512 research outputs found
Particle current in symmetric exclusion process with time-dependent hopping rates
In a recent study, (Jain et al 2007 Phys. Rev. Lett. 99 190601), a symmetric
exclusion process with time-dependent hopping rates was introduced. Using
simulations and a perturbation theory, it was shown that if the hopping rates
at two neighboring sites of a closed ring vary periodically in time and have a
relative phase difference, there is a net DC current which decreases inversely
with the system size. In this work, we simplify and generalize our earlier
treatment. We study a model where hopping rates at all sites vary periodically
in time, and show that for certain choices of relative phases, a DC current of
order unity can be obtained. Our results are obtained using a perturbation
theory in the amplitude of the time-dependent part of the hopping rate. We also
present results obtained in a sudden approximation that assumes large
modulation frequency.Comment: 17 pages, 2 figure
Edge Magnetoplasmons in Quantum Hall Line Junction Systems
A quantum Hall line junction system consists of a one-dimensional Luttinger
liquid (LL) and two chiral channels that allow density waves incident upon and
reflected by the LL to be measured separately. We demonstrate that interactions
in a quantum Hall line junction system can be probed by studying edge
magnetoplasmon absorption spectra and their polarization dependences. Strong
interactions in the junction lead to collective modes that are isolated in
either Luttinger liquid or contact subsystems.Comment: 4 pages, 3 figures, submitted to Phys. Rev. B Rapid Communicatio
Nonequilibrium thermodynamics as a gauge theory
We assume that markovian dynamics on a finite graph enjoys a gauge symmetry
under local scalings of the probability density, derive the transformation law
for the transition rates and interpret the thermodynamic force as a gauge
potential. A widely accepted expression for the total entropy production of a
system arises as the simplest gauge-invariant completion of the time derivative
of Gibbs's entropy. We show that transition rates can be given a simple
physical characterization in terms of locally-detailed-balanced heat
reservoirs. It follows that Clausius's measure of irreversibility along a
cyclic transformation is a geometric phase. In this picture, the gauge symmetry
arises as the arbitrariness in the choice of a prior probability. Thermostatics
depends on the information that is disposable to an observer; thermodynamics
does not.Comment: 6 pages. Non-fatal errors in eq.(6), eq.(26) and eq.(31) have been
amende
Stochastic pump effect and geometric phases in dissipative and stochastic systems
The success of Berry phases in quantum mechanics stimulated the study of
similar phenomena in other areas of physics, including the theory of living
cell locomotion and motion of patterns in nonlinear media. More recently,
geometric phases have been applied to systems operating in a strongly
stochastic environment, such as molecular motors. We discuss such geometric
effects in purely classical dissipative stochastic systems and their role in
the theory of the stochastic pump effect (SPE).Comment: Review. 35 pages. J. Phys. A: Math, Theor. (in press
Comment on "Exact results for survival probability in the multistate Landau-Zener model"
We correct the proof of Brundobler-Elser formula (BEF) provided in [2004
\textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{37} 4069] and continued in
Appendix of [2005 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{38} 907].
After showing that some changes of variables employed in these articles are
used erroneously, we propose an alternative change of variables which solves
the problem. In our proof, we reveal the connection between the BEF for a
general -level Landau-Zener system and the exactly solvable bow-tie model.
The special importance of the diabatic levels with maximum/minimum slope is
emphasized throughout.Comment: 10 page
Mathematical modelling of proton migration in Earth mantle
In the study, we address the mathematical problem of proton migration in the Earth’s mantle and suggest a prototype for exploring the Earth’s interior to map the effects of superionic proton conduction. The problem can be mathematically solved by deriving the self-consistent electromagnetic field potential U(x, t) and then reconstructing the distribution function f(x, v, t). Reducing the Vlasov-Maxwell system of equations to non-linear sh-Gordon hyperbolic and transport equations, the propagation of a non-linear wavefront within the domain and transport of the boundary conditions in the form of a non-linear wave are examined. By computing a 3D model and through Fourier-analysis, the spatial and electrical characteristics of potential U(x, t) are investigated. The numerical results are compared to the Fourier transformed quantities of the potential (V ) obtained through field observations of the electric potential (Kuznetsov method). The non-stationary solutions for the forced oscillation of two-component system, and therefore, the oscillatory strengths of two types of charged particles can be usefully addressed by the proposed mathematical model. Moreover, the model, along with data analysis of the electric potential observations and probabilistic seismic hazard maps, can be used to develop an advanced seismic risk metric
Dependence of the intrinsic spin Hall effect on spin-orbit interaction character
We report on a comparative numerical study of the spin Hall conductivity in
two-dimensions for three different spin-orbit interaction models; the standard
k-linear Rashba model, the k-cubic Rashba model that describes two-dimensional
hole systems, and a modified k-linear Rashba model in which the spin-orbit
coupling strength is energy dependent. Numerical finite-size Kubo formula
results indicate that the spin Hall conductivity of the k-linear Rashba model
vanishes for frequency much smaller than the scattering rate
, with order one relative fluctuations surviving out to large system
sizes. For the k-cubic Rashba model case, the spin Hall conductivity does not
depend noticeably on and is finite in the {\em dc} limit, in
agreement with experiment. For the modified k-linear Rashba model the spin Hall
conductivity is noticeably dependent but approaches a finite
value in the {\em dc} limit. We discuss these results in the light of a
spectral decomposition of the spin Hall conductivity and associated sum rules,
and in relation to a proposed separation of the spin Hall conductivity into
skew-scattering, intrinsic, and interband vertex correction contributions.Comment: 10 pages, 4 figure
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