30 research outputs found
Exact Green's Function For The Step And Square-barrier Potentials
We calculate both the exact retarded and advanced Green's function for the one-dimensional step and square-barrier potentials in the space-energy representation. Some of the results for the square barrier are also extended to general symmetric potentials of finite range. © 1993 The American Physical Society.4842567257
A semiclassical trace formula for the canonical partition function of one dimensional systems
We present a semiclassical trace formula for the canonical partition function
of arbitrary one-dimensional systems. The approximation is obtained via the
stationary exponent method applied to the phase-space integration of the
density operator in the coherent state representation. The formalism is valid
in the low temperature limit, presenting accurate results in this regime. As
illustrations we consider a quartic Hamiltonian that cannot be split into
kinetic and potential parts, and a system with two local minima. Applications
to spin systems are also presented.Comment: 22 pages, 4 figures new section with applications to spin system
Controlling Phase Space Caustics in the Semiclassical Coherent State Propagator
The semiclassical formula for the quantum propagator in the coherent state
representation is not
free from the problem of caustics. These are singular points along the complex
classical trajectories specified by , and where
the usual quadratic approximation fails, leading to divergences in the
semiclassical formula. In this paper we derive third order approximations for
this propagator that remain finite in the vicinity of caustics. We use Maslov's
method and the dual representation proposed in Phys. Rev. Lett. {\bf 95},
050405 (2005) to derive uniform, regular and transitional semiclassical
approximations for coherent state propagator in systems with two degrees of
freedom.Comment: 24 pages, to appear in Ann. of Phy
Robustness of spontaneous pattern formation in spatially distributed genetic populations
Spatially distributed genetic populations that compete locally for resources and mate only with sufficiently close neighbors, may give rise to spontaneous pattern formation. Depending on the population parameters, like death rate per generation and size of the competition and mating neighborhoods, isolated groups of individuals, or demes, may appear. The existence of such groups in a population has consequences for genetic diversity and for speciation. In this paper we discuss the robustness of demes formation with respect to two important characteristics of the population: the way individuals recognize the demarcation of the local neighborhoods and the way competition for resources affects the birth rate in an overcrowed situation. Our results indicate that demes are expected to form only for sufficiently sharp demarcations and for sufficiently intense competition.51452
Quantum linear mutual information and classical correlations in globally pure bipartite systems
We investigate the correlations of initially separable probability
distributions in a globally pure bipartite system with two degrees of freedom
for classical and quantum systems. A classical version of the quantum linear
mutual information is introduced and the two quantities are compared for a
system of oscillators coupled with both linear and non-linear interactions. The
classical correlations help to understand how much of the quantum loss of
purity are due to intrinsic quantum effects and how much is related to the
probabilistic character of the initial states, a characteristic shared by both
the classical and quantum pictures. Our examples show that, for initially
localized Gaussian states, the classical statistical mutual linear entropy
follows its quantum counterpart for short times. For non-Gaussian states the
behavior of the classical and quantum measures of information are still
qualitatively similar, although the fingerprints of the non-classical nature of
the initial state can be observed in their different amplitudes of oscillation.Comment: (16 pages, 4 figures
Resonant helical deformations in nonhomogeneous Kirchhoff filaments
We study the three-dimensional static configurations of nonhomogeneous
Kirchhoff filaments with periodically varying Young's modulus. This type of
variation may occur in long tandemly repeated sequences of DNA. We analyse the
effects of the Young's modulus frequence and amplitude of oscillation in the
stroboscopic maps, and in the regular (non chaotic) spatial configurations of
the filaments. Our analysis shows that the tridimensional conformations of long
filaments may depend critically on the Young's modulus frequence in case of
resonance with other natural frequencies of the filament. As expected, far from
resonance the shape of the solutions remain very close to that of the
homogeneous case. In the case of biomolecules, it is well known that various
other elements, besides sequence-dependent effects, combine to determine their
conformation, like self-contact, salt concentration, thermal fluctuations,
anisotropy and interaction with proteins. Our results show that
sequence-dependent effects alone may have a significant influence on the shape
of these molecules, including DNA. This could, therefore, be a possible
mechanical function of the ``junk'' sequences.Comment: 18 pages (twocolumn), 5 figures Revised manuscrip
Rectangular quantum dots in high magnetic fields
We use density-functional methods to study the effects of an external
magnetic field on two-dimensional quantum dots with a rectangular hard-wall
confining potential. The increasing magnetic field leads to spin polarization
and formation of a highly inhomogeneous maximum-density droplet at the
predicted magnetic field strength. At higher fields, we find an oscillating
behavior in the electron density and in the magnetization of the dot. We
identify a rich variety of phenomena behind the periodicity and analyze the
complicated many-electron dynamics, which is shown to be highly dependent on
the shape of the quantum dot.Comment: 6 pages, 6 figures, submitted to Phys. Rev.
Multiple Bifurcations in atom optics
We report the observation of multiple bifurcations in a nonlinear Hamiltionian system: laser-cooled atoms in a standing wave with single-frequency intensity modulation. We provide clear evidence of the occurrence of bifurcations by analyzing the atomic momentum distributions