2,249 research outputs found
Suppression of weak-localization (and enhancement of noise) by tunnelling in semiclassical chaotic transport
We add simple tunnelling effects and ray-splitting into the recent
trajectory-based semiclassical theory of quantum chaotic transport. We use this
to derive the weak-localization correction to conductance and the shot-noise
for a quantum chaotic cavity (billiard) coupled to leads via
tunnel-barriers. We derive results for arbitrary tunnelling rates and arbitrary
(positive) Ehrenfest time, . For all Ehrenfest times, we show
that the shot-noise is enhanced by the tunnelling, while the weak-localization
is suppressed. In the opaque barrier limit (small tunnelling rates with large
lead widths, such that Drude conductance remains finite), the weak-localization
goes to zero linearly with the tunnelling rate, while the Fano factor of the
shot-noise remains finite but becomes independent of the Ehrenfest time. The
crossover from RMT behaviour () to classical behaviour
() goes exponentially with the ratio of the Ehrenfest time
to the paired-paths survival time. The paired-paths survival time varies
between the dwell time (in the transparent barrier limit) and half the dwell
time (in the opaque barrier limit). Finally our method enables us to see the
physical origin of the suppression of weak-localization; it is due to the fact
that tunnel-barriers ``smear'' the coherent-backscattering peak over reflection
and transmission modes.Comment: 20 pages (version3: fixed error in sect. VC - results unchanged) -
Contents: Tunnelling in semiclassics (3pages), Weak-localization (5pages),
Shot-noise (5pages
Matrix Element Distribution as a Signature of Entanglement Generation
We explore connections between an operator's matrix element distribution and
its entanglement generation. Operators with matrix element distributions
similar to those of random matrices generate states of high multi-partite
entanglement. This occurs even when other statistical properties of the
operators do not conincide with random matrices. Similarly, operators with some
statistical properties of random matrices may not exhibit random matrix element
distributions and will not produce states with high levels of multi-partite
entanglement. Finally, we show that operators with similar matrix element
distributions generate similar amounts of entanglement.Comment: 7 pages, 6 figures, to be published PRA, partially supersedes
quant-ph/0405053, expands quant-ph/050211
Universal spectral statistics in quantum graphs
We prove that the spectrum of an individual chaotic quantum graph shows
universal spectral correlations, as predicted by random--matrix theory. The
stability of these correlations with regard to non--universal corrections is
analyzed in terms of the linear operator governing the classical dynamics on
the graph.Comment: 4 pages, reftex, 1 figure, revised version to be published in PR
Fidelity Decay as an Efficient Indicator of Quantum Chaos
Recent work has connected the type of fidelity decay in perturbed quantum
models to the presence of chaos in the associated classical models. We
demonstrate that a system's rate of fidelity decay under repeated perturbations
may be measured efficiently on a quantum information processor, and analyze the
conditions under which this indicator is a reliable probe of quantum chaos and
related statistical properties of the unperturbed system. The type and rate of
the decay are not dependent on the eigenvalue statistics of the unperturbed
system, but depend on the system's eigenvector statistics in the eigenbasis of
the perturbation operator. For random eigenvector statistics the decay is
exponential with a rate fixed precisely by the variance of the perturbation's
energy spectrum. Hence, even classically regular models can exhibit an
exponential fidelity decay under generic quantum perturbations. These results
clarify which perturbations can distinguish classically regular and chaotic
quantum systems.Comment: 4 pages, 3 figures, LaTeX; published version (revised introduction
and discussion
Field quantization for chaotic resonators with overlapping modes
Feshbach's projector technique is employed to quantize the electromagnetic
field in optical resonators with an arbitray number of escape channels. We find
spectrally overlapping resonator modes coupled due to the damping and noise
inflicted by the external radiation field. For wave chaotic resonators the mode
dynamics is determined by a non--Hermitean random matrix. Upon including an
amplifying medium, our dynamics of open-resonator modes may serve as a starting
point for a quantum theory of random lasing.Comment: 4 pages, 1 figur
Entanglement Generation of Nearly-Random Operators
We study the entanglement generation of operators whose statistical
properties approach those of random matrices but are restricted in some way.
These include interpolating ensemble matrices, where the interval of the
independent random parameters are restricted, pseudo-random operators, where
there are far fewer random parameters than required for random matrices, and
quantum chaotic evolution. Restricting randomness in different ways allows us
to probe connections between entanglement and randomness. We comment on which
properties affect entanglement generation and discuss ways of efficiently
producing random states on a quantum computer.Comment: 5 pages, 3 figures, partially supersedes quant-ph/040505
Semiclassical spectral correlator in quasi one-dimensional systems
We investigate the spectral statistics of chaotic quasi one dimensional
systems such as long wires. To do so we represent the spectral correlation
function through derivatives of a generating function and
semiclassically approximate the latter in terms of periodic orbits. In contrast
to previous work we obtain both non-oscillatory and oscillatory contributions
to the correlation function. Both types of contributions are evaluated to
leading order in for systems with and without time-reversal
invariance. Our results agree with expressions from the theory of disordered
systems.Comment: 10 pages, no figure
Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories
Electronic transport through chaotic quantum dots exhibits universal, system
independent, properties, consistent with random matrix theory. The quantum
transport can also be rooted, via the semiclassical approximation, in sums over
the classical scattering trajectories. Correlations between such trajectories
can be organized diagrammatically and have been shown to yield universal
answers for some observables. Here, we develop the general combinatorial
treatment of the semiclassical diagrams, through a connection to factorizations
of permutations. We show agreement between the semiclassical and random matrix
approaches to the moments of the transmission eigenvalues. The result is valid
for all moments to all orders of the expansion in inverse channel number for
all three main symmetry classes (with and without time reversal symmetry and
spin-orbit interaction) and extends to nonlinear statistics. This finally
explains the applicability of random matrix theory to chaotic quantum transport
in terms of the underlying dynamics as well as providing semiclassical access
to the probability density of the transmission eigenvalues.Comment: Refereed version. 5 pages, 4 figure
Eigenvalue statistics of the real Ginibre ensemble
The real Ginibre ensemble consists of random matrices formed
from i.i.d. standard Gaussian entries. By using the method of skew orthogonal
polynomials, the general -point correlations for the real eigenvalues, and
for the complex eigenvalues, are given as Pfaffians with explicit
entries. A computationally tractable formula for the cumulative probability
density of the largest real eigenvalue is presented. This is relevant to May's
stability analysis of biological webs.Comment: 4 pages, to appear PR
Coherence and Decoherence in Radiation off Colliding Heavy Ions
We discuss the kinetics of a disoriented chiral condensate, treated as an
open quantum system. We suggest that the problem is analogous to that of a
damped harmonic oscillator. Master equations are used to establish a hierarchy
of relevant time scales. Some phenomenological consequences are briefly
outlined.Comment: 15 latex pages, LPTHE Orsay 93/19, e-mail: [email protected]
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