Results 1  10
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136
Renormalization group and asymptotics of solutions of nonlinear parabolic equations
 Comm. Pure Appl. Math
, 1994
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Moment Analysis for Localization in Random Schrödinger Operators
, 2005
"... We study localization effects of disorder on the spectral and dynamical properties of Schrödinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection kernels, including in the mean. These are derived through the ..."
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Cited by 39 (12 self)
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We study localization effects of disorder on the spectral and dynamical properties of Schrödinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection kernels, including in the mean. These are derived through the analysis of fractional moments of the resolvent, which are finite due to the resonancediffusing effects of the disorder. The main difficulty which has up to now prevented an extension of this method to the continuum can be traced to the lack of a uniform bound on the LifshitzKrein spectral shift associated with the local potential terms. The difficulty is avoided here through the use of a weakL¹ estimate concerning the boundaryvalue distribution of resolvents of maximally dissipative operators, combined with standard tools of relative compactness theory.
Continuity properties of Schrödinger semigroups with magnetic fields
 MATHEMATICAL PHYSICS PREPRINT ARCHIVE
, 2000
"... Published in slightly different form in Rev. Math. Phys. 12, 181–225 (2000) The objects of the present study are oneparameter semigroups generated by Schrödinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on th ..."
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Cited by 39 (9 self)
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Published in slightly different form in Rev. Math. Phys. 12, 181–225 (2000) The objects of the present study are oneparameter semigroups generated by Schrödinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Katolike conditions. The configuration space is supposed to be an arbitrary open subset of multidimensional Euclidean space; in case that it is a proper subset, the Schrödinger operator is rendered symmetric by imposing Dirichlet boundary conditions. We discuss the continuity of the image functions of the semigroup and show localnormcontinuity of the semigroup in the potentials. Finally, we prove that the semigroup has a continuous integral kernel given by a Brownianbridge expectation. Altogether, the article is meant to extend some of the results in B. Simon’s landmark paper [Bull. Amer. Math. Soc. (N.S.) 7, 447–526
Exponential mixing for the 2D stochastic NavierStokes dynamics
 Commun. Math. Phys
, 2002
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Selfadjointness of the PauliFierz Hamiltonian for arbitrary coupling constants
, 2001
"... The PauliFierz Hamiltonian describes a system of N electrons interacting with a quantized radiation field. The electrons have spin and an ultraviolet cutoff is imposed on the quantized radiation field. For arbitrary coupling constants, selfadjointness and essential selfadjointness of the PauliFi ..."
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Cited by 35 (8 self)
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The PauliFierz Hamiltonian describes a system of N electrons interacting with a quantized radiation field. The electrons have spin and an ultraviolet cutoff is imposed on the quantized radiation field. For arbitrary coupling constants, selfadjointness and essential selfadjointness of the PauliFierz Hamiltonian are proven under a class of ultraviolet cutoffs. 1 Introduction The purpose of this paper is to establish the selfadjointness and the essential selfadjointness of the PauliFierz Hamiltonian [24] for arbitrary coupling constants. The PauliFierz Hamiltonian governs a system of N electrons interacting with a quantized radiation field. The N electrons are assumed to have spin and the quantized radiation field is smeared by an ultraviolet cutoff. The dynamics of the system is determined by the oneparameter unitary timeevolution generated by the PauliFierz Hamiltonian. So, as a first step, it is necessary to establish the selfadjointness of the PauliFierz Hamiltonian. Gener...
Trace Class Perturbations and the Absence of Absolutely Continuous Spectra
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1989
"... We show that various Hamiltonians and Jacobi matrices have no absolutely continuous spectrum by showing that under a trace class perturbation they become a direct sum of finite matrices. ..."
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Cited by 26 (9 self)
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We show that various Hamiltonians and Jacobi matrices have no absolutely continuous spectrum by showing that under a trace class perturbation they become a direct sum of finite matrices.
The Classical Limit of Quantum Partition Functions
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1980
"... We extend Lieb's limit theorem [which asserts that SO(3) quantum spins approach S² classical spins as L> ∞] to general compact Lie groups. We also discuss the classical limit for various continuum systems. To control the compact group case, we discuss coherent states built up from a maxima ..."
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Cited by 23 (0 self)
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We extend Lieb's limit theorem [which asserts that SO(3) quantum spins approach S² classical spins as L> ∞] to general compact Lie groups. We also discuss the classical limit for various continuum systems. To control the compact group case, we discuss coherent states built up from a maximal weight vector in an irreducible representation and we prove that every bounded operator is an integral of projections onto coherent vectors (i.e. every operator has "diagonal form").
Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials, Rev
 Math. Phys
"... The object of the present study is the integrated density of states of a quantum particle in multidimensional Euclidean space which is characterized by a Schrödinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic rando ..."
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Cited by 21 (6 self)
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The object of the present study is the integrated density of states of a quantum particle in multidimensional Euclidean space which is characterized by a Schrödinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinitevolume limits of spatial eigenvalue concentrations of finitevolume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinitevolume operator, the integrated density of states is almost surely nonrandom and independent of the chosen boundary condition. Our proof of the
Ground state properties of the Nelson Hamiltonian  A Gibbs measurebased approach
 Rev. Math. Phys
, 2001
"... The Nelson model describes a quantum particle coupled to a scalar Bose field. We study properties of its ground state through functional integration techniques in case the particle is confined by an external potential. We obtain bounds on the average and the variance of the Bose field both in positi ..."
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Cited by 19 (12 self)
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The Nelson model describes a quantum particle coupled to a scalar Bose field. We study properties of its ground state through functional integration techniques in case the particle is confined by an external potential. We obtain bounds on the average and the variance of the Bose field both in position and momentum space, on the distribution of the number of bosons, and on the position space distribution of the particle.
Coupling constant thresholds in nonrelativisitic quantum mechanics, III. Some long range potentials
"... Abstract. We extend the analysis of absorbtion of eigenvalues for the two body case to situations where absorbtion occurs at a two cluster threshold in an JVbody system. The result depends on a BirmanSchwinger kernel for such an ATbody system, an object which we apply in other ways. In particular ..."
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Cited by 19 (1 self)
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Abstract. We extend the analysis of absorbtion of eigenvalues for the two body case to situations where absorbtion occurs at a two cluster threshold in an JVbody system. The result depends on a BirmanSchwinger kernel for such an ATbody system, an object which we apply in other ways. In particular, we control the number of discrete eigenvalues in the h> 0 limit. 1.