Justino R. Madureira

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.

A nonequilibrium statistical grand-canonical ensemble: Description in terms of flux operators

In the domain of Statistical Mechanics of nonequilibrium-nonlinear (dissipative) systems based on a generalized Gibbs–Boltzmann ensemble formalism, it may be highlighted the so-called Nonequilibrium Statistical Operator Method, and, particularly, Zubarev’s approach. We report here a detailed analysis of a case consisting in a generalized nonequilibrium grand-canonical ensemble. Its construction requires to introduce besides the traditional densities of energy and the particle number their nonconserving-dissipative fluxes of all order. The description is quite appropriate to provide a framework for the construction of a nonclassical thermo-hydrodynamics, which is briefly described.

Evolution of dissipative processes via a statistical thermodynamic approach. II. Thermodynamic properties of a fluid of bosons

On the basis of the generalized Mori–Heisenberg–Langevin equations presented in the preceding paper, we derive and analyze the informational-statistical thermodynamic properties of a fluid of bosons away from equilibrium. We derive the informational entropy and its production, proceeding to an analysis of the several contributions to these state functions arising out of the evolution of dissipative processes in the system.

Spatially indirect excitons in type-II quantum dots

The authors have calculated the electronic structure for type-II InP∕GaAs quantum dot systems considering a three-dimensional geometry including the wetting layer and the electron-hole interaction, which is the only responsible for the hole localization. Their results for the InP∕GaAs structure show the electron confined inside the dot and the hole in the GaAs layer, partially above and below the dot. The authors propose structures with InGaAs or InGaP layers, where the hole wave function forms a ring around the dot walls. The electron-hole overlap, and therefore, the carrier lifetimes are very sensitive to the structural geometry, which is an important tool for device engineering.

Higher-order hydrodynamics: Extended Fick's Law, evolution equation, and Bobylev's instability

A higher-order hydrodynamics for material motion in fluids, under arbitrary nonequilibrium conditions, is constructed. We obtain what is a generalized—to that conditions—Fick-type Law. It includes a representation of Burnett-type contributions of all order, in the form of a continuous-fraction expansion. Also, the equation includes generalized thermodynamic forces, which are characterized and discussed. All kinetic coefficients are given as correlations of microscopic mechanical quantities averaged over the nonequilibrium ensemble, and then are time- and space-dependent as a consequence of accounting for the dissipative processes that are unfolding in the medium. An extended evolution equation for the density of particles is derived, and the conditions when it goes over restricted forms of the type of the telegraphist equation and Fick’s diffusion equation are presented.

ENERGY TRANSPORT IN A MESOSCOPIC THERMO-HYDRODYNAMICS

We analyse the question of transport of energy in fluids, done, for specificity, for the case of a system of fermions interacting with a boson system. Resorting to a generalized thermo-hydrodynamics based on a nonequilibrium ensemble formalism, the so-called MaxEnt-NESOM, we derive the equations of evolution for the energy density and its first and second fluxes in a truncated description. We obtain a generalized Fouriers law, relating the flux of energy with extended thermodynamic forces which include contributions of the Guyer–Krumhansl–type. An extended evolution equation for the density of energy is derived, and the conditions when it goes over restricted forms of the type of the telegraphist equation and the traditional Fourier heat diffusion equation are discussed.

Optical properties of semiconductors via pump-probe experiments: statistical-thermodynamical approach, hot plasma and coherent phonon states

We present an analysis of the nonequilibrium thermodynamics and, mainly, a response function theory for the study of optical properties in ultrafast-spectroscopy pump-probe experiments. These experiments give rise to the formation of a photoinjected plasma in semiconductors in far-from-equilibrium conditions. The dissipative processes that evolve in this medium greatly influence optical and transport properties. The theory is centred on the application to the study of the phenomenon of modulated changes in the time-resolved reflectivity spectrum. In particular, we show that this phenomenon consists in the coupled effect of coherent-LO-phonon and carrier-charge-density motions, which are driven through the action of the coherent photons of the laser electromagnetic radiation. In the given conditions the modulation effect decays in time and has associated a frequency close to the zone-centre upper LO phonon-optical plasma hybrid mode, as experimentally observed.

Carrier dynamics in stacked InP∕GaAs quantum dots

We investigated two stacked layers of InP∕GaAs type-II quantum dots by transmission electron microscopy and optical spectroscopy. The results reveal that InP quantum dots formed in two quantum dot layers are more uniform than those from a single layer structure. The thermal activation energies as well as the photoluminescence decays are rather independent of the separation between quantum dot layers and the presence of the second layer. The quantum dot optical emission persists for thermal activation energy larger than the calculated exciton binding energy. The photoluminescence decay is relatively fast for type-II alignment.

Exciton spin precessions in a biased double quantum dot

We investigated the electric field effects on the spin precessions of excitons in a double quantum dot embedded in a semiconductor nanowire under an applied magnetic field. The electric field moves the carriers in the dots along the nanowire axis, modifying their confinement and therefore the effective g factors and the electron-hole exchange interaction. We obtain the time evolution of the excitonic spin and show, from the spin precession spectra, how the applied electric field affects the excitonic spin dynamics.

Terahertz-field-induced tunneling current with nonlinear effects in a double quantum well coupled to a continuum

We have theoretically investigated the tunneling current induced by a terahertz (THz) field applied to an asymmetric double quantum well. The excitation couples an initially localized state to a nearby continuum of extended states. We have shown that the calculated current has similar features as those present in the optical spectra, such as interference effects due to the interaction between the continuum and the localized states, in addition to many-photon transition effects. The induced current is calculated as a function of the intensity of the THz field. A second THz field is used to yield nonlinear processes, useful to control the interference effects. We believe that part of the issues studied here can be useful for the integration of novel switching mechanisms based on optics (THz) and electronic current.