Results 1  10
of
459
Spectra of selfadjoint extensions and applications to solvable Schrödinger operators
, 2007
"... ..."
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 ..."
Abstract

Cited by 59 (7 self)
 Add to MetaCart
(Show Context)
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.
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 ..."
Abstract

Cited by 53 (4 self)
 Add to MetaCart
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
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. ..."
Abstract

Cited by 53 (11 self)
 Add to MetaCart
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)
Wellposedness for the fene dumbbell model of polymeric flows
 2008. WELLPOSEDNESS FOR THE MICROSCOPIC FENE MODEL 15
"... interactions, wellposedness. ..."
(Show Context)
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 ..."
Abstract

Cited by 44 (3 self)
 Add to MetaCart
(Show Context)
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.
The integrated density of states for random Schrödinger operators
"... We survey some aspects of the theory of the integrated density of states (IDS) of random Schrödinger operators. The first part motivates the problem and introduces the relevant models as well as quantities of interest. The proof of the existence of this interesting quantity, the IDS, is discussed i ..."
Abstract

Cited by 43 (3 self)
 Add to MetaCart
We survey some aspects of the theory of the integrated density of states (IDS) of random Schrödinger operators. The first part motivates the problem and introduces the relevant models as well as quantities of interest. The proof of the existence of this interesting quantity, the IDS, is discussed in the second section. One central topic of this survey is the asymptotic behavior of the integrated density of states at the boundary of the spectrum. In particular, we are interested in Lifshitz tails and the occurrence of a classical and a quantum regime. In the last section we discuss regularity properties of the IDS. Our emphasis is on the discussion of fundamental problems and central ideas to handle them. Finally, we discuss further developments and problems
The Theory Of Generalized Dirichlet Forms And Its Applications In Analysis And Stochastics
, 1996
"... We present an introduction (also for nonexperts) to a new framework for the analysis of (up to) second order differential operators (with merely measurable coefficients and in possibly infinitely many variables) on L²spaces via associated bilinear forms. This new framework, in particular, covers b ..."
Abstract

Cited by 42 (1 self)
 Add to MetaCart
We present an introduction (also for nonexperts) to a new framework for the analysis of (up to) second order differential operators (with merely measurable coefficients and in possibly infinitely many variables) on L²spaces via associated bilinear forms. This new framework, in particular, covers both the elliptic and the parabolic case within one approach. To this end we introduce a new class of bilinear forms, socalled generalized Dirichlet forms, which are in general neither symmetric nor coercive, but still generate associated C0 semigroups. Particular examples of generalized Dirichlet forms are symmetric and coercive Dirichlet forms (cf. [FOT], [MR1]) as well as time dependent Dirichlet forms (cf. [O1]). We discuss many applications to differential operators that can be treated within the new framework only, e.g. parabolic differential operators with unbounded drifts satisfying no L p conditions, singular and fractional diffusion operators. Subsequently, we analyz...
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 i ..."
Abstract

Cited by 41 (12 self)
 Add to MetaCart
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.