90 research outputs found
Density and current response functions in strongly disordered electron systems: Diffusion, electrical conductivity and Einstein relation
We study consequences of gauge invariance and charge conservation of an
electron gas in a strong random potential perturbed by a weak electromagnetic
field. We use quantum equations of motion and Ward identities for one- and
two-particle averaged Green functions to establish exact relations between
density and current response functions. In particular we find precise
conditions under which we can extract the current-current correlation function
from the density-density correlation function and vice versa. We use these
results in two different ways to extend validity of a formula associating the
density response function with the electrical conductivity from semiclassical
equilibrium to quantum nonequilibrium systems. Finally we introduce quantum
diffusion via a response relating the current with the negative gradient of the
charge density. With the aid of this response function we derive a quantum
version of the Einstein relation and prove the existence of the diffusion pole
in the zero-temperature electron-hole correlation function with the the
long-range spatial fluctuations controlled by the static diffusion constant.Comment: 16 pages, REVTeX4, 6 EPS figure
Kinetic equation for strongly interacting dense Fermi systems
We review the non-relativistic Green's-function approach to the kinetic
equations for Fermi liquids far from equilibrium. The emphasis is on the
consistent treatment of the off-shell motion between collisions and on the
non-instant and non-local picture of binary collisions. The resulting kinetic
equation is of the Boltzmann type, and it represents an interpolation between
the theory of transport in metals and the theory of moderately dense gases. The
free motion of particles is renormalised by various mean field and mass
corrections in the spirit of Landau's quasiparticles in metals. The collisions
are non-local in the spirit of Enskog's theory of non-ideal gases. The
collisions are moreover non-instant, a feature which is absent in the theory of
gases, but which is shown to be important for dense Fermi systems. In spite of
its formal complexity, the presented theory has a simple implementation within
the Monte-Carlo simulation schemes. Applications in nuclear physics are given
for heavy-ion reactions and the results are compared with the former theory and
recent experimental data. The effect of the off-shell motion and the non-local
and non-instant collisions on the dynamics of the system can be characterised
in terms of thermodynamic functions such as the energy density or the pressure
tensor. Non-equilibrium counterparts of these functions and the corresponding
balance equations are derived and discussed from two points of view. Firstly,
they are used to prove the conservation laws. Secondly, the role of individual
microscopic mechanisms in fluxes of particles and momenta and in
transformations of the energy is clarified.Comment: Boo
POVMs: a small but important step beyond standard quantum mechanics
It is the purpose of the present contribution to demonstrate that the
generalization of the concept of a quantum mechanical observable from the
Hermitian operator of standard quantum mechanics to a positive operator-valued
measure is not a peripheral issue, allegedly to be understood in terms of a
trivial nonideality of practical measurement procedures, but that this
generalization touches the very core of quantum mechanics, viz. complementarity
and violation of the Bell inequalities.Comment: Contribution to Proceedings of the Workshop `Beyond the quantum',
Leiden, May/June 200
A time-dependent approach to electron pumping in open quantum systems
We propose a time-dependent approach to investigate the motion of electrons
in quantum pump device configurations. The occupied one-particle states are
propagated in real time and used to calculate the local electron density and
current. An advantage of the present computational scheme is that the same
computational effort is required to simulate monochromatic, polychromatic and
nonperiodic drivings. Furthermore, initial state dependence and history effects
are naturally accounted for. This approach can also be embedded in the
framework of time-dependent density functional theory to include
electron-electron interactions. In the special case of periodic drivings we
combine the Floquet theory with nonequilibrium Green's functions and obtain a
general expression for the pumped current in terms of inelastic transmission
probabilities. This latter result is used for benchmarking our propagation
scheme in the long-time limit. Finally, we discuss the limitations of
Floquet-based schemes and suggest our approach as a possible way to go beyond
them.Comment: 14 pages, 8 figure
Quasiparticle transport equation with collision delay. II. Microscopic Theory
For a system of non-interacting electrons scattered by neutral impurities, we
derive a modified Boltzmann equation that includes quasiparticle and virial
corrections. We start from quasiclassical transport equation for
non-equilibrium Green's functions and apply limit of small scattering rates.
Resulting transport equation for quasiparticles has gradient corrections to
scattering integrals. These gradient corrections are rearranged into a form
characteristic for virial corrections
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