115 research outputs found
Mott law as lower bound for a random walk in a random environment
We consider a random walk on the support of a stationary simple point process
on , which satisfies a mixing condition w.r.t.the translations
or has a strictly positive density uniformly on large enough cubes. Furthermore
the point process is furnished with independent random bounded energy marks.
The transition rates of the random walk decay exponentially in the jump
distances and depend on the energies through a factor of the Boltzmann-type.
This is an effective model for the phonon-induced hopping of electrons in
disordered solids within the regime of strong Anderson localization. We show
that the rescaled random walk converges to a Brownian motion whose diffusion
coefficient is bounded below by Mott's law for the variable range hopping
conductivity at zero frequency. The proof of the lower bound involves estimates
for the supercritical regime of an associated site percolation problem
Geometric measures of quantum correlations : characterization, quantification, and comparison by distances and operations
We investigate and compare three distinguished geometric measures of bipartite quantum correlations that have been recently introduced in the literature: the geometric discord, the measurement-induced geometric discord, and the discord of response, each one defined according to three contractive distances on the set of quantum states, namely the trace, Bures, and Hellinger distances. We establish a set of exact algebraic relations and inequalities between the different measures. In particular, we show that the geometric discord and the discord of response based on the Hellinger distance are easy to compute analytically for all quantum states whenever the reference subsystem is a qubit. These two measures thus provide the first instance of discords that are simultaneously fully computable, reliable (since they satisfy all the basic Axioms that must be obeyed by a proper measure of quantum correlations), and operationally viable (in terms of state distinguishability). We apply the general mathematical structure to determine the closest classical-quantum state of a given state and the maximally quantum-correlated states at fixed global state purity according to the different distances, as well as a necessary condition for a channel to be quantumness breaking
Mott law as lower bound for a random walk in a random environment
We consider a random walk on the support of a stationary simple point
process on \RR^d, which satisfies a mixing condition w.r.t. the
translations or has a strictly positive density uniformly on large enough
cubes. Furthermore the point process is furnished with independent random
bounded energy marks. The transition rates of the random walk decay
exponentially in the jump distances and depend on the energies through a
factor of the Boltzmann-type. This is an effective model for the
phonon-induced hopping of electrons in disordered solids within the regime of
strong Anderson localisation. We show that the rescaled random walk
converges to a Brownian motion whose diffusion coefficient is bounded below
by Mott's law for the variable range hopping conductivity at zero
frequency. The proof of the lower bound involves estimates for the
supercritical regime of an associated site percolation problem
Noise in Bose Josephson junctions: Decoherence and phase relaxation
Squeezed states and macroscopic superpositions of coherent states have been
predicted to be generated dynamically in Bose Josephson junctions. We solve
exactly the quantum dynamics of such a junction in the presence of a classical
noise coupled to the population-imbalance number operator (phase noise),
accounting for, for example, the experimentally relevant fluctuations of the
magnetic field. We calculate the correction to the decay of the visibility
induced by the noise in the non-Markovian regime. Furthermore, we predict that
such a noise induces an anomalous rate of decoherence among the components of
the macroscopic superpositions, which is independent of the total number of
atoms, leading to potential interferometric applications.Comment: Fig 2 added; version accepted for publicatio
Universal spectral form factor for chaotic dynamics
We consider the semiclassical limit of the spectral form factor of
fully chaotic dynamics. Starting from the Gutzwiller type double sum over
classical periodic orbits we set out to recover the universal behavior
predicted by random-matrix theory, both for dynamics with and without time
reversal invariance. For times smaller than half the Heisenberg time
, we extend the previously known -expansion to
include the cubic term. Beyond confirming random-matrix behavior of individual
spectra, the virtue of that extension is that the ``diagrammatic rules'' come
in sight which determine the families of orbit pairs responsible for all orders
of the -expansion.Comment: 4 pages, 1 figur
Quantum measurements without macroscopic superpositions
We study a class of quantum measurement models. A microscopic object is
entangled with a macroscopic pointer such that each eigenvalue of the measured
object observable is tied up with a specific pointer deflection. Different
pointer positions mutually decohere under the influence of a bath.
Object-pointer entanglement and decoherence of distinct pointer readouts
proceed simultaneously. Mixtures of macroscopically distinct object-pointer
states may then arise without intervening macroscopic superpositions.
Initially, object and apparatus are statistically independent while the latter
has pointer and bath correlated according to a metastable local thermal
equilibrium. We obtain explicit results for the object-pointer dynamics with
temporal coherence decay in general neither exponential nor Gaussian. The
decoherence time does not depend on details of the pointer-bath coupling if it
is smaller than the bath correlation time, whereas in the opposite Markov
regime the decay depends strongly on whether that coupling is Ohmic or
super-Ohmic.Comment: 50 pages, 5 figures, changed conten
On the Form Factor for the Unitary Group
We study the combinatorics of the contributions to the form factor of the
group U(N) in the large limit. This relates to questions about
semiclassical contributions to the form factor of quantum systems described by
the unitary ensemble.Comment: 35 page
Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations
We introduce an infinite family of quantifiers of quantum correlations beyond
entanglement which vanish on both classical-quantum and quantum-classical
states and are in one-to-one correspondence with the metric-adjusted skew
informations. The `quantum correlations' are defined as the maximum
metric-adjusted correlations between pairs of local observables with the
same fixed equispaced spectrum. We show that these quantifiers are entanglement
monotones when restricted to pure states of qubit-qudit systems. We also
evaluate the quantum correlations in closed form for two-qubit systems and
discuss their behaviour under local commutativity preserving channels. We
finally provide a physical interpretation for the quantifier corresponding to
the average of the Wigner-Yanase-Dyson skew informations.Comment: 20 pages, 1 figure. Published versio
Heat kernel of integrable billiards in a magnetic field
We present analytical methods to calculate the magnetic response of
non-interacting electrons constrained to a domain with boundaries and submitted
to a uniform magnetic field. Two different methods of calculation are
considered - one involving the large energy asymptotic expansion of the
resolvent (Stewartson-Waechter method) is applicable to the case of separable
systems, and another based on the small time asymptotic behaviour of the heat
kernel (Balian-Bloch method). Both methods are in agreement with each other but
differ from the result obtained previously by Robnik. Finally, the Balian-Bloch
multiple scattering expansion is studied and the extension of our results to
other geometries is discussed.Comment: 13 pages, Revte
- …