76 research outputs found
Interacting electrons in a one-dimensional random array of scatterers - A Quantum Dynamics and Monte-Carlo study
The quantum dynamics of an ensemble of interacting electrons in an array of
random scatterers is treated using a new numerical approach for the calculation
of average values of quantum operators and time correlation functions in the
Wigner representation. The Fourier transform of the product of matrix elements
of the dynamic propagators obeys an integral Wigner-Liouville-type equation.
Initial conditions for this equation are given by the Fourier transform of the
Wiener path integral representation of the matrix elements of the propagators
at the chosen initial times. This approach combines both molecular dynamics and
Monte Carlo methods and computes numerical traces and spectra of the relevant
dynamical quantities such as momentum-momentum correlation functions and
spatial dispersions. Considering as an application a system with fixed
scatterers, the results clearly demonstrate that the many-particle interaction
between the electrons leads to an enhancement of the conductivity and spatial
dispersion compared to the noninteracting case.Comment: 10 pages and 8 figures, to appear in PRB April 1
Quantum simulations of strongly coupled quark-gluon plasma
A strongly coupled quark-gluon plasma (QGP) of heavy constituent
quasiparticles is studied by a path-integral Monte-Carlo method, which improves
the corresponding classical simulations by extending them to the quantum
regime. It is shown that this method is able to reproduce the lattice equation
of state and also yields valuable insight into the internal structure of the
QGP. The results indicate that the QGP reveals liquid-like rather than gas-like
properties. At temperatures just above the critical one it was found that bound
quark-antiquark states still survive. These states are bound by effective
string-like forces. Quantum effects turned out to be of prime importance in
these simulations.Comment: 8 pages, 10 figures, revised version of the contribution to
proceedings of "Int. Workshop on High Density Nuclear Matter", Cape Town,
5-10 Apr., 201
Quantum dynamics in canonical and micro-canonical ensembles. Part I. Anderson localization of electrons
The new numerical approach for consideration of quantum dynamics and
calculations of the average values of quantum operators and time correlation
functions in the Wigner representation of quantum statistical mechanics has
been developed. The time correlation functions have been presented in the form
of the integral of the Weyl's symbol of considered operators and the Fourier
transform of the product of matrix elements of the dynamic propagators. For the
last function the integral Wigner- Liouville's type equation has been derived.
The numerical procedure for solving this equation combining both molecular
dynamics and Monte Carlo methods has been developed. For electrons in
disordered systems of scatterers the numerical results have been obtained for
series of the average values of the quantum operators including position and
momentum dispersions, average energy, energy distribution function as well as
for the frequency dependencies of tensor of electron conductivity and
permittivity according to quantum Kubo formula. Zero or very small value of
static conductivity have been considered as the manifestation of Anderson
localization of electrons in 1D case. Independent evidence of Anderson
localization comes from the behaviour of the calculated time dependence of
position dispersion.Comment: 8 pages, 10 figure
Dynamic properties and the roton mode attenuation in the liquid 3He: an ab initio study within the self-consistent method of moments
The dynamic structure factor and the eigenmodes of density fluctuations in
the uniform liquid He are studied using a novel non-perturbative approach.
This new version of the self-consistent method of moments invokes up to nine
sum rules and other exact relations involving the spectral density, the
two-parameter Shannon information entropy maximization procedure, and the ab
initio path integral Monte Carlo (PIMC) simulations which provide crucial
reliable input information on the system static properties. Detailed analysis
of the dispersion relations of collective excitations, the modes decrements and
the static structure factor (SSF) of He at the saturated vapor pressure is
performed. The results are compared to available experimental data~[1,2]. The
theory reveals a clear signature of the roton-like feature in the particle-hole
segment of the excitation spectrum with a significant reduction of the roton
decrement in the wavenumber range . The
observed roton mode remains a well defined collective excitation even in the
particle-hole band, where, however, it is strongly damped. Hence, the existence
of the roton-like mode in the bulk liquid He is confirmed like in other
strongly interacting quantum fluids~[3]. The phonon branch of the spectrum is
also studied with a reasonable agreement with the same experimental data being
achieved. The presented combined approach permits to produce ab initio data on
the system dynamic characteristics in a wide range of physical parameters and
for other physical systems.Comment: 20 pages, 18 figure
Thermodynamic properties and electrical conductivity of strongly correlated plasma media
We study thermodynamic properties and the electrical conductivity of dense
hydrogen and deuterium using three methods: classical reactive Monte Carlo
(REMC), direct path integral Monte Carlo (PIMC) and a quantum dynamics method
in the Wigner representation of quantum mechanics. We report the calculation of
the deuterium compression quasi-isentrope in good agreement with experiments.
We also solve the Wigner-Liouville equation of dense degenerate hydrogen
calculating the initial equilibrium state by the PIMC method. The obtained
particle trajectories determine the momentum-momentum correlation functions and
the electrical conductivity and are compared with available theories and
simulations
Monte Carlo results for the hydrogen Hugoniot
We propose a theoretical Hugoniot obtained by combining results for the
equation of state (EOS) from the Direct Path Integral Monte Carlo technique
(DPIMC) and those from Reaction Ensemble Monte Carlo (REMC) simulations. The
main idea of such proposal is based on the fact that DPMIC provides
first-principle results for a wide range of densities and temperatures
including the region of partially ionized plasmas. On the other hand, for lower
temperatures where the formation of molecules becomes dominant, DPIMC
simulations become cumbersome and inefficient. For this region it is possible
to use accurate REMC simulations where bound states (molecules) are treated on
the Born-Oppenheimer level using a binding potential calculated by Kolos and
Wolniewicz. The remaining interaction is then reduced to the scattering between
neutral particles which is reliably treated classically applying effective
potentials. The resulting Hugoniot is located between the experimental values
of Knudson {\textit{et al.}} \cite{1} and Collins {\textit{et al.}} \cite{2}.Comment: 10 pges, 2 figures, 2 table
Path integral Monte Carlo calculations of helium and hydrogen-helium plasma thermodynamics and of the deuterium shock Hugoniot
In this work we calculate the thermodynamic properties of hydrogen-helium
plasmas with different mass fractions of helium by the direct path integral
Monte Carlo method. To avoid unphysical approximations we use the path integral
representation of the density matrix. We pay special attention to the region of
weak coupling and degeneracy and compare the results of simulation with a model
based on the chemical picture. Further with the help of calculated deuterium
isochors we compute the shock Hugoniot of deuterium. We analyze our results in
comparison with recent experimental and calculated data on the deuterium
Hugoniot.Comment: 7 pages, 5 Postscript figures, accepted for publication in J. Phys.
A: Math. Ge
Correlational Origin of the Roton Minimum
We present compelling evidence supporting the conjecture that the origin of
the roton in Bose-condensed systems arises from strong correlations between the
constituent particles. By studying the two dimensional bosonic dipole systems a
paradigm, we find that classical molecular dynamics (MD) simulations provide a
faithful representation of the dispersion relation for a low- temperature
quantum system. The MD simulations allow one to examine the effect of coupling
strength on the formation of the roton minimum and to demonstrate that it is
always generated at a sufficiently high enough coupling. Moreover, the
classical images of the roton-roton, roton-maxon, etc. states also appear in
the MD simulation spectra as a consequence of the strong coupling.Comment: 7 pages, 4 figure
Transmission time of wave packets through tunneling barriers
The transmission of wave packets through tunneling barriers is studied in
detail by the method of quantum molecular dynamics. The distribution function
of the times describing the arrival of a tunneling packet in front of and
behind a barrier and the momentum distribution function of the packet are
calculated. The behavior of the average coordinate of a packet, the average
momentum, and their variances is investigated. It is found that under the
barrier a part of the packet is reflected and a Gaussian barrier increases the
average momentum of the transmitted packet and its variance in momentum space.Comment: 23 pages, 5 figure
Collective excitations in electron-hole bilayers
We report a combined analytic and Molecular Dynamics analysis of the
collective mode spectrum of an electron-hole (bipolar) bilayer in the strong
coupling quasi-classical limit. A robust, isotropic energy gap is identified in
the out-of-phase spectra, generated by the combined effect of correlations and
of the excitation of the bound dipoles; the in-phase spectra exhibit a
correlation governed acoustic dispersion for the longitudinal and transverse
modes. Strong nonlinear generation of higher harmonics of the fundamental
dipole oscillation frequency and the transfer of harmonics between different
modes is observed. The mode dispersions in the liquid state are compared with
the phonon spectrum in the crystalline solid phase, reinforcing a coherent
physical picture.Comment: 4 pages, 5 figure
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