics at ± oo, for example 2 4 V(x) where V(x) = 0 (resp. sin x) if x < 0 (resp. x> 0). We then extend our results to higher dimensional systems periodic, except for a localised impurity, in all but one space dimension. A new method, "the twisting trick", is presented for proving the absence of singular continuous spectrum, and some independent applications of this trick are given in an appendix.
WKB analysis for nonlinear Schrödinger equations with a potential
 Comm. Math. Phys
"... Abstract. We justify the WKB analysis for the semiclassical nonlinear Schrödinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. ..."
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Cited by 28 (10 self)
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Abstract. We justify the WKB analysis for the semiclassical nonlinear Schrödinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besides subquadratic potentials, we consider initial phases which may be unbounded. For this, we construct solutions for some compressible Euler equations with unbounded source term and unbounded initial velocity. (1.1) (1.2)
Essential selfadjointness for semibounded magnetic Schrödinger operators on noncompact manifolds
, 2001
"... We prove essential selfadjointness for semibounded below magnetic Schrödinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar potential are allowed. This is an extension of the Povzner–Wie ..."
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Cited by 23 (3 self)
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We prove essential selfadjointness for semibounded below magnetic Schrödinger operators on complete Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. Some singularities of the scalar potential are allowed. This is an extension of the Povzner–Wienholtz–Simader theorem. The proof uses the scheme of Wienholtz but requires a refined invariant integration by parts technique, as well as a use of a family of cutoff functions which are constructed by a nontrivial smoothing procedure due to Karcher.
Center Manifold for Nonintegrable Nonlinear Schrödinger Equations on the Line
, 2000
"... In this paper we study the following nonlinear Schrodinger equation on the line, i @ @t u(t; x) = \Gamma d 2 dx 2 u(t; x) + V (x)u(t; x) + f(x; juj) u(t; x) ju(t; x)j ; u(0; x) = OE(x); where f is realvalued, and it satisfies suitable conditions on regularity, on grow as a function of u and ..."
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Cited by 22 (2 self)
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In this paper we study the following nonlinear Schrodinger equation on the line, i @ @t u(t; x) = \Gamma d 2 dx 2 u(t; x) + V (x)u(t; x) + f(x; juj) u(t; x) ju(t; x)j ; u(0; x) = OE(x); where f is realvalued, and it satisfies suitable conditions on regularity, on grow as a function of u and on decay as x ! \Sigma1. The generic potential, V , is realvalued and it is chosen so that the spectrum of H := \Gamma d 2 dx 2 + V consists of one simple negative eigenvalue and absolutelycontinuous spectrum filling [0; 1). The solutions to this equation have, in general, a localized and a dispersive component. The nonlinear bound states, that bifurcate from the zero solution at the energy of the eigenvalue of H, define an invariant center manifold that consists of the orbits of timeperiodic localized solutions . We prove that all small solutions approach a particular periodic orbit in the center manifold as t ! \Sigma1. In general, the periodic orbits are different for t ! \Sigma1. O...