340 research outputs found
Stochastic Green's function approach to disordered systems
Based on distributions of local Green's functions we present a stochastic
approach to disordered systems. Specifically we address Anderson localisation
and cluster effects in binary alloys. Taking Anderson localisation of Holstein
polarons as an example we discuss how this stochastic approach can be used for
the investigation of interacting disordered systems.Comment: 12 pages, 7 figures, conference proceedings: Progress in
Nonequilibrium Green's Functions III, 22-26 August 2005, University of Kiel,
German
Non-equilibrium current and electron pumping in nanostructures
We discuss a numerical method to study electron transport in mesoscopic
devices out of equilibrium. The method is based on the solution of operator
equations of motion, using efficient Chebyshev time propagation techniques. Its
peculiar feature is the propagation of operators backwards in time. In this way
the resource consumption scales linearly with the number of states used to
represent the system. This allows us to calculate the current for
non-interacting electrons in large one-, two- and three-dimensional lead-device
configurations with time-dependent voltages or potentials. We discuss the
technical aspects of the method and present results for an electron pump device
and a disordered system, where we find transient behaviour that exists for a
very long time and may be accessible to experiments.Comment: 4 pages, 3 figures. Contribution to the International Conference on
Magnetism (ICM) 2009 in Karlsruh
A Green's function decoupling scheme for the Edwards fermion-boson model
Holes in a Mott insulator are represented by spinless fermions in the
fermion-boson model introduced by Edwards. Although the physically interesting
regime is for low to moderate fermion density the model has interesting
properties over the whole density range. It has previously been studied at
half-filling in the one-dimensional (1D) case by numerical methods, in
particular exact diagonalization and density matrix renormalization group
(DMRG). In the present study the one-particle Green's function is calculated
analytically by means of a decoupling scheme for the equations of motion, valid
for arbitrary density in 1D, 2D and 3D with fairly large boson energy and zero
boson relaxation parameter. The Green's function is used to compute some ground
state properties, and the one-fermion spectral function, for fermion densities
n=0.1, 0.5 and 0.9 in the 1D case. The results are generally in good agreement
with numerical results obtained by DMRG and dynamical DMRG and new light is
shed on the nature of the ground state at different fillings. The Green's
function approximation is sufficiently successful in 1D to justify future
application to the 2D and 3D cases.Comment: 19 pages, 7 figures, final version with updated reference
Solution of the Holstein polaron anisotropy problem
We study Holstein polarons in three-dimensional anisotropic materials. Using
a variational exact diagonalization technique we provide highly accurate
results for the polaron mass and polaron radius. With these data we discuss the
differences between polaron formation in dimension one and three, and at small
and large phonon frequency. Varying the anisotropy we demonstrate how a polaron
evolves from a one-dimensional to a three-dimensional quasiparticle. We thereby
resolve the issue of polaron stability in quasi-one-dimensional substances and
clarify to what extent such polarons can be described as one-dimensional
objects. We finally show that even the local Holstein interaction leads to an
enhancement of anisotropy in charge carrier motion.Comment: 6 pages, 7 figures; extended version accepted for publication in
Phys. Rev.
Collapse-revival dynamics and atom-field entanglement in the non-resonant Dicke model
We consider the dynamics of atomic and field coherent states in the
non-resonant Dicke model. At weak coupling an initial product state evolves
into a superposition of multiple field coherent states that are correlated with
the atomic configuration. This process is accompanied by the buildup and decay
of atom-field entanglement and leads to the periodic collapse and revival of
Rabi oscillations. We provide a perturbative derivation of the underlying
dynamical mechanism that complements the rotating wave approximation at
resonance. The identification of two different time scales explains how the
dynamical signatures depend on the sign of detuning between the atomic and
field frequency, and predicts the generation of either atomic or field cat
states in the two opposite cases. We finally discuss the restrictions that the
buildup of atom-field entanglement during the collapse of Rabi oscillations
imposes on the validity of semi-classical approximations that neglect
entanglement.Comment: 9 pages, 10 figures. Published versio
Sparse polynomial space approach to dissipative quantum systems: Application to the sub-ohmic spin-boson model
We propose a general numerical approach to open quantum systems with a
coupling to bath degrees of freedom. The technique combines the methodology of
polynomial expansions of spectral functions with the sparse grid concept from
interpolation theory. Thereby we construct a Hilbert space of moderate
dimension to represent the bath degrees of freedom, which allows us to perform
highly accurate and efficient calculations of static, spectral and dynamic
quantities using standard exact diagonalization algorithms. The strength of the
approach is demonstrated for the phase transition, critical behaviour, and
dissipative spin dynamics in the spin boson modelComment: 4 pages, 4 figures, revised version accepted for publication in PR
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