arXiv subjects

R. E. Lagos

Publications and source records attributed to R. E. Lagos.

6 recordsLinked to original sources

arXiv2013

Charged Brownian Particles: Kramers and Smoluchowski Equations and the Hydrothermodynamical Picture

We consider a charged Brownian gas under the influence of external and non uniform electric, magnetic and mechanical fields, immersed in a non uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle's density, a Smoluchowski-reactive like equation; for the particle's momentum density, a generalized Ohm's like equation; and for the particle's energy density, a Maxwell-Cattaneo like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non linear reactive kinetics and a mean field approach to interacting Brownian particles.

cond-mat.stat-mech↗

arXiv2013

Hot Brownian Carriers in the Langevin Picture: Application to a simple model for the Gunn Effect in GaAs

We consider a charged Brownian gas under the influence of external, static and uniform electric and magnetic fields, immersed in a uniform bath temperature. We obtain the solution for the associated Langevin equation, and thereafter the evolution of the nonequilibrium temperature towards a nonequilibrium (hot) steady state. We apply our results to a simple yet relevant Brownian model for carrier transport in GaAs. We obtain a negative differential conductivity regime (Gunn effect) and discuss and compare our results with experimental results.

cond-mat.stat-mech↗

arXiv2003

A two band model for Superconductivity: Probing interband pair formation

We propose a two band model for superconductivity. It turns out that the simplest nontrivial case considers solely interband scattering, and both bands can be modeled as symmetric (around the Fermi level) and flat, thus each band is completely characterized by its half-band width $W_{n}$ (n=1,2). A useful dimensionless parameter is $δ$, proportional to $W_{2}-W_{1}$. The case $δ=0$ retrieves the conventional BCS model. We probe the specific heat, the ratio gap over critical temperature, the thermodynamic critical field and tunneling conductance as functions of $δ$ and temperature (from zero to $T_{c}$). We compare our results with experimental results for $MgB_{2}$ and good quantitative agreement is obtained, indicating the relevance of interband coupling. Work in progress also considers the inclusion of band hybridization and general interband as well as intra-band scattering mechanisms.

cond-mat.supr-con↗

arXiv2000

The thermohydrodynamical picture of a charged Brownian particle

We study a charged Brownian gas with a non uniform bath temperature, and present a thermohydrodynamical picture. Expansion on the collision time probes the validity of the local equilibrium approach and the relevant thermodynamical variables. For the linear regime we present several applications (including some novel results). For the lowest nonlinear expansion and uniform bath temperature we compute the gradient corrections to the local equilibrium approach and the fundamental (Smoluchowsky) equation for the nonequilibrium particle density.

cond-mat.stat-mech↗

arXiv2000

A Generalized Smoluchowsky Equation: The Hydrodynamical and Thermodynamical Picture of Brownian Motion

We present a systematic expansion of Kramers equation in the high friction limit. The latter is expanded within an operator continued fraction scheme. The relevant operators include both temporal and spatial derivatives and a covariant derivate or gauge like operator associated to the potential energy. Trivially, the first order term yields the Smoluchowsky equation. The second order term is readily obtained, known as the corrected Smoluchowsky equation. Further terms are computed in compact and straightforward fashion. As an application, the nonequilibrium thermodynamics and hydrodynamical schemes for the one dimensional Brownian motion is presented.

cond-mat.stat-mech↗

arXiv1998

A Model for the Schottky Anomaly in Metallic $Nd_{2-y}Ce_{y}CuO_{4}$

We present a simple model for the doped compound $Nd_{2-y}Ce_{y}CuO_{4}$, in order to explain some recent experimental results on the latter. Within a Hartree-Fock context, we start from an impurity Anderson-like model and consider the magnetic splitting of the $Nd$-$4f$ ground state Kramers doublet due to exchange interactions with the ordered $Cu$ moments. Our results are in very good agreement with the experimental data, yielding a Schottky anomaly peak for the specific heat that reduces its amplitude, broadens and shifts to lower temperatures, upon $Ce$ doping. For overdoped compounds at low temperatures, the specific heat behaves linearly and the magnetic susceptibility is constant. A smooth transition from this Fermi liquid like behavior ocurrs as temperature is increased and at high temperatures the susceptibility exhibits a Curie-like behavior. Finally, we discuss some improvements our model is amenable to incorporate.

cond-mat.str-el↗