Áurea R. Vasconcellos

A nonlinear quantum transport theory

A nonlinear quantum transport theory for many-body systems arbitrarily far away from equilibrium, based on the nonequilibrium statistical operator method, is discussed. An iterative process is described that allows for the calculation of the collision operator in a series of instantaneous in time partial contributions of ever increasing power in the interaction strengths. These partial collision operators are shown to be composed of three contributions to the dissipative processes: one is a direct result of the collisions, another is accounted for in the internal state variables, and the third arises from memory effects. In the lowest order, the so-called linear theory of relaxation, the equations become Markovian.

Response Function Theory for Far-from-Equilibrium Statistical Systems

A formalism to determine the response function of a sample in conditions far from thermal equilibrium is presented. It consists in a generalization of scattering theory coupled to the statistical theory of irreversible processes, the nonequilibrium statistical operator method, developed by Zubarev. The scattering cross section is expressed in terms of double-time correlation functions, which are related to appropriate nonequilibrium thermodynamic Greens functions. The latter are also used to treat generalized transport equations, and, as an illustration, the method is applied to the study of the time-resolved Raman spectroscopy of a photoexcited semiconductor plasma.

Thermodynamic variables in the context of a nonequilibrium statistical ensemble approach

We consider the question of the definition of thermodynamic-like variables in the context of a statistical thermodynamics, which is a large generalization of Gibbs statistical thermostatics and linear and local-equilibrium classical irreversible thermodynamics. It is based on a nonequilibrium ensemble approach known as the nonequilibrium statistical operator method. Some of these quasithermodynamic variables are characteristic of the nonequilibrium state and go to zero in the limit of local or global equilibrium, but others go over the thermodynamic variables that are present in such a limit. We consider in particular temperature-like variables for the different subsystems of the sample. For illustration we apply the theory to the study of optical properties of highly photoexcited plasma in semiconductors, following a good agreement between theory and experimental data. It is shown that high-resolution spectroscopy provides an excellent experimental testing ground for corroboration of the theoretical concepts, and a quite appropriate way for characterizing and measuring nonequilibrium thermodynamic-like variables.

On the relaxation time hierarchy in dissipative systems: An example from semiconductor physics

We consider the question of the contraction of the macroscopic nonequilibrium thermodynamic description of dissipative dynamic systems. As argumented by Bogoliubov, this process is associated to the determination of a spectrum (hierarchy) of relaxation times. We have used studies of the irreversible evolution of highly photoexcited plasmas in polar semiconductors to provide a way to exemplify and test the existence of such a spectrum of characteristic times. It is shown that, in fact, several kinetic stages can be characterized, each accompanied by a successive contraction in the description of the macroscopic state of the system. A proper choice, depending on the experimental conditions, leads to good agreement with observational data.

Velocity overshoot onset in nitride semiconductors

A theoretical study on the electron drift velocity and some nonequilibrium thermodynamic characteristics of wurtzite GaN, AlN, and InN is presented. It is based on a nonlinear quantum kinetic theory which provides a description of the dissipative phenomena developing in the system. The ultrafast time evolution of the electron drift velocity and quasitemperature is obtained, and overshoot effects are evidenced on both. The overshoot onsets are shown to occur at 20 kV/cm in GaN, 60 kV/cm in AlN, and 10 kV/cm in InN, electric field intensities which are considerably smaller than those that have been recently derived resorting to Monte Carlo simulations.

On the selection of the state space in nonequilibrium thermodynamics

We address here the question of the choice and interpretation of state variables in the thermodynamical description of systems arbitrarily away from equilibrium. It is presented a discussion of the topic in the framework of informational statistical thermodynamics, an approach based on Gibbs algorithm for nonequilibrium dissipative systems, which provides mechano-statistical foundations to phenomenological theories of irreversible thermodynamics. The theory is applied in the case of a particular system consisting of the mobile carriers in a highly excited photo-injected plasma in semiconductors. The concepts and results thus obtained are tested against experimental data in time-resolved and time-integrated optical laser spectroscopy. It is shown how equilibrium thermodynamic variables are evidenced and measured in such experiments. It is also discussed the influence on them of the inclusion of dissipative fluxes among the basic variables.

A Kinetic Theory for Nonlinear Quantum Transport

ABSTRACT It is described a kinetic theory providing bases for an analytical treatment of nonlinear quantum transport. It is founded on a nonequilibrium statistical ensemble formalism, which constitutes a soundly approach for the study of dissipative many-body systems driven arbitrarily away from equilibrium. This theory is applied to the study of transport of charge in n- and p- type doped polar semiconductors. Evolution of the carriers’ quasitemperature and mobility as well as of the relaxation times for energy and momentum are derived. Some comparison with experimental data is done.

Evolution of dissipative processes via a statistical thermodynamic approach. I. Generalized Mori–Heisenberg–Langevin equations

Within the scope of a nonequilibrium statistical ensemble formalism we derive a hierarchy of equations of evolution for a set of basic thermo-hydrodynamic variables, which describe the macroscopic nonequilibrium state of a fluid of bosons. This set is composed of the energy density and number density and their fluxes of all order. The resulting equations can be considered as far-reaching generalizations of those in Mori’s approach. They involve nonlocality in space and retro-effects (i.e. correlations in space and time respectively), are highly nonlinear, and account for irreversible behavior in the macroscopic evolution of the system. The different contributions to these kinetic equations are analyzed and the Markovian limit is obtained. In the follow up article we consider the nonequilibrium thermodynamic properties that the formalism provides.

Nonlinear transport properties of III-nitrides in electric field

We consider the transport properties of polar direct-gap semiconductors in an electric field, specializing the numerical calculation of the general theory to the case of n-doped III-nitrides, in particular, GaN, AlN, and InN. The nonequilibrium thermodynamic state of these materials—characterized by the variables so-called quasitemperature, quasichemical potential, and drift velocity of the carriers, and the quasitemperatures of longitudinal optical and acoustical phonons—is studied. The evolution equations of these variables—which are highly nonlinear—are derived, and the transient regime and the ensuing steady state are analyzed. The nonlinear transport is characterized and its main properties are discussed. In one case comparison with a recent Monte Carlo calculation is made and good agreement is obtained. In this paper we mainly consider the ultrafast transient, and in the following paper the steady state.

Hot-phonon bottleneck in the photoinjected plasma in GaN

The evolution on the picosecond scale of the macroscopic (nonequilibrium thermodynamic) state of a highly excited photoinjected plasma in bulk GaN is analyzed. We present the equations of evolution for the quasitemperature (level of excitation) of the hot carriers and of the optical phonons. A hot-phonon temperature overshoot is evidenced, as well as a preferential production of phonons in excess of equilibrium in a reduced off-center region of the Brillouin zone. A comparative analysis of the influence of the length of the exciting laser pulse is also performed.