95 research outputs found
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 -theory.Comment: To be published in Physica
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
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
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
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
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 , 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 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
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
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
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
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
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