Fluktuationen von Besetzungszahlen

Kinetic equations for the fluctuations and the fluctuation spectrum of the occupation numbers in a nonequilibrium stationary state are derived within a stochastic theory. The probability of changes of the distribution in infinitesimal time intervals is given by the “Stoßzahlansatz”. It is assumed for the decoupling of the higher correlations, that the occupation numbers are macroscopic variables.     

Exact three-body local correlations for excited states of the 1D Bose gas

We derive an exact analytic expression for the three-body local correlations in the Lieb-Liniger model of 1D Bose gas with contact repulsion. The local three-body correlations control the thermalization and particle loss rates in the presence of terms which break integrability, as is realized in the case of 1D ultracold bosons. Our result is valid not only at finite temperature but also for a large class of nonthermal excited states in the thermodynamic limit. We present finite temperature calculations in the presence of external harmonic confinement within local density approximation, and for a highly excited state that resembles an experimentally realized configuration.     

Emergence of Fermi-Dirac thermalization in the quantum computer core

We model an isolated quantum computer as a two-dimensional lattice of qubits (spin halves) with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. In the limit when fluctuations and couplings are small compared to the one-qubit energy spacing, the spectrum has a band structure and we study the quantum computer core (central band) with the highest density of states. Above a critical inter-qubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of eigenstates in an isolated quantum computer. The onset of chaos results in the interaction induced dynamical thermalization and the occupation numbers well described by the Fermi-Dirac distribution. This thermalization destroys the noninteracting qubit structure and sets serious requirements for the quantum computer operability. Received 3 July 2001 and Received in final form 9 September 2001     

Phase space theory of Bose–Einstein condensates and time-dependent modes

A phase space theory approach for treating dynamical behaviour of Bose–Einstein condensates applicable to situations such as interferometry with BEC in time-dependent double well potentials is presented. Time-dependent mode functions are used, chosen so that one, two,…highly occupied modes describe well the physics of interacting condensate bosons in time dependent potentials at well below the transition temperature. Time dependent mode annihilation, creation operators are represented by time dependent phase variables, but time independent total field annihilation, creation operators are represented by time independent field functions. Two situations are treated, one (mode theory) is where specific mode annihilation, creation operators and their related phase variables and distribution functions are dealt with, the other (field theory) is where only field creation, annihilation operators and their related field functions and distribution functionals are involved. The field theory treatment is more suitable when large boson numbers are involved. The paper focuses on the hybrid approach, where the modes are divided up between condensate (highly occupied) modes and non-condensate (sparsely occupied) modes. It is found that there are extra terms in the Ito stochastic equations both for the stochastic phases and stochastic fields, involving coupling coefficients defined via overlap integrals between mode functions and their time derivatives. For the hybrid approach both the Fokker–Planck and functional Fokker–Planck equations differ from those derived via the correspondence rules, the drift vectors are unchanged but the diffusion matrices contain additional terms involving the coupling coefficients.Results are also presented for the combined approach where all the modes are treated as one set. Here both the Fokker–Planck and functional Fokker–Planck equations are exactly the same as those derived via the correspondence rules. However, although the Ito stochastic field equations are also unchanged, the Ito equations for the stochastic phases contain an extra classical term involving the coupling coefficients.     

Duality for Stochastic Models of Transport

We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process which is obtained by placing the system in contact with proper reservoirs, working at different particle densities or different temperatures. We show that all the models are exactly solvable by duality, using a dual process with absorbing boundaries. The solution does also apply to the so-called thermalization limit in which particles or energy is instantaneously redistributed among sites. The results shows that duality is a versatile tool for analyzing stochastic models of transport, while the analysis in the literature has been so far limited to particular instances. Long-range correlations naturally emerge as a result of the interaction of dual particles at the microscopic level and the explicit computations of covariances match, in the scaling limit, the predictions of the macroscopic fluctuation theory.     

State-filling and magneto-photoluminescence of excited states in InGaAs/GaAs self-assembled quantum dots

We present the first radiative lifetime measurements and magneto-photoluminescence results of excited states in InGaAs/GaAs semiconductor self-assembled quantum dots. By increasing the photo-excitation intensity, excited state interband transitions up ton= 5 can be observed in the emission spectrum. The dynamics of the interband transitions and the inter-sublevel relaxation in these zero-dimensional energy levels lead to state-filling of the lower-energy states, allowing the quasi-Fermi level to be raised by more than 200 meV due to the combined large inter-sublevel spacing and the low density of states. The decay time of each energy level obtained under various excitation conditions is used to evaluate the inter-sublevel thermalization time. Finally, the emission spectrum of the dots filled with an average of about eight excitons is measured in magnetic fields up to 13 Tesla. The dependences of the spectrum as a function of carrier density and magnetic field are compared to calculations and interpreted in terms of coherent many-exciton states and their destruction by the magnetic field.     

Exchange monte carlo for molecular simulations with monoelectronic hamiltonians

We introduce a general Monte Carlo scheme for achieving atomistic simulations with monoelectronic Hamiltonians including the thermalization of both nuclear and electronic degrees of freedom. The kinetic Monte Carlo algorithm is used to obtain the exact occupation numbers of the electronic levels at canonical equilibrium, and comparison is made with Fermi-Dirac statistics in infinite and finite systems. The effects of a nonzero electronic temperature on the thermodynamic properties of liquid silver and sodium clusters are presented.     

Relaxation to Stationary Nonequilibrium States in Stochastic Ginzburg–Landau Models

We propose an approach to investigate properties of the time relaxation to stationary nonequilibrium states of correlation functions of stochastic Ginzburg–Landau models with noise (temperature of the reservoirs in contact with the system) changing in space. The formalism relates the stochastic expectations to correlation functions of an imaginary time field theory, and it allows us to study the nonlinear dynamics in terms of a field theory given by a perturbation of a Gaussian measure related to the (easier) linear dynamical problem. To show the usefulness of the formalism, we argue that a perturbative analysis within the integral representation is enough to give us the time relaxation rates of the correlations in some situations.     

The effect of coulomb correlations on the nonequilibrium charge redistribution tuned by the tunneling current

We demonstrate that the tunneling current flowing through a system with Coulomb correlations leads to a charge redistribution between the different localized states. A simple model consisting of two electron levels is analyzed by means of the Heisenberg equations of motion taking correlations of electron filling numbers in localized states into account exactly in all orders. We consider various relations between the Coulomb interaction and localized electron energies. Sudden jumps of the electron density at each level in a certain range of the applied bias are found. We find that for some parameter range, inverse occupation in the two-level system appears due to Coulomb correlations. It is also shown that Coulomb correlations lead to the appearance of negative tunneling conductivity at a certain relation between the values of tunneling rates from the two electron levels.     

Kinetics of a local “magnetic” moment and a non-stationary spin-polarized current in the single impurity Anderson model

We perform theoretical investigation of the localized state dynamics in the presence of interaction with the reservoir and Coulomb correlations. We analyze kinetic equations for electron occupation numbers with different spins taking into account high order correlation functions for the localized electrons. We reveal that in the stationary state electron occupation numbers with the opposite spins always have the same value: the stationary state is a “paramagnetic” one. “Magnetic” properties can appear only in the non-stationary characteristics of the single-impurity Anderson model and in the dynamics of the localized electrons second order correlation functions. We found that for deep energy levels and strong Coulomb correlations, relaxation time for initial “magnetic” state can be several orders larger than for “paramagnetic” one. So, long-living “magnetic” moment can exist in the system. We also found non-stationary spin polarized currents flowing in opposite directions for the different spins in the particular time interval.     

Functional equations for path integrals

We consider the density matrices that arise in the statistical mechanics of the electron-phonon systems. In the path integral representation the phonon coordinates can be eliminated. This leads to an action that depends on pairs of points on a path, that depends explicitly on time differences, and that contains the phonon occupation numbers. The integral is reduced to a standard form by scaling to the thermal length. We use the technique of integration by parts and add specially chosen generating functionals to the action. We set down functional derivative equations for the source-dependent density matrix and for the mass operator. This allows us to develop a series of approximations for the operator in terms of exact propagators. The crudest approximation is a coherent potential approximation applicable at a general temperature.     

Electron propagators based on generalised density operators

ABSTRACT

Electron binding energies and Dyson orbitals may be obtained from the poles and residues of the electron propagator. The Dyson quasiparticle equation provides a convenient route to computing this information. Systematic approximations to the latter equation's self-energy, wherein electron correlation and final-state orbital relaxation are described, may be expressed in terms of the elements of the superoperator Hamiltonian matrix. Perturbative methods of electron propagator theory in wide use are based on a reference determinant constructed with canonical, Hartree–Fock orbitals. Generalised matrix elements of the superoperator Hamiltonian that accommodate non-integer occupation numbers associated with general, orthogonal spin orbitals are presented for the first time. Non-Hermitian terms may be systematically eliminated with perturbative corrections to generalised reference density operators. The structure of self-energy approximations that are complete through second, third, fourth or fifth order is presented in terms of superoperator Hamiltonian matrix elements. The present extensions pertain when generalised, zeroth-order density operators expressed in terms of orthonormal spin orbitals are employed.     

Correlation induced switching of the local spatial charge distribution in a two-level system

It was found that tunneling current through a nanometer scale structure with strongly coupled localized states causes spatial redistribution of localized charges induced by Coulomb correlations. We present here theoretical investigation of this effect by means of Heisenberg equations for localized states electron filling numbers. This method makes it possible to take into account pair correlations of local electron density exactly. It is shown that inverse occupation of the two-level system caused by Coulomb correlations appears in particular range of applied bias. Described effects can give a possibility of charge manipulation in the proposed system. We also expect that described results can be observed in tunneling structures with impurities or with small quantum dots.     

Coulomb drag for strongly localized electrons: a pumping mechanism

The mutual influence of two layers with strongly localized electrons is exercised though the random Coulomb shifts of site energies in one layer caused by electron hops in the other layer. We trace how these shifts give rise to a voltage drop in the passive layer, when a current is passed through the active layer. We find that the microscopic origin of drag lies in the time correlations of the occupation numbers of the sites involved in a hop. These correlations are neglected within the conventional Miller-Abrahams scheme for calculating the hopping resistance.     

Interpretation and resolution of pinch singularities in non-equilibrium quantum field theory

Ill-defined pinch singularities arising in a perturbative expansion in out of equilibrium quantum field theory have a natural analogue to standard scattering theory. We explicitly demonstrate that the occurrence of such terms is directly related to Fermi's golden rule known from elementary scattering theory and is thus of no mystery. We further argue that within the process of thermalization of a plasma one has to resum such contributions to all orders as the process itself is of non-perturbative nature. In this way the resummed propagators obtain a finite width. Within the Markov approximation of kinetic theory the actual phase space distribution at a given time of the evolution enters explicitly. Received: 28 September 1998 / Published online: 11 March 1999     

Lower subband splitting and superconductivity of 2D Hubbard fermions with strong intersite correlations

The effect of the strong intersite Coulomb correlations on the formation of an electron structure in the Shubin-Vonsowsky model in the regime of strong one-site correlations is studied. The results reveal a split-off band of the Fermi states. The spectral intensity of this band grows with the enhancement of the doping level and is determined by the mean-square fluctuation of occupation numbers. This changes the structure of the electron density of states qualitatively.     

The influence of state dependent short range correlations on the depletion of the nuclear Fermi sea

The inlfuence of state dependent short range correlations on the occupation numbers of the single particle shell model orbits of the doubly closed shell nuclei¹⁶O and⁴⁰Ca is examined. The study shows that the effect of the state dependence of the short range correlations is rather small. The total depletion of the nuclear Fermi sea changes slightly compared with the one calculated by considering state independent short range correlations.     

Static correlated functionals for reduced density matrix functional theory

Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities stemming from the generalized Pauli principle, the many-body wave-function can be written explicitly in terms of the natural occupation numbers and the natural orbitals. This leads to an expression for the two-particle reduced density matrix and therefore for the correlation energy functional. This functional is tested for a three-electron Hubbard model where it shows excellent performance both in the weak and strong correlation regimes.