2,705 research outputs found

### Analysis of the second order exchange self energy of a dense electron gas

We investigate the evaluation of the six-fold integral representation for the
second order exchange contribution to the self energy of a three dimensional
electron gas at the Fermi surface.Comment: 6 page

### Fluctuation relations for a driven Brownian particle

We consider a driven Brownian particle, subject to both conservative and
non-conservative applied forces, whose probability evolves according to the
Kramers equation. We derive a general fluctuation relation, expressing the
ratio of the probability of a given Brownian path in phase space with that of
the time-reversed path, in terms of the entropy flux to the heat reservoir.
This fluctuation relation implies those of Seifert, Jarzynski and
Gallavotti-Cohen in different special cases

### Onsager reciprocity relations without microscopic reversibility

In this paper we show that Onsager--Machlup time reversal properties of
thermodynamic fluctuations and Onsager reciprocity relations for transport
coefficients can hold also if the microscopic dynamics is not reversible. This
result is based on the explicit construction of a class of conservative models
which can be analysed rigorously.Comment: revtex, no figure

### Anomalous scaling of passive scalar in turbulence and in equilibrium

We analyze multi-point correlation functions of a tracer in an incompressible
flow at scales far exceeding the scale $L$ at which fluctuations are generated
(quasi-equilibrium domain) and compare them with the correlation functions at
scales smaller than $L$ (turbulence domain). We demonstrate that the scale
invariance can be broken in the equilibrium domain and trace this breakdown to
the statistical integrals of motion (zero modes) as has been done before for
turbulence. Employing Kraichnan model of short-correlated velocity we identify
the new type of zero modes, which break scale invariance and determine an
anomalously slow decay of correlations at large scales

### Electroviscous effects of simple electrolytes under shear

On the basis of a hydrodynamical model analogous to that in critical fluids,
we investigate the influences of shear flow upon the electrostatic contribution
to the viscosity of binary electrolyte solutions in the Debye-H\"{u}ckel
approximation. Within the linear-response theory, we reproduce the classical
limiting law that the excess viscosity is proportional to the square root of
the concentration of the electrolyte. We also extend this result for finite
shear. An analytic expression of the anisotropic structure factor of the charge
density under shear is obtained, and its deformation at large shear rates is
discussed. A non-Newtonian effect caused by deformations of the ionic
atmosphere is also elucidated for $\tau_D\dot{\gamma}>1$. This finding
concludes that the maximum shear stress that the ionic atmosphere can support
is proportional to $\lambda_D^{-3}$, where $\dot{\gamma}$, $\lambda_D$ and
$\tau_D=\lambda_D^2/D$ are, respectively, the shear rate, the Debye screening
length and the Debye relaxation time with $D$ being the relative diffusivity at
the infinite dilution limit of the electrolyte.Comment: 13pages, 2figure

### Cyclotron radiation and emission in graphene

Peculiarity in the cyclotron radiation and emission in graphene is
theoretically examined in terms of the optical conductivity and relaxation
rates to propose that graphene in magnetic fields can be a candidate to realize
the Landau level laser, proposed decades ago [H. Aoki, Appl. Phys. Lett. {\bf
48}, 559 (1986)].Comment: 4 pages, 3 figure

### A new magnetic field dependence of Landau levels on a graphene like structure

We consider a tight-binding model on the honeycomb lattice in a magnetic
field. For special values of the hopping integrals, the dispersion relation is
linear in one direction and quadratic in the other. We find that, in this case,
the energy of the Landau levels varies with the field B as E_n(B) ~
[(n+\gamma)B]^{2/3}. This result is obtained from the low-field study of the
tight-binding spectrum on the honeycomb lattice in a magnetic field (Hofstadter
spectrum) as well as from a calculation in the continuum approximation at low
field. The latter links the new spectrum to the one of a modified quartic
oscillator. The obtained value $\gamma=1/2$ is found to result from the
cancellation of a Berry phase.Comment: 4 pages, 4 figure

### Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems

In this paper we present a self-contained macroscopic description of
diffusive systems interacting with boundary reservoirs and under the action of
external fields. The approach is based on simple postulates which are suggested
by a wide class of microscopic stochastic models where they are satisfied. The
description however does not refer in any way to an underlying microscopic
dynamics: the only input required are transport coefficients as functions of
thermodynamic variables, which are experimentally accessible. The basic
postulates are local equilibrium which allows a hydrodynamic description of the
evolution, the Einstein relation among the transport coefficients, and a
variational principle defining the out of equilibrium free energy. Associated
to the variational principle there is a Hamilton-Jacobi equation satisfied by
the free energy, very useful for concrete calculations. Correlations over a
macroscopic scale are, in our scheme, a generic property of nonequilibrium
states. Correlation functions of any order can be calculated from the free
energy functional which is generically a non local functional of thermodynamic
variables. Special attention is given to the notion of equilibrium state from
the standpoint of nonequilibrium.Comment: 21 page

### Some comments on developments in exact solutions in statistical mechanics since 1944

Lars Onsager and Bruria Kaufman calculated the partition function of the
Ising model exactly in 1944 and 1949. Since then there have been many
developments in the exact solution of similar, but usually more complicated,
models. Here I shall mention a few, and show how some of the latest work seems
to be returning once again to the properties observed by Onsager and Kaufman.Comment: 28 pages, 5 figures, section on six-vertex model revise

### Quantum Hall effects of graphene with multi orbitals: Topological numbers, Boltzmann conductance and Semi-classical quantization

Hall conductance $\sigma_{xy}$ as the Chern numbers of the Berry connection
in the magnetic Brillouin zone is calculated for a realistic multi band
tight-band model of graphene with non-orthogonal basis. It is confirmed that
the envelope of $\sigma_{xy}$ coincides with a semi-classical result when
magnetic field is sufficiently small.
The Hall resistivity $\rho_{xy}$ from the weak-field Boltzmann theory also
explains the overall behaviour of the $\sigma_{xy}$ if the Fermi surface is
composed of a single energy band. The plateaux of $\sigma_{xy}$ are explained
from semi-classical quantization and necessary modification is proposed for the
Dirac fermion regimes.Comment: 5pages, 3figure

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