3,752 research outputs found
Long-time and unitary properties of semiclassical initial value representations
We numerically compare the semiclassical ``frozen Gaussian'' Herman-Kluk
propagator [Chem. Phys. 91, 27 (1984)] and the ``thawed Gaussian'' propagator
put forward recently by Baranger et al. [J. Phys. A 34, 7227 (2001)] by
studying the quantum dynamics in some nonlinear one-dimensional potentials. The
reasons for the lack of long time accuracy and norm conservation in the latter
method are uncovered. We amend the thawed Gaussian propagator with a global
harmonic approximation for the stability of the trajectories and demonstrate
that this revised propagator is a true alternative to the Herman-Kluk
propagator with similar accuracy.Comment: 14 pages, 4 figures, corrected typos and figure 1 (d
Spectra of Harmonium in a magnetic field using an initial value representation of the semiclassical propagator
For two Coulombically interacting electrons in a quantum dot with harmonic
confinement and a constant magnetic field, we show that time-dependent
semiclassical calculations using the Herman-Kluk initial value representation
of the propagator lead to eigenvalues of the same accuracy as WKB calculations
with Langer correction. The latter are restricted to integrable systems,
however, whereas the time-dependent initial value approach allows for
applications to high-dimensional, possibly chaotic dynamics and is extendable
to arbitrary shapes of the potential.Comment: 11 pages, 1 figur
Kohn-Sham equations for nanowires with direct current
The paper describes the derivation of the Kohn-Sham equations for a nanowire
with direct current. A value of the electron current enters the problem as an
input via a subsidiary condition imposed by pointwise Lagrange multiplier.
Using the constrained minimization of the Hohenberg-Kohn energy functional, we
derive a set of self-consistent equations for current carrying orbitals of the
molecular wire
The role of contacts in molecular electronics
Molecular electronic devices are the upmost destiny of the miniaturization
trend of electronic components. Although not yet reproducible on large scale,
molecular devices are since recently subject of intense studies both
experimentally and theoretically, which agree in pointing out the extreme
sensitivity of such devices on the nature and quality of the contacts. This
chapter intends to provide a general theoretical framework for modelling
electronic transport at the molecular scale by describing the implementation of
a hybrid method based on Green function theory and density functional
algorithms. In order to show the presence of contact-dependent features in the
molecular conductance, we discuss three archetypal molecular devices, which are
intended to focus on the importance of the different sub-parts of a molecular
two-terminal setup.Comment: 17 pages, 8 figure
Yang-Lee zeroes for an urn model for the separation of sand
We apply the Yang-Lee theory of phase transitions to an urn model of
separation of sand. The effective partition function of this nonequilibrium
system can be expressed as a polynomial of the size-dependent effective
fugacity . Numerical calculations show that in the thermodynamic limit, the
zeros of the effective partition function are located on the unit circle in the
complex -plane. In the complex plane of the actual control parameter certain
roots converge to the transition point of the model. Thus the Yang-Lee theory
can be applied to a wider class of nonequilibrium systems than those considered
previously.Comment: 4 pages, 3 eps figures include
Electron-Ion Interaction Effects in Attosecond Time-Resolved Photoelectron Spectra
Photoionization by attosecond (as) extreme ultraviolet (xuv) pulses into the
laser-dressed continuum of the ionized atom is commonly described in
strong-field approximation (SFA), neglecting the Coulomb interaction between
the emitted photoelectron (PE) and residual ion. By solving the time-dependent
Sch\"{o}dinger equation (TDSE), we identify a temporal shift in
streaked PE spectra, which becomes significant at small PE energies. Within an
eikonal approximation, we trace this shift to the combined action of Coulomb
and laser forces on the released PE, suggesting the experimental and
theoretical scrutiny of their coupling in streaked PE spectra. The initial
state polarization effect by the laser pulse on the xuv streaked spectrum is
also examined.Comment: 9 pages, Accepted by Phys. Rev.
Quantum approach to the thermalization of the toppling pencil interacting with a finite bath
We investigate the longstanding problem of thermalization of quantum systems coupled to an environment by focusing on a bistable quartic oscillator interacting with a finite number of harmonic oscillators. In order to overcome the exponential wall that one usually encounters in grid-based approaches to solve the time-dependent Schrodinger equation of the extended system, methods based on the time-dependent variational principle are best suited. Here we will apply the method of coupled coherent states [D. V. Shalashilin and M. S. Child, J. Chem. Phys. 113, 10028 (2000)]. By investigating the dynamics of an initial wave function on top of the barrier of the double well, it will be shown that only a handful of oscillators with suitably chosen frequencies, starting in their ground states, is enough to drive the bistable system close to its uncoupled ground state. The long-time average of the double-well energy is found to be a monotonously decaying function of the number of environmental oscillators in the parameter range that was numerically accessible
Tunneling in a cavity
The mechanism of coherent destruction of tunneling found by Grossmann et al.
[Phys. Rev. Lett. 67, 516 (1991)] is studied from the viewpoint of quantum
optics by considering the photon statistics of a single mode cavity field which
is strongly coupled to a two-level tunneling system (TS). As a function of the
interaction time between TS and cavity the photon statistics displays the
tunneling dynamics. In the semi-classical limit of high photon occupation
number , coherent destruction of tunneling is exhibited in a slowing down of
an amplitude modulation for certain parameter ratios of the field. The
phenomenon is explained as arising from interference between displaced number
states in phase space which survives the large limit due to identical
scaling between orbit width and displacement.Comment: 4 pages Revtex, 2 PS-figures, appears in The Physical Review
Exact variational dynamics of the multimode Bose-Hubbard model based on SU(M) coherent states
We propose a variational approach to the dynamics of the Bose-Hubbard model beyond the mean-field approximation. To develop a numerical scheme, we use a discrete overcomplete set of Glauber coherent states and its connection to the generalized coherent states studied in depth by Perelomov [Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986)]. The variational equations of motion of the generalized coherent state parameters as well as of the coefficients in an expansion of the wave function in terms of those states are derived and solved for many-particle problems with large particle numbers S and increasing mode number M. For M = 6, it is revealed that the number of complex-valued parameters that have to be propagated is more than one order of magnitude less than in an expansion in terms of Fock states
Semiclassical Coherent States propagator
In this work, we derived a semiclassical approximation for the matrix
elements of a quantum propagator in coherent states (CS) basis that avoids
complex trajectories, it only involves real ones. For that propose, we used
the, symplectically invariant, semiclassical Weyl propagator obtained by
performing a stationary phase approximation (SPA) for the path integral in the
Weyl representation. After what, for the transformation to CS representation
SPA is avoided, instead a quadratic expansion of the complex exponent is used.
This procedure also allows to express the semiclassical CS propagator uniquely
in terms of the classical evolution of the initial point, without the need of
any root search typical of Van Vleck Gutzwiller based propagators. For the case
of chaotic Hamiltonian systems, the explicit time dependence of the CS
propagator has been obtained. The comparison with a
\textquotedbl{}realistic\textquotedbl{} chaotic system that derives from a
quadratic Hamiltonian, the cat map, reveals that the expression here derived is
exact up to quadratic Hamiltonian systems.Comment: 13 pages, 2 figure. Accepted for publication in PR
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