359 research outputs found
Energy spectrum of strongly correlated particles in quantum dots
The ground state and the excitation spectrum of strongly correlated electrons
in quantum dots are investigated. An analytical solution is constructed by
exact diagonalization of the Hamiltonian in terms of the -particle
eigenmodes.Comment: 10 pages, 10 figures, to appear in Journal of Physics: Conf. Serie
Quantum Potential for Diffraction and Exchange Effects
Semi-classical methods of statistical mechanics can incorporate essential
quantum effects by using effective quantum potentials. An ideal Fermi gas
interacting with an impurity is represented by a classical fluid with effective
electron-electron and electron-impurity quantum potentials. The
electron-impurity quantum potential is evaluated at weak coupling, leading to a
generalization of the Kelbg potential to include both diffraction and
degeneracy effects. The electron-electron quantum potential for exchange
effects only is the same as that discussed earlier by others.Comment: to appear in the International Journal of Quantum Chemistr
Classical Representation of a Quantum System at Equilibrium
A quantum system at equilibrium is represented by a corresponding classical
system, chosen to reproduce the thermodynamic and structural properties. The
objective is to develop a means for exploiting strong coupling classical
methods (e.g., MD, integral equations, DFT) to describe quantum systems. The
classical system has an effective temperature, local chemical potential, and
pair interaction that are defined by requiring equivalence of the grand
potential and its functional derivatives with respect to the external and pair
potentials for the classical and quantum systems. Practical inversion of this
mapping for the classical properties is effected via the hypernetted chain
approximation, leading to representations as functionals of the quantum pair
correlation function. As an illustration, the parameters of the classical
system are determined approximately such that ideal gas and weak coupling RPA
limits are preserved
Crystallization in mass-asymmetric electron-hole bilayers
We consider a \textit{mass-asymmetric} electron and hole bilayer. Electron
and hole Coulomb correlations and electron and hole quantum effects are treated
on first princles by path integral Monte Carlo methods. For a fixed layer
separation we vary the mass ratio of holes and electrons between 1 and 100
and analyze the structural changes in the system. While, for the chosen
density, the electrons are in a nearly homogeneous state, the hole arrangement
changes from homogeneous to localized, with increasing which is verified
for both, mesoscopic bilayers in a parabolic trap and for a macroscopic system.Comment: 10 pages, latex (styles files included
Phase Transition in Strongly Degenerate Hydrogen Plasma
Direct fermionic path-integral Monte-Carlo simulations of strongly coupled
hydrogen are presented. Our results show evidence for the hypothetical plasma
phase transition. Its most remarkable manifestation is the appearance of
metallic droplets which are predicted to be crucial for the electrical
conductivity allowing to explain the rapid increase observed in recent shock
compression measurments.Comment: 1 LaTeX file using jetpl.cls (included), 5 ps figures. Manuscript
submitted to JETP Letter
Numerical approaches to time evolution of complex quantum systems
We examine several numerical techniques for the calculation of the dynamics
of quantum systems. In particular, we single out an iterative method which is
based on expanding the time evolution operator into a finite series of
Chebyshev polynomials. The Chebyshev approach benefits from two advantages over
the standard time-integration Crank-Nicholson scheme: speedup and efficiency.
Potential competitors are semiclassical methods such as the Wigner-Moyal or
quantum tomographic approaches. We outline the basic concepts of these
techniques and benchmark their performance against the Chebyshev approach by
monitoring the time evolution of a Gaussian wave packet in restricted
one-dimensional (1D) geometries. Thereby the focus is on tunnelling processes
and the motion in anharmonic potentials. Finally we apply the prominent
Chebyshev technique to two highly non-trivial problems of current interest: (i)
the injection of a particle in a disordered 2D graphene nanoribbon and (ii) the
spatiotemporal evolution of polaron states in finite quantum systems. Here,
depending on the disorder/electron-phonon coupling strength and the device
dimensions, we observe transmission or localisation of the matter wave.Comment: 8 pages, 3 figure
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
Wigner function quantum molecular dynamics
Classical molecular dynamics (MD) is a well established and powerful tool in
various fields of science, e.g. chemistry, plasma physics, cluster physics and
condensed matter physics. Objects of investigation are few-body systems and
many-body systems as well. The broadness and level of sophistication of this
technique is documented in many monographs and reviews, see for example
\cite{Allan,Frenkel,mdhere}. Here we discuss the extension of MD to quantum
systems (QMD). There have been many attempts in this direction which differ
from one another, depending on the type of system under consideration. One
direction of QMD has been developed for condensed matter systems and will not
discussed here, e.g. \cite{fermid}. In this chapter we are dealing with unbound
electrons as they occur in gases, fluids or plasmas. Here, one strategy is to
replace classical point particles by wave packets, e.g.
\cite{fermid,KTR94,zwicknagel06} which is quite successful. At the same time,
this method struggles with problems related to the dispersion of such a packet
and difficulties to properly describe strong electron-ion interaction and bound
state formation. We, therefore, avoid such restrictions and consider a
completely general alternative approach. We start discussion of quantum
dynamics from a general consideration of quantum distribution functions.Comment: 18 pages, based on lecture at Hareaus school on computational phyics,
Greifswald, September 200
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