Alan A. Dzhioev

Super-fermion representation of quantum kinetic equations for the electron transport problem.

We discuss the use of super-fermion formalism to represent and solve quantum kinetic equations for the electron transport problem. Starting with the Lindblad master equation for the molecule connected to two metal electrodes, we convert the problem of finding the nonequilibrium steady state to the many-body problem with non-hermitian liouvillian in super-Fock space. We transform the liouvillian to the normal ordered form, introduce nonequilibrium quasiparticles by a set of canonical nonunitary transformations and develop general many-body theory for the electron transport through the interacting region. The approach is applied to the electron transport through a single level. We consider a minimal basis hydrogen atom attached to two metal leads in Coulomb blockade regime (out of equilibrium Anderson model) within the nonequilibrium Hartree-Fock approximation as an example of the system with electron interaction. Our approach agrees with exact results given by the Landauer theory for the considered models.

Gamow-Teller strength distributions at finite temperatures and electron capture in stellar environments

We propose a new method to calculate stellar weak-interaction rates. It is based on the thermofield dynamics formalism and allows calculation of the weak-interaction response of nuclei at finite temperatures. The thermal evolution of the GT{sub +} distributions is presented for the sample nuclei {sup 54,56}Fe and {sup 76,78,80}Ge. For Ge we also calculate the strength distribution of first-forbidden transitions. We show that thermal effects shift the GT{sub +} centroid to lower excitation energies and make possible negative- and low-energy transitions. In our model we demonstrate that the unblocking effect for GT{sub +} transitions in neutron-rich nuclei is sensitive to increasing temperature. The results are used to calculate electron capture rates and are compared to those obtained from the shell model.

Kramers problem for nonequilibrium current-induced chemical reactions

We discuss the use of tunneling electron current to control and catalyze chemical reactions. Assuming the separation of time scales for electronic and nuclear dynamics we employ Langevin equation for a reaction coordinate. The Langevin equation contains nonconservative current-induced forces and gives nonequilibrium, effective potential energy surface for current-carrying molecular systems. The current-induced forces are computed via Keldysh nonequilibrium Greens functions. Once a nonequilibrium, current-depended potential energy surface is defined, the chemical reaction is modeled as an escape of a Brownian particle from the potential well. We demonstrate that the barrier between the reactant and the product states can be controlled by the bias voltage. When the molecule is asymmetrically coupled to the electrodes, the reaction can be catalyzed or stopped depending on the polarity of the tunneling current.

Nonequilibrium perturbation theory in Liouville–Fock space for inelastic electron transport

We use a superoperator representation of the quantum kinetic equation to develop nonequilibrium perturbation theory for an inelastic electron current through a quantum dot. We derive a Lindblad-type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville-Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron-vibronic and electron-electron interactions. Our perturbation theory becomes equivalent to a Keldysh nonequilibrium Greens function perturbative treatment provided that the buffer zone is large enough to alleviate the problems associated with approximations of the Lindblad kinetic equation.

Stability analysis of multiple nonequilibrium fixed points in self-consistent electron transport calculations

We present a method to perform stability analysis of nonequilibrium fixed points appearing in self-consistent electron transport calculations. The nonequilibrium fixed points are given by the self-consistent solution of stationary, nonlinear kinetic equation for single-particle density matrix. We obtain the stability matrix by linearizing the kinetic equation around the fixed points and analyze the real part of its spectrum to assess the asymptotic time behavior of the fixed points. We derive expressions for the stability matrices within Hartree-Fock and linear response adiabatic time-dependent density functional theory. The stability analysis of multiple fixed points is performed within the nonequilibrium Hartree-Fock approximation for the electron transport through a molecule with a spin-degenerate single level with local Coulomb interaction.

Out-of-equilibrium catalysis of chemical reactions by electronic tunnel currents

We present an escape rate theory for current-induced chemical reactions. We use Keldysh nonequilibrium Greens functions to derive a Langevin equation for the reaction coordinate. Due to the out of equilibrium electronic degrees of freedom, the friction, noise, and effective temperature in the Langevin equation depend locally on the reaction coordinate. As an example, we consider the dissociation of diatomic molecules induced by the electronic current from a scanning tunnelling microscope tip. In the resonant tunnelling regime, the molecular dissociation involves two processes which are intricately interconnected: a modification of the potential energy barrier and heating of the molecule. The decrease of the molecular barrier (i.e., the current induced catalytic reduction of the barrier) accompanied by the appearance of the effective, reaction-coordinate-dependent temperature is an alternative mechanism for current-induced chemical reactions, which is distinctly different from the usual paradigm of pumping vibrational degrees of freedom.

Second-order post-Hartree-Fock perturbation theory for the electron current

Based on the super-fermion representation of quantum kinetic equations we develop nonequilibrium, post-Hartree-Fock many-body perturbation theory for the current through a region of interacting electrons. We apply the theory to out of equilibrium Anderson model and discuss practical implementation of the approach. Our calculations show that nonequilibrium electronic correlations may produce significant quantitative and qualitative corrections to mean-field electronic transport properties.

Nonequilibrium configuration interaction method for transport in correlated quantum systems

We present a new approach to treat correlations in nonequilibrium quantum many-particle system. The method is based on ideas of configuration interaction theory of exact nonperturbative ground state electronic structure calculations. We use superoperator techniques in Liouville–Fock space and represent the nonequilibrium density matrix as a linear combination of all possible nonequilibrium quasiparticle excitations built on the appropriate reference state. As an example we consider the electron transport through the system with electron–phonon interaction. The concept of embedding (buffer zones between the reservoirs and the correlated quantum system) is used to derive an exact master equation for the reduced density matrix. Using approximate (truncated) expansion of the trial density matrix we obtain the linear system of equations for two-quasiparticle amplitudes. Then we compute the steady-state current and compare the result with other approaches. The current conserving property of the method is proven.

Superoperator coupled cluster method for nonequilibrium density matrix

We develop a superoperator coupled cluster method for nonequilibrium open many-body quantum systems described by the Lindblad master equation. The method is universal and applicable to systems of interacting fermions, bosons or their mixtures. We present a general theory and consider its application to the problem of quantum transport through the system with electron-phonon correlations. The results are assessed against the perturbation theory and nonequilibrium configuration interaction theory calculations.

ON THE TFD TREATMENT OF COLLECTIVE VIBRATIONS IN HOT NUCLEI

The approach in a theory of collective excitations in hot nuclei exploring the formalism of thermo field dynamics and the model Hamiltonian consisting of a mean field, the BCS paring interaction, and long-range particle–hole effective forces is reexamined. In contrast with earlier studies, it is found that a wave function of a thermal phonon is depended not only on the Fermi–Dirac thermal occupation numbers of the Bogoliubov quasiparticles consisting the phonon but also on the Bose thermal occupation numbers of the phonon. This strongly affects a thermal phonon coupling due to the renormalization of a phonon–phonon interaction and enlarging the number of thermal two-phonon configurations coupled with one-phonon ones. Moreover, it is shown that the formulation of the double tilde conjugation rule for fermions proposed by I. Ojima is more appropriate in the context of the present study than the original one by H. Umezawa and co-workers.