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

Numerical calculation of the combinatorial entropy of partially ordered ice

Using a one-parameter case as an example, we demonstrate that multicanonical simulations allow for accurate estimates of the residual combinatorial entropy of partially ordered ice. For the considered case corrections to an (approximate) analytical formula are found to be small, never exceeding 0.5%. The method allows one as well to calculate combinatorial entropies for many other systems.Comment: Extended version: 7 pages, 10 figures (v1 is letter-type version

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