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.     

Difference between canonical and grand canonical ensembles in discrete lattice gas models

We calculate the site occupation probabilities of one-dimensional lattice gas models within the canonical and grand canonical ensembles. The appearing differences do not vanish if we increase the system size keeping the site energies discrete. In this way one can explain the surprising numerical results of Barszczak and Kutner. This effect in the single-site occupation number disappears in higher dimensions.     

Masterequation,H-theorem and stationary solution for coupled quantum systems

We extend the Zwanzig projector formalism to coupled systems taking into account the mutual interactions of the reduced density matrices of both systems. In the Born- and Markoff-approximation we end up with a bilinear masterequation for occupation probabilities, in contrast to the usually studied linear equations. We derive theH-theorem for this equation and show that the stationary solution is the canonical or more generally a grand canonical density matrix.     

On the thermodynamic potential expressed as a trace over scattering phases and occupation numbers

A formula is presented which expresses the thermodynamic potential as a trace over the product of occupation numbers and a phase operator referring to the transitions among the “excitations” associated with the absorbtive parts of the many body single particle propagators. The entropy and the statistical average of each conserved, non-spontaneously violated, charge are given simply by appropriately differentiating the occupation numbers appearing in the trace. The formula is a generalization to arbitrary temperature and density of a previously discussed formula (Ref. [2]) relating the thermodynamic potential in the regime of weak degeneracy to a trace involving the logarithm of the elementary particle S-matrix. How this latter formula arises from summing up the graphs of finite temperature field theory is also discussed.     

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.     

Typicality versus thermality: an analytic distinction

In systems with a large degeneracy of states such as black holes, one expects that the average value of probe correlation functions will be well approximated by the thermal ensemble. To understand how correlation functions in individual microstates differ from the canonical ensemble average and from each other, we study the variances in correlators. Using general statistical considerations, we show that the variance between microstates will be exponentially suppressed in the entropy. However, by exploiting the analytic properties of correlation functions we argue that these variances are amplified in imaginary time, thereby distinguishing pure states from the thermal density matrix. We demonstrate our general results in specific examples and argue that our results apply to the microstates of black holes.     

Steady state statistics of driven diffusions

We consider overdamped diffusion processes driven out of thermal equilibrium and we analyze their dynamical steady fluctuations. We discuss the thermodynamic interpretation of the joint fluctuations of occupation times and currents; they incorporate respectively the time-symmetric and the time-antisymmetric sector of the fluctuations. We highlight the canonical structure of the joint fluctuations. The novel concept of traffic complements the entropy production for the study of the occupation statistics. We explain how the occupation and current fluctuations get mutually coupled out of equilibrium. Their decoupling close-to-equilibrium explains the validity of entropy production principles.     

Hole states based on the 112−[505] neutron orbital within the pairing gap

Coupled-channel calculations have been performed for (d, p) and (d, t) reactions on the stable doubly even isotopes of Gd, Dy and Er for $\text{11}\text{2}$^? neutron transfer to the [505] band heads. Comparison to published data permitted reliable extraction of the occupation numbers for this orbital. The occupation numbers V² were found to be much greater than the emptiness numbers U², even for very low-lying excitations. These results can only be obtained for a very small pairing parameter, Δ, consistent with other less direct determinations. These results are as expected for a diminution of the pairing interaction for this oblate [505] orbital.     

Occupation dynamics of anE-e Jahn-Teller system

The internal dynamics of a Jahn-Teller system (E-e type) is given. The time-dependent occupation numbers and the energy-transfer between the different uncoupled states are calculated. It is shown that the resonant behaviour of the system, as already known from optical calculations and measurements, manifests itself in the time-dependent occupation probabilities of each single state.     

Statistical mechanics of quenched inhomogeneous systems with random disorder

We propose a method to treat quenched disordered systems within the frame of an inhomogeneous ensemble of configurations. To describe a definite configuration, we make use of occupation numbers. By choosing an appropriate representation of these occupation numbers, we are able to deal with an inhomogeneous ensemble by elementary techniques as for instance used for uncorrelated occupation numbers in the frame of a translation invariant ensemble.     

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.     

Heat capacity study of the first monolayer of adsorbed methane on grafoil

The heat capacity of CH₄ adsorbed on Grafoil below monolayer completion has been determined experimentally for the first time. The specific heat at constant density shows two characteristic features, very broad, weak anomalies at 47.6 K (around one third of a monolayer) and (for occupation numbers below two thirds of a monolayer) very narrow, strong peaks at 56.35 K. The anomalies at 47.6 K are interpreted as being due to a registry — out-of-registry transition of the two dimensional (2D) solid CH₄ adsorbate into an incommensurate expanded structure. The anomalies at 56.35 K define the 2D triple point of adsorbed CH₄. For higher occupation numbers the liquid-solid phase boundary shifts to higher temperatures. The present data make partial re-definition of the 2D-CH₄ phase diagram necessary.     

Excitation energy of the lowest 2+ and 3− levels in 32Mg and 146Gd

The excitation energy of the lowest 2⁺ and 3^? levels is calculated for neutron rich Mg-isotopes as well as for N=82 isotones. The calculations are made by assuming quadrupole-quadrupole and octupole-octupole forces. The quasiparticle energies and occupation numbers are taken from the energy density method.     

Thermodynamic properties of a finite Bose gas in a harmonic trap

We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of total number $N$ of particles and using a saddle-point approximation, we derive analytically the simple explicit expression of mean occupation number in any state of the finite system. The temperature dependence of the chemical potential, specific heat, and condensate fraction for the trapped finite-size Bose system is obtained numerically. We compare our results with the usual treatment which is based on the grand canonical ensemble. It is shown that there exists a considerable difference between them at sufficiently low temperatures, specially for the relative small numbers of Bose atoms. The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed. We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.     

Ion distribution preferences in ternary crystals ZnxCd1−xTe, Zn1−xHgxTe and Cd1−xHgxTe

Similar ternary semiconductors are sometimes associated with widely different structures characterized by different site occupation preferences. We have used far-infrared (FIR) spectra to determine the site occupation preference coefficients for three ternary semiconductor alloys: ZnCdTe, ZnHgTe and CdHgTe and, in the case of ZnHgTe, have validated it by X-ray absorption fine structure (EXAFS) analysis. While ZnCdTe spectra exhibit the canonical configuration with eight phonon lines free of vibrational defect lines and only a slight departure from a random ion distribution, CdHgTe spectra show the eight canonical phonon modes plus an additional vibrational defect line and constant preference coefficients. In contrast, two defect lines and only four modes characterize ZnHgTe spectra, as extreme preferences prevent the formation of two of the five expected tetrahedral configuration arrangements. Moreover, for this system, comparison with EXAFS data points out the vibrational nature of both the extra lines. The analysis clearly shows that assuming a Bernoulli distribution of the component configurations of semiconductors may lead to wrong assessments of the evolution of its properties with relative content.     

Bose gases in one-dimensional harmonic trap

Thermodynamic quantities, occupation numbers and their fluctuations of a one-dimensional Bose gas confined by a harmonic potential are studied using different ensemble approaches. Combining number theory methods, a new approach is presented to calculate the occupation numbers of different energy levels in microcanonical ensemble. The visible difference of the ground state occupation number in grand-canonical ensemble and microcanonical ensemble is found to decrease by power law as the number of particles increases.     

The electronic structure of a series of tin complexes studied by XPS and Mössbauer spectroscopy

The isomer shift and 3d_5/2 core electron binding energy shift have been measured for a series of complexes. By using a simple model for the interpretation of these shifts in terms of occupation numbers of valence orbitals an estimate of the electronic structure is obtained.     

Characterisation of backflow events over a wing section

Rare backflow (negative wall-shear stress) events have recently been found and quantified in the near-wall region of canonical wall-bounded turbulent flows. Although their existence and correlation with large-scale events have been established beyond numerical and measurement technique uncertainties, their occurrence at numerically high Reynolds numbers is still rare (less than 1 per thousand and 1 per million at the wall and beyond the viscous sublayer, respectively). To better quantify these rare events, the turbulent boundary layer developing over the suction side of a wing section, experiencing an increasing adverse pressure gradient (APG) without separation along its chord c, is considered in the present work. We find that the backflow level of 0.06% documented in turbulent channels and zero-pressure-gradient (ZPG) turbulent boundary layers is already exceeded on the suction side for x/c > 0.3, at friction Reynolds numbers three times lower, while close to the trailing edge the backflow level reaches 30%. Conditional analysis of extreme events indicates that for increasing Clauser pressure-gradient parameters (reaching β ? 35), the flow reaches a state in which the extreme events are more likely aligned with or against the freestream, and that the otherwise strong spanwise component of the wall-shear stress reduces towards the vicinity of the trailing edge. Backflow events subjected to moderate up to strong APG conditions (0.6 < β < 4.1) exhibit an average width of Δz⁺ ? 20, and an average lifetime of Δt⁺ ? 2. This directly connects with the findings by Lenaers et al., and implies that there is a connection between high-Re ZPG and strong APG conditions.     

One plus two-body random matrix ensemble with spin: Analysis using spectral variances

For one plus two-body random matrix ensembles with spin, the chaos measure inverse participation ratio is calculated for 6, 7 and 8 fermion systems with good total spin S. Propagation equations for fixed-spin spectral variances explain the numerical results. Similarly, lower order correlations between spectra with different particle numbers and spins are analyzed using fixed-spin energy centroids and spectral variances. The correlations are found to be small for low-spin members.