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

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

Solving real time evolution problems by constructing excitation operators

In this paper we study the time evolution of an observable in the interacting fermion systems driven out of equilibrium. We present a method for solving the Heisenberg equations of motion by constructing excitation operators which are defined as the operators A satisfying [H,A]=\lambda A. It is demonstrated how an excitation operator and its excitation energy \lambda can be calculated. By an appropriate supposition of the form of A we turn the problem into the one of diagonalizing a series of matrices whose dimension depends linearly on the size of the system. We perform this method to calculate the evolution of the creation operator in a toy model Hamiltonian which is inspired by the Hubbard model and the nonequilibrium current through the single impurity Anderson model. This method is beyond the traditional perturbation theory in Keldysh-Green's function formalism, because the excitation energy \lambda is modified by the interaction and it will appear in the exponent in the function of time.Comment: 8 page

Non-equilibrium dynamics of a system with Quantum Frustration

Using flow equations, equilibrium and non-equilibrium dynamics of a two-level system are investigated, which couples via non-commuting components to two independent oscillator baths. In equilibrium the two-level energy splitting is protected when the TLS is coupled symmetrically to both bath. A critical asymmetry angle separates the localized from the delocalized phase. On the other hand, real-time decoherence of a non-equilibrium initial state is for a generic initial state faster for a coupling to two baths than for a single bath.Comment: 22 pages, 9 figure

Scaling and Decoherence in the Out-of-Equilibrium Kondo Model

We study the Kondo effect in quantum dots in an out-of-equilibrium state due to an applied dc-voltage bias. Using the method of infinitesimal unitary transformations (flow equations), we develop a perturbative scaling picture that naturally contains both equilibrium coherent and non-equilibrium decoherence effects. This framework allows one to study the competition between Kondo effect and current-induced decoherence, and it establishes a large regime dominated by single-channel Kondo physics for asymmetrically coupled quantum dots.Comment: 4 pages, 3 figures; v2: minor changes (typos corrected, esp. in Eqs. (3), (4), references updated, improved layout for figures

Nonequilibrium Spin Dynamics in the Ferromagnetic Kondo Model

Motivated by recent experiments on molecular quantum dots we investigate the relaxation of pure spin states when coupled to metallic leads. Under suitable conditions these systems are well described by a ferromagnetic Kondo model. Using two recently developed theoretical approaches, the time-dependent numerical renormalization group and an extended ow equation method, we calculate the real-time evolution of a Kondo spin into its partially screened steady state. We obtain exact analytical results which agree well with numerical implementations of both methods. Analytical expressions for the steady state magnetization and the dependence of the long-time relaxation on microscopic parameters are established. We find the long-time relaxation process to be much faster in the regime of anisotropic Kondo couplings. The steady state magnetization is found to deviate significantly from its thermal equilibrium value.Comment: 4 pages, 3 figures, final version as accepted by Physical Review Letter

Non-linear feedback effects in coupled Boson-Fermion systems

We address ourselves to a class of systems composed of two coupled subsystems without any intra-subsystem interaction: itinerant Fermions and localized Bosons on a lattice. Switching on an interaction between the two subsystems leads to feedback effects which result in a rich dynamical structure in both of them. Such feedback features are studied on the basis of the flow equation technique - an infinite series of infinitesimal unitary transformations - which leads to a gradual elimination of the inter-subsystem interaction. As a result the two subsystems get decoupled but their renormalized kinetic energies become mutually dependent on each other. Choosing for the inter - subsystem interaction a charge exchange term (the Boson-Fermion model) the initially localized Bosons acquire itinerancy through their dependence on the renormalized Fermion dispersion. This latter evolves from a free particle dispersion into one showing a pseudogap structure near the chemical potential. Upon lowering the temperature both subsystems simultaneously enter a macroscopic coherent quantum state. The Bosons become superfluid, exhibiting a soundwave like dispersion while the Fermions develop a true gap in their dispersion. The essential physical features described by this technique are already contained in the renormalization of the kinetic terms in the respective Hamiltonians of the two subsystems. The extra interaction terms resulting in the process of iteration only strengthen this physics. We compare the results with previous calculations based on selfconsistent perturbative approaches.Comment: 14 pages, 16 figures, accepted for publication in Phys. Rev.

High-gradient operators in the N-vector model

It has been shown by several authors that a certain class of composite operators with many fields and gradients endangers the stability of nontrivial fixed points in 2+eps expansions for various models. This problem is so far unresolved. We investigate it in the N-vector model in an 1/N-expansion. By establishing an asymptotic naive addition law for anomalous dimensions we demonstrate that the first orders in the 2+eps expansion can lead to erroneous interpretations for high--gradient operators. While this makes us cautious against over--interpreting such expansions (either 2+eps or 1/N), the stability problem in the N-vector model persists also in first order in 1/N below three dimensions.Comment: 18 pages, 4 Postscript figures; revised version contains two additional references and "Note added in proof