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J. Froehlich

Publications and source records attributed to J. Froehlich.

At least 19 recordsLinked to original sources
arXiv2011

Diffusion of a massive quantum particle coupled to a quasi-free thermal medium

We consider a heavy quantum particle with an internal degree of freedom moving on the $d$-dimensional lattice $\bbZ^d$ (e.g., a heavy atom with finitely many excited states). The particle is coupled to a thermal medium (bath) consisting of free relativistic bosons through an interaction of strength $\la$ linear in creation and annihilation operators. The mass of the quantum particle is assumed to be of order $\la^{-2}$, and we assume that the internal degree of freedom is coupled "effectively" to the thermal medium. We prove that the motion of the quantum particle is diffusive in $d\geq 4$ and for $\la$ small enough.

math-ph↗
arXiv2010

Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

We show that, in a model where a non-relativistic particle is coupled to a quantized relativistic scalar Bose field, the embedded mass shell of the particle dissolves in the continuum when the interaction is turned on, provided the coupling constant is sufficiently small. More precisely, under the assumption that the fiber eigenvectors corresponding to the putative mass shell are differentiable as functions of the total momentum of the system, we show that a mass shell could exist only at a strictly positive distance from the unperturbed embedded mass shell near the boundary of the energy-momentum spectrum.

math-ph↗
arXiv2009

Local Decay in Non-relativistic QED

We prove the limiting absorption principle for a dressed electron at a fixed total momentum in the standard model of non-relativistic quantum electrodynamics. Our proof is based on an application of the smooth Feshbach-Schur map in conjunction with Mourre's theory.

math-ph↗
arXiv2008

Colliding solitons for the nonlinear Schrodinger equation

We study the collision of two fast solitons for the nonlinear Schrödinger equation in the presence of a spatially adiabatic external potential. For a high initial relative speed $\|v\|$ of the solitons, we show that, up to times of order $\log\|v\|$ after the collision, the solitons preserve their shape (in $L^2$-norm), and the dynamics of the centers of mass of the solitons is approximately determined by the external potential, plus error terms due to radiation damping and the extended nature of the solitons. We remark on how to obtain longer time scales under stronger assumptions on the initial condition and the external potential.

math-ph↗
arXiv2008

On the theory of resonances in non-relativistic QED and related models

We study the mathematical theory of quantum resonances in the standard model of non-relativistic QED and in Nelson's model. In particular, we estimate the survival probability of metastable states corresponding to quantum resonances and relate the resonances to poles of an analytic continuation of matrix elements of the resolvent of the quantum Hamiltonian.

math-ph↗
arXiv2007

Spectral Theory for the Standard Model of Non-Relativistic QED

For a model of atoms and molecules made from static nuclei and non-relativistic electrons coupled to the quantized radiation field (the standard model of non-relativistic QED), we prove a Mourre estimate and a limiting absorption principle in a neighborhood of the ground state energy. As corollaries we derive local decay estimates for the photon dynamics, and we prove absence of (excited) eigenvalues and absolute continuity of the energy spectrum near the ground state energy, a region of the spectrum not understood in previous investigations. The conjugate operator in our Mourre estimate is the second quantized generator of dilatations on Fock space.

math-ph↗
arXiv2007

Semi-Classical Dynamics in Quantum Spin Systems

We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a corresponding Hamiltonian dynamics of classical spins. This result can be viewed as a Egorov-type theorem. We extend our results to the thermodynamic limit of lattice spin systems and continuum domains of infinite size, and we study the time evolution of coherent spin states in these limiting regimes.

math-ph↗
arXiv2005

Rayleigh Scattering at Atoms with Dynamical Nuclei

Scattering of photons at an atom with a dynamical nucleus is studied on the subspace of states of the system with a total energy below the threshold for ionization of the atom (Rayleigh scattering). The kinematics of the electron and the nucleus is chosen to be non-relativistic, and their spins are neglected. In a simplified model of a hydrogen atom or a one-electron ion interacting with the quantized radiation field in which the helicity of photons is neglected and the interactions between photons and the electron and nucleus are turned off at very high photon energies and at photon energies below an arbitrarily small, but fixed energy (infrared cutoff), asymptotic completeness of Rayleigh scattering is established rigorously. On the way towards proving this result, it is shown that, after coupling the electron and the nucleus to the photons, the atom still has a stable ground state, provided its center of mass velocity is smaller than the velocity of light; but its excited states are turned into resonances. The proof of asymptotic completeness then follows from extensions of a positive commutator method and of propagation estimates for the atom and the photons developed in previous papers. The methods developed in this paper can be extended to more realistic models. It is, however, not known, at present, how to remove the infrared cutoff.

math-ph↗
arXiv2005

Magnetism and the Weiss Exchange Field - A Theoretical Analysis Inspired by Recent Experiments

The huge spin precession frequency observed in recent experiments with spin-polarized beams of hot electrons shot through magnetized films is interpreted as being caused by Zeeman coupling of the electron spins to the so-called Weiss exchange field in the film. A "Stern-Gerlach experiment" for electrons moving through an inhomogeneous exchange field is proposed. The microscopic origin of exchange interactions and of large mean exchange fields, leading to different types of magnetic order, is elucidated. A microscopic derivation of the equations of motion of the Weiss exchange field is presented. Novel proofs of the existence of phase transitions in quantum XY-models and antiferromagnets, based on an analysis of the statistical distribution of the exchange field, are outlined.

cond-mat.str-el↗
arXiv2005

Long time motion of NLS solitary waves in a confining potential

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential $V(x)$ over a long time interval.

math-ph↗
arXiv2003

Asymptotic Completeness for Compton Scattering

Scattering in a model of a massive quantum-mechanical particle, an ``electron'', interacting with massless, relativistic bosons, ``photons'', is studied. The interaction term in the Hamiltonian of our model describes emission and absorption of ``photons'' by the ``electron''; but ``electron-positron'' pair production is suppressed. An ultraviolet cutoff and an (arbitrarily small, but fixed) infrared cutoff are imposed on the interaction term. In a range of energies where the propagation speed of the dressed ``electron'' is strictly smaller than the speed of light, unitarity of the scattering matrix is proven, provided the coupling constant is small enough; (asymptotic completeness of Compton scattering). The proof combines a construction of dressed one--electron states with propagation estimates for the ``electron'' and the ``photons''.

math-ph↗
arXiv2002

KMS, etc

A general form of the ``Wick rotation'', starting from imaginary-time Green functions of quantum-mechanical systems in thermal equilibrium at positive temperature, is established. Extending work of H. Araki, the role of the KMS condition and of an associated anti-unitary symmetry operation, the ``modular conjugation'', in constructing analytic continuations of Green functions from real- to imaginary times, and back, is clarified. The relationship between the KMS condition for the vacuum with respect to Lorentz boosts, on one hand, and the spin-statistics connection and the PCT theorem, on the other hand, in local, relativistic quantum field theory is recalled. General results on the reconstruction of local quantum theories in various non-trivial gravitational backgrounds from ``Euclidian amplitudes'' are presented. In particular, a general form of the KMS condition is proposed and applied, e.g., to the Unruh- and the Hawking effects. This paper is dedicated to Huzihiro Araki on the occasion of his seventieth birthday, with admiration, affection and best wishes.

math-ph↗
arXiv2002

Axions, Quantum Mechanical Pumping, and Primeval Magnetic Fields

We discuss the ordinary quantum Hall effect and a higher-dimensional cousin. We consider the dimensional reduction of these effects to 1+1 and 3+1 space-time dimensions, respectively. After dimensional reduction, an axion field appears, which plays the role of a space-time dependent difference of chemical potentials of chiral modes. As applications, we sketch a theory of quantum pumps and a mechanism for the generation of primeval magnetic fields in the early universe.

cond-mat↗
arXiv2001

Monopole fields from vortex sheets reconciling Abelian and center dominance

We describe a new order parameter for the confinement-deconfinement transition in lattice SU(2) Yang-Mills theory. It is expressed in terms of magnetic monopole field correlators represented as sums over sheets of center vortices. Our construction establishes a link between "abelian" and "center dominance". It avoids an inconsistency in the treatment of small scales present in earlier definitions of monopole fields by respecting Dirac's quantization condition for magnetic fluxes.

hep-lat↗
arXiv2001

Quantum lattice models at intermediate temperatures

We analyze the free energy and construct the Gibbs-KMS states for a class of quantum lattice systems, at low temperatures and when the interactions are almost diagonal in a suitable basis. We study systems with continuous symmetry, but our results are valid for discrete symmetry breaking only. Such phase transitions occur at intermediate temperatures where the continuous symmetry is not broken, while at very low temperature continuous symmetry breaking may occur.

math-ph↗
arXiv2001

Asymptotic Completeness for Rayleigh Scattering

It is expected that the state of an atom or molecule, initially put into an excited state with an energy below the ionization threshold, relaxes to a groundstate by spontaneous emission of photons which propagate to spatial infinity. In this paper, this picture is established for a large class of models of non-relativistic atoms and molecules coupled to the quantized radiation field, but with the simplifying feature that an (arbitrarily tiny, but positive) infrared cutoff is imposed on the interaction Hamiltonian. This result relies on a proof of asymptotic completeness for Rayleigh scattering of light on an atom. We establish asymptotic completeness of Rayleigh scattering for a class of model Hamiltonians with the features that the atomic Hamiltonian has point spectrum coexisting with absolutely continuous spectrum, and that either an infrared cutoff is imposed on the interaction Hamiltonian or photons are treated as massive particles. We show that, for models of massless photons, the spectrum of the Hamiltonian strictly below the ionization threshold is purely continuous, except for the groundstate energy.

math-ph↗
arXiv2000

An Order Parameter Reconciling Abelian and Center Dominance in SU(2) Yang-Mills Theory

We analyze previously proposed order parameters for the confinement - deconfinement transition in lattice SU(2) Yang-Mills theory, defined as vacuum expectation value (v.e.v.) of monopole fields in abelian projection gauges. We show that they exhibit some inconsistency in the treatment of small scales, due to a violation of Dirac quantization condition for fluxes. We propose a new order parameter avoiding this inconsistency. It can be interpreted as v.e.v. of the field of a regular monopole in any abelian projection gauge, but it is independent of the choice of the abelian projection. Furthermore, being constructed in terms of surfaces of center vortices, it has also a natural interpretation in the approach of center dominance.

hep-th↗