Flow Equations for Electron-Phonon Interactions

A recently proposed method of continuous unitary transformations is used to eliminate the interaction between electrons and phonons. The differential equations for the couplings represent an infinitesimal formulation of a sequence of Fr\"ohlich-transformations. The two approaches are compared. Our result will turn out to be less singular than Fr\"ohlich's. Furthermore the interaction between electrons belonging to a Cooper-pair will always be attractive in our approach. Even in the case where Fr\"ohlich's transformation is not defined (Fr\"ohlich actually excluded these regions from the transformation), we obtain an elimination of the electron-phonon interaction. This is due to a sufficiently slow change of the phonon energies as a function of the flow parameter.Comment: 25 pages LATEX (use a4.sty v1.2) including 5 PostScript figures (tarred,gzipped,uuencoded

Interaction Quench in the Hubbard model

Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics for weak interaction U in a systematic expansion and find three clearly separated time regimes: i) An initial buildup of correlations where the quasiparticles are formed. ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function. iii) The long time limit described by a quantum Boltzmann equation leading to thermalization with a temperature T proportional to U.Comment: Final version as publishe

Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory

We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical perturbation theory, secular terms are avoided in a systematic expansion and one obtains stable long-time behavior. These general ideas are illustrated by applying them to the spin-boson model and studying its non-equilibrium spin dynamics.Comment: Final version as accepted for publication in Phys. Rev. B (4 pages, 3 figures

The Crooks relation in optical spectra - universality in work distributions for weak local quenches

We show that work distributions and non-equilibrium work fluctuation theorems can be measured in optical spectra for a wide class of quantum systems. We consider systems where the absorption or emission of a photon corresponds to the sudden switch on or off of a local perturbation. For the particular case of a weak local perturbation, the Crooks relation establishes a universal relation in absorption as well as in emission spectra. Due to a direct relation between the spectra and work distribution functions this is equivalent to universal relations in work distributions for weak local quenches. As two concrete examples we treat the X-ray edge problem and the Kondo exciton.Comment: 4+ pages, 1 figure; version as publishe

On the spin--boson model with a sub--Ohmic bath

We study the spin--boson model with a sub--Ohmic bath using infinitesimal unitary transformations. Contrary to some results reported in the literature we find a zero temperature transition from an untrapped state for small coupling to a trapped state for strong coupling. We obtain an explicit expression for the renormalized level spacing as a function of the bare papameters of the system. Furthermore we show that typical dynamical equilibrium correlation functions exhibit an algebaric decay at zero temperature.Comment: 9 pages, 2 Postscript figure

The spectrum of the anomalous dimensions of the composite operators in the ϵ\epsilon - expansion in the scalar ϕ4\phi^4 - field theory

The spectrum of the anomalous dimensions of the composite operators (with arbitrary number of fields $n$ and derivatives $l$) in the scalar $\phi^4$ - theory in the first order of the $\epsilon$ -expansion is investigated. The exact solution for the operators with number of fields $\leq 4$ is presented. The behaviour of the anomalous dimensions in the large $l$ limit has been analyzed. It is given the qualitative description of the %structure of the spectrum for the arbitrary $n$.Comment: 25 pages, latex, a few changes in latex command

Scaling approach for the time-dependent Kondo model

We present a new nonperturbative method to deal with the time-dependent quantum many-body problem, which is an extension of Wegner's flow equations to time-dependent Hamiltonians. The formalism provides a scaling procedure for the set of time-dependent interaction constants. We apply these ideas to a Kondo model with a ferromagnetic exchange coupling switched on over a time scale $\tau$. We show that the asymptotic expectation value of the impurity spin interpolates continuously between its quenched and adiabatic value

Diagonalization of system plus environment Hamiltonians

A new approach to dissipative quantum systems modelled by a system plus environment Hamiltonian is presented. Using a continuous sequence of infinitesimal unitary transformations the small quantum system is decoupled from its thermodynamically large environment. Dissipation enters through the observation that system observables generically decay completely into a different structure when the Hamiltonian is transformed into diagonal form. The method is particularly suited for studying low-temperature properties. This is demonstrated explicitly for the super-Ohmic spin-boson model.Comment: 4 pages, Latex, uses Revte