2,829 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 $n$ leads via
tunnel-barriers. We derive results for arbitrary tunnelling rates and arbitrary
(positive) Ehrenfest time, $\tau_{\rm E}$. 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 ($\tau_{\rm E}=0$) to classical behaviour
($\tau_{\rm E}=\infty$) 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

### 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

### 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

### Fluctuations and Ergodicity of the Form Factor of Quantum Propagators and Random Unitary Matrices

We consider the spectral form factor of random unitary matrices as well as of
Floquet matrices of kicked tops. For a typical matrix the time dependence of
the form factor looks erratic; only after a local time average over a suitably
large time window does a systematic time dependence become manifest. For
matrices drawn from the circular unitary ensemble we prove ergodicity: In the
limits of large matrix dimension and large time window the local time average
has vanishingly small ensemble fluctuations and may be identified with the
ensemble average. By numerically diagonalizing Floquet matrices of kicked tops
with a globally chaotic classical limit we find the same ergodicity. As a
byproduct we find that the traces of random matrices from the circular
ensembles behave very much like independent Gaussian random numbers. Again,
Floquet matrices of chaotic tops share that universal behavior. It becomes
clear that the form factor of chaotic dynamical systems can be fully faithful
to random-matrix theory, not only in its locally time-averaged systematic time
dependence but also in its fluctuations.Comment: 12 pages, RevTEX, 4 figures in eps forma

### Non Thermal Equilibrium States of Closed Bipartite Systems

We investigate a two-level system in resonant contact with a larger
environment. The environment typically is in a canonical state with a given
temperature initially. Depending on the precise spectral structure of the
environment and the type of coupling between both systems, the smaller part may
relax to a canonical state with the same temperature as the environment (i.e.
thermal relaxation) or to some other quasi equilibrium state (non thermal
relaxation). The type of the (quasi) equilibrium state can be related to the
distribution of certain properties of the energy eigenvectors of the total
system. We examine these distributions for several abstract and concrete (spin
environment) Hamiltonian systems, the significant aspect of these distributions
can be related to the relative strength of local and interaction parts of the
Hamiltonian.Comment: RevTeX, 8 pages, 13 figure

### Multifractality and intermediate statistics in quantum maps

We study multifractal properties of wave functions for a one-parameter family
of quantum maps displaying the whole range of spectral statistics intermediate
between integrable and chaotic statistics. We perform extensive numerical
computations and provide analytical arguments showing that the generalized
fractal dimensions are directly related to the parameter of the underlying
classical map, and thus to other properties such as spectral statistics. Our
results could be relevant for Anderson and quantum Hall transitions, where wave
functions also show multifractality.Comment: 4 pages, 4 figure

### Entanglement in the classical limit: quantum correlations from classical probabilities

We investigate entanglement for a composite closed system endowed with a
scaling property allowing to keep the dynamics invariant while the effective
Planck constant hbar_eff of the system is varied. Entanglement increases as
hbar_eff goes to 0. Moreover for sufficiently low hbar_eff the evolution of the
quantum correlations, encapsulated for example in the quantum discord, can be
obtained from the mutual information of the corresponding \emph{classical}
system. We show this behavior is due to the local suppression of path
interferences in the interaction that generates the entanglement. This behavior
should be generic for quantum systems in the classical limit.Comment: 10 pages 3 figure

### Dynamically localized systems: entanglement exponential sensitivity and efficient quantum simulations

We study the pairwise entanglement present in a quantum computer that
simulates a dynamically localized system. We show that the concurrence is
exponentially sensitive to changes in the Hamiltonian of the simulated system.
Moreover, concurrence is exponentially sensitive to the ``logic'' position of
the qubits chosen. These sensitivities could be experimentally checked
efficiently by means of quantum simulations with less than ten qubits. We also
show that the feasibility of efficient quantum simulations is deeply connected
to the dynamical regime of the simulated system.Comment: 5 pages, 6 figure

### Universal features of spin transport and breaking of unitary symmetries

When time-reversal symmetry is broken, quantum coherent systems with and without spin rotational symmetry exhibit the same universal behavior in their electric transport properties. We show that spin transport discriminates between these two cases. In systems with large charge conductance, spin transport is essentially insensitive to the breaking of time-reversal symmetry, while in the opposite limit of a single exit transport channel, spin currents vanish identically in the presence of time-reversal symmetry but can be turned on by breaking it with an orbital magnetic field

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