2,403 research outputs found
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
Extended phase diagram of the Lorenz model
The parameter dependence of the various attractive solutions of the three
variable nonlinear Lorenz model equations for thermal convection in
Rayleigh-B\'enard flow is studied. Its bifurcation structure has commonly been
investigated as a function of r, the normalized Rayleigh number, at fixed
Prandtl number \sigma. The present work extends the analysis to the entire
(r,\sigma) parameter plane. An onion like periodic pattern is found which is
due to the alternating stability of symmetric and non-symmetric periodic
orbits. This periodic pattern is explained by considering non-trivial limits of
large r and \sigma. In addition to the limit which was previously analyzed by
Sparrow, we identify two more distinct asymptotic regimes in which either
\sigma/r or \sigma^2/r is constant. In both limits the dynamics is
approximately described by Airy functions whence the periodicity in parameter
space can be calculated analytically. Furthermore, some observations about
sequences of bifurcations and coexistence of attractors, periodic as well as
chaotic, are reported.Comment: 36 pages, 20 figure
Finite size corrections to scaling in high Reynolds number turbulence
We study analytically and numerically the corrections to scaling in
turbulence which arise due to the finite ratio of the outer scale of
turbulence to the viscous scale , i.e., they are due to finite size
effects as anisotropic forcing or boundary conditions at large scales. We find
that the deviations \dzm from the classical Kolmogorov scaling of the velocity moments \langle |\u(\k)|^m\rangle \propto k^{-\zeta_m}
decrease like . Our numerics employ a
reduced wave vector set approximation for which the small scale structures are
not fully resolved. Within this approximation we do not find independent
anomalous scaling within the inertial subrange. If anomalous scaling in the
inertial subrange can be verified in the large limit, this supports the
suggestion that small scale structures should be responsible, originating from
viscosity either in the bulk (vortex tubes or sheets) or from the boundary
layers (plumes or swirls)
Perturbative evolution of far off-resonance driven two-level systems: Coherent population trapping, localization, and harmonic generation
The time evolution of driven two-level systems in the far off-resonance
regime is studied analytically. We obtain a general first-order perturbative
expression for the time-dependent density operator which is applicable
regardless of the coupling strength value. In the strong field regime, our
perturbative expansion remains valid even when the far off-resonance condition
is not fulfilled. We find that, in the absence of dissipation, driven two-level
systems exhibit coherent population trapping in a certain region of parameter
space, a property which, in the particular case of a symmetric double-well
potential, implies the well-known localization of the system in one of the two
wells. Finally, we show how the high-order harmonic generation that this kind
of systems display can be obtained as a straightforward application of our
formulation.Comment: 14 pages, LaTeX, 2 figures, acknowledgments adde
Modified semiclassical approximation for trapped Bose gases
A generalization of the semiclassical approximation is suggested allowing for
an essential extension of its region of applicability. In particular, it
becomes possible to describe Bose-Einstein condensation of a trapped gas in
low-dimensional traps and in traps of low confining dimensions, for which the
standard semiclassical approximation is not applicable. The results of the
modified approach are shown to coincide with purely quantum-mechanical
calculations for harmonic traps, including the one-dimensional harmonic trap.
The advantage of the semiclassical approximation is in its simplicity and
generality. Power-law potentials of arbitrary powers are considered. Effective
thermodynamic limit is defined for any confining dimension. The behaviour of
the specific heat, isothermal compressibility, and density fluctuations is
analyzed, with an emphasis on low confining dimensions, where the usual
semiclassical method fails. The peculiarities of the thermodynamic
characteristics in the effective thermodynamic limit are discussed.Comment: Revtex file, 13 page
Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros
We present a detailed description of a classification scheme for phase
transitions in finite systems based on the distribution of Fisher zeros of the
canonical partition function in the complex temperature plane. We apply this
scheme to finite Bose-systems in power law traps within a semi-analytic
approach with a continuous one-particle density of states for different values of and to a three dimensional harmonically
confined ideal Bose-gas with discrete energy levels. Our results indicate that
the order of the Bose-Einstein condensation phase transition sensitively
depends on the confining potential.Comment: 7 pages, 9 eps-figures, For recent information on physics of small
systems see "http://www.smallsystems.de
Heisenberg Evolution WKB and Symplectic Area Phases
The Schrodinger and Heisenberg evolution operators are represented in quantum
phase space by their Weyl symbols. Their semiclassical approximations are
constructed in the short and long time regimes. For both evolution problems,
the WKB representation is purely geometrical: the amplitudes are functions of a
Poisson bracket and the phase is the symplectic area of a region in phase space
bounded by trajectories and chords. A unified approach to the Schrodinger and
Heisenberg semiclassical evolutions is developed by introducing an extended
phase space. In this setting Maslov's pseudodifferential operator version of
WKB analysis applies and represents these two problems via a common higher
dimensional Schrodinger evolution, but with different extended Hamiltonians.
The evolution of a Lagrangian manifold in the extended phase space, defined by
initial data, controls the phase, amplitude and caustic behavior. The
symplectic area phases arise as a solution of a boundary condition problem.
Various applications and examples are considered.Comment: 32 pages, 7 figure
Numerical Simulations of Shock Wave-Driven Jets
We present the results of numerical simulations of shock wave-driven jets in
the solar atmosphere. The dependence of observable quantities like maximum
velocity and deceleration on parameters such as the period and amplitude of
initial disturbances and the inclination of the magnetic field is investigated.
Our simulations show excellent agreement with observations, and shed new light
on the correlation between velocity and deceleration and on the regional
differences found in observations.Comment: 7 pages, 11 figures, submitted to Ap
Visualization of Coherent Destruction of Tunneling in an Optical Double Well System
We report on a direct visualization of coherent destruction of tunneling
(CDT) of light waves in a double well system which provides an optical analog
of quantum CDT as originally proposed by Grossmann, Dittrich, Jung, and Hanggi
[Phys. Rev. Lett. {\bf 67}, 516 (1991)]. The driven double well, realized by
two periodically-curved waveguides in an Er:Yb-doped glass, is designed so that
spatial light propagation exactly mimics the coherent space-time dynamics of
matter waves in a driven double-well potential governed by the Schr\"{o}dinger
equation. The fluorescence of Er ions is exploited to image the spatial
evolution of light in the two wells, clearly demonstrating suppression of light
tunneling for special ratios between frequency and amplitude of the driving
field.Comment: final versio
Efeito do processamento e das condições ambientais nas propriedades de materiais biodegradáveis de amido de aveia.
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