4,598 research outputs found
Semiclassical Theory of Chaotic Quantum Transport
We present a refined semiclassical approach to the Landauer conductance and
Kubo conductivity of clean chaotic mesoscopic systems. We demonstrate for
systems with uniformly hyperbolic dynamics that including off-diagonal
contributions to double sums over classical paths gives a weak-localization
correction in quantitative agreement with results from random matrix theory. We
further discuss the magnetic field dependence. This semiclassical treatment
accounts for current conservation.Comment: 4 pages, 1 figur
Escape Orbits for Non-Compact Flat Billiards
It is proven that, under some conditions on , the non-compact flat
billiard
has no orbits going {\em directly} to . The relevance of such
sufficient conditions is discussed.Comment: 9 pages, LaTeX, 3 postscript figures available at
http://www.princeton.edu/~marco/papers/ . Minor changes since previously
posted version. Submitted to 'Chaos
Semiclassical universality of parametric spectral correlations
We consider quantum systems with a chaotic classical limit that depend on an
external parameter, and study correlations between the spectra at different
parameter values. In particular, we consider the parametric spectral form
factor which depends on a scaled parameter difference . For
parameter variations that do not change the symmetry of the system we show by
using semiclassical periodic orbit expansions that the small expansion
of the form factor agrees with Random Matrix Theory for systems with and
without time reversal symmetry.Comment: 18 pages, no figure
Periodic orbit bifurcations and scattering time delay fluctuations
We study fluctuations of the Wigner time delay for open (scattering) systems
which exhibit mixed dynamics in the classical limit. It is shown that in the
semiclassical limit the time delay fluctuations have a distribution that
differs markedly from those which describe fully chaotic (or strongly
disordered) systems: their moments have a power law dependence on a
semiclassical parameter, with exponents that are rational fractions. These
exponents are obtained from bifurcating periodic orbits trapped in the system.
They are universal in situations where sufficiently long orbits contribute. We
illustrate the influence of bifurcations on the time delay numerically using an
open quantum map.Comment: 9 pages, 3 figures, contribution to QMC200
Particle creation and annihilation at interior boundaries:One-dimensional models
We describe creation and annihilation of particles at external sources in one
spatial dimension in terms of interior-boundary conditions (IBCs). We derive
explicit solutions for spectra, (generalised) eigenfunctions, as well as Green
functions, spectral determinants, and integrated spectral densities. Moreover,
we introduce a quantum graph version of IBC-Hamiltonians.Comment: 32 page
Scattering induced dynamical entanglement and the quantum-classical correspondence
The generation of entanglement produced by a local potential interaction in a
bipartite system is investigated. The degree of entanglement is contrasted with
the underlying classical dynamics for a Rydberg molecule (a charged particle
colliding on a kicked top). Entanglement is seen to depend on the structure of
classical phase-space rather than on the global dynamical regime. As a
consequence regular classical dynamics can in certain circumstances be
associated with higher entanglement generation than chaotic dynamics. In
addition quantum effects also come into play: for example partial revivals,
which are expected to persist in the semiclassical limit, affect the long time
behaviour of the reduced linear entropy. These results suggest that
entanglement may not be a pertinent universal signature of chaos.Comment: Published versio
Semiclassical structure of chaotic resonance eigenfunctions
We study the resonance (or Gamow) eigenstates of open chaotic systems in the
semiclassical limit, distinguishing between left and right eigenstates of the
non-unitary quantum propagator, and also between short-lived and long-lived
states. The long-lived left (right) eigenstates are shown to concentrate as
on the forward (backward) trapped set of the classical dynamics.
The limit of a sequence of eigenstates is found
to exhibit a remarkably rich structure in phase space that depends on the
corresponding limiting decay rate. These results are illustrated for the open
baker map, for which the probability density in position space is observed to
have self-similarity properties.Comment: 4 pages, 4 figures; some minor corrections, some changes in
presentatio
Geometrical theory of diffraction and spectral statistics
We investigate the influence of diffraction on the statistics of energy
levels in quantum systems with a chaotic classical limit. By applying the
geometrical theory of diffraction we show that diffraction on singularities of
the potential can lead to modifications in semiclassical approximations for
spectral statistics that persist in the semiclassical limit . This
result is obtained by deriving a classical sum rule for trajectories that
connect two points in coordinate space.Comment: 14 pages, no figure, to appear in J. Phys.
Randomly incomplete spectra and intermediate statistics
By randomly removing a fraction of levels from a given spectrum a model is
constructed that describes a crossover from this spectrum to a Poisson
spectrum. The formalism is applied to the transitions towards Poisson from
random matrix theory (RMT) spectra and picket fence spectra. It is shown that
the Fredholm determinant formalism of RMT extends naturally to describe
incomplete RMT spectra.Comment: 9 pages, 2 figures. To appear in Physical Review
On the evolutionary origins of host–microbe associations
Animals can provide benefits to their associated microbes—}and these can, in turn, positively affect their hosts. But how do such mutually beneficial associations arise in the first place? In particular, when animal and microbe initially have independent lifestyles, this is not clear. By developing a model of animal and microbial life cycles on patchy habitats, we show how their overlapping ecologies of development and dispersal can lead to the enrichment of certain microbes in the dispersing animals, even in the absence of specific mutualistic benefits. This enrichment can then set the stage for the evolution of more specific host{–}microbe associations, which also implies that host enrichment per se is not an indicator of a beneficial host{–}microbe symbiosis.Many microorganisms with high prevalence in host populations are beneficial to the host and maintained by specialized transmission mechanisms. Although microbial promotion of host fitness and specificity of the associations undoubtedly enhance microbial prevalence, it is an open question whether these symbiotic traits are also a prerequisite for the evolutionary origin of prevalent microbial taxa. To address this issue, we investigate how processes without positive microbial effects on host fitness or host choice can influence the prevalence of certain microbes in a host population. Specifically, we develop a theoretical model to assess the conditions under which particular microbes can become enriched in animal hosts even when they are not providing a specific benefit to a particular host. We find increased prevalence of specific microbes in a host when both show some overlap in their lifecycles, and especially when both share dispersal routes across a patchy habitat distribution. Our results emphasize that host enrichment per se is not a reliable indicator of beneficial host{–microbe interactions. The resulting increase in time spent associated with a host may nevertheless give rise to new selection conditions, which can favor microbial adaptations toward a host-associated lifestyle, and, thus, it could be the foundation for subsequent evolution of mutually beneficial coevolved symbioses.A Python implementation of the model underlying the results in this paper has been deposited in GitHub (https://github.com/misieber/patchbiota)
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