Non-equilibrium properties of the S=1/2 Heisenberg model in a time-dependent magnetic field

The time-dependent behavior of the Heisenberg model in contact with a phonon heat bath and in an external time-dependent magnetic field is studied by means of a path integral approach. The action of the phonon heat bath is taken into account up to the second order in the coupling to the heath bath. It is shown that there is a minimal value of the magnetic field below which the average magnetization of the system does not relax to equilibrium when the external magnetic field is flipped. This result is in qualitative agreement with the mean field results obtained within $\phi^{4}$-theory.Comment: To be published in Physica

Steady-state nonequilibrium dynamical mean-field theory and the quantum Boltzman

We derive the formalism for steady state nonequilibrium dynamical mean-field theory in a real-time formalism along the Kadanoff-Baym contour. The resulting equations of motion are first transformed to Wigner coordinates (average and relative time), and then re-expressed in terms of differential operators. Finally, we perform a Fourier transform with respect to the relative time, and take the first-order limit in the electric field to produce the quantum Boltzmann equation for dynamical mean-field theory. We next discuss the structure of the equations and their solutions, describing how these equations reduce to the Drude result in the limit of a constant relaxation time. We also explicitly demonstrate the equivalence between the Kubo and nonequilibrium approaches to linear response. There are a number of interesting modifications of the conventional quantum Boltzmann equation that arise due to the underlying bandstructure of the lattice.Comment: (14 pages, proceedings of the Workshop on Progress in Nonequilibrium Green's Functions III, Kiel Germany

Time-dependent density-matrix functional theory for biexcitonic phenomena

We formulate a time-dependent density-matrix functional theory (TDDMFT) approach for higher-order correlation effects like biexcitons in optical processes in solids based on the reduced two-particle density-matrix formalism within the normal orbital representation. A TDDMFT version of the Schr\"odinger equation for biexcitons in terms of one- and two-body reduced density matrices is derived, which leads to finite biexcitonic binding energies already with an adiabatic approximation. Biexcitonic binding energies for several bulk semiconductors are calculated using a contact biexciton model

Time-dependent density-functional theory for ultrafast interband excitations

We formulate a time-dependent density functional theory (TDDFT) in terms of the density matrix to study ultrafast phenomena in semiconductor structures. A system of equations for the density matrix components, which is equivalent to the time-dependent Kohn-Sham equation, is derived. From this we obtain a TDDFT version of the semiconductor Bloch equations, where the electronic many-body effects are taken into account in principle exactly. As an example, we study the optical response of a three-dimensional two-band insulator to an external short-time pulsed laser field. We show that the optical absorption spectrum acquires excitonic features when the exchange-correlation potential contains a $1/q^{2}$ Coulomb singularity. A qualitative comparison of the TDDFT optical absorption spectra with the corresponding results obtained within the Hartree-Fock approximation is made

F-electron spectral function of the Falicov-Kimball model in infinite dimensions: the half-filled case

The f-electron spectral function of the Falicov-Kimball model is calculated via a Keldysh-based many-body formalism originally developed by Brandt and Urbanek. We provide results for both the Bethe lattice and the hypercubic lattice at half filling. Since the numerical computations are quite sensitive to the discretization along the Kadanoff-Baym contour and to the maximum cutoff in time that is employed, we analyze the accuracy of the results using a variety of different moment sum-rules and spectral formulas. We find that the f-electron spectral function has interesting temperature dependence becoming a narrow single-peaked function for small U and developing a gap, with two broader peaks for large U.Comment: (13 pages, 11 figures, typeset in RevTex 4

Quasi-classical Lie algebras and their contractions

After classifying indecomposable quasi-classical Lie algebras in low dimension, and showing the existence of non-reductive stable quasi-classical Lie algebras, we focus on the problem of obtaining sufficient conditions for a quasi-classical Lie algebras to be the contraction of another quasi-classical algebra. It is illustrated how this allows to recover the Yang-Mills equations of a contraction by a limiting process, and how the contractions of an algebra may generate a parameterized families of Lagrangians for pairwise non-isomorphic Lie algebras.Comment: 17 pages, 2 Table

Superconductivity and superconducting order parameter phase fluctuations in a weakly doped antiferromagnet

The superconducting properties of a recently proposed phenomenological model for a weakly doped antiferromagnet are analyzed, taking into account fluctuations of the phase of the order parameter. In this model, we assume that the doped charge carriers can't move out of the antiferromagnetic sublattice they were introduced. This case corresponds to the free carrier spectra with the maximum at ${\bf k}=(\pm \pi /2 ,\pm \pi /2)$, as it was observed in ARPES experiments in some of the cuprates in the insulating state [1]. The doping dependence of the superconducting gap and the temperature-carrier density phase diagram of the model are studied in the case of the $d_{x^{2}-y^{2}}$ pairing symmetry and different values of the effective coupling. A possible relevance of the results to the experiments on high-temperature superconductors is discussed.Comment: 16 pages, 4 figure

Nonequilibrium perturbation theory of the spinless Falicov-Kimball model

We perform a perturbative analysis for the nonequilibrium Green functions of the spinless Falicov-Kimball model in the presence of an arbitrary external time-dependent but spatially uniform electric field. The conduction electron self-energy is found from a strictly truncated second-order perturbative expansion in the local electron-electron repulsion U. We examine the current at half-filling, and compare to both the semiclassical Boltzmann equation and exact numerical solutions for the contour-ordered Green functions from a transient-response formalism (in infinite dimensions) on the Kadanoff-Baym-Keldysh contour. We find a strictly truncated perturbation theory in the two-time formalism cannot reach the long-time limit of the steady state; instead it illustrates pathological behavior for times larger than approximately 2/U

Symmetry classification of third-order nonlinear evolution equations. Part I: Semi-simple algebras

We give a complete point-symmetry classification of all third-order evolution equations of the form $u_t=F(t,x,u,u_x, u_{xx})u_{xxx}+G(t,x,u,u_x, u_{xx})$ which admit semi-simple symmetry algebras and extensions of these semi-simple Lie algebras by solvable Lie algebras. The methods we employ are extensions and refinements of previous techniques which have been used in such classifications.Comment: 53 page