603 research outputs found
Asymptotic entanglement in 1D quantum walks with a time-dependent coined
Discrete-time quantum walk evolve by a unitary operator which involves two
operators a conditional shift in position space and a coin operator. This
operator entangles the coin and position degrees of freedom of the walker. In
this paper, we investigate the asymptotic behavior of the coin position
entanglement (CPE) for an inhomogeneous quantum walk which determined by two
orthogonal matrices in one-dimensional lattice. Free parameters of coin
operator together provide many conditions under which a measurement perform on
the coin state yield the value of entanglement on the resulting position
quantum state. We study the problem analytically for all values that two free
parameters of coin operator can take and the conditions under which
entanglement becomes maximal are sought.Comment: 23 pages, 4 figures, accepted for publication in IJMPB. arXiv admin
note: text overlap with arXiv:1001.5326 by other author
Sub-6-fs blue pulses generated by quasi-phase-matching second-harmonic generation pulse compression
Abstract. : We demonstrate a novel scalable and engineerable approach for the frequency-doubling of ultrashort pulses. Our technique is based on quasi-phase-matching and simultaneously provides tailored dispersion and nonlinear frequency conversion of few-cycle optical pulses. The method makes use of the spatial localization of the conversion process and the group velocity mismatch in a chirped grating structure. The total group delay of the nonlinear device can be designed to generate nearly arbitrarily chirped second-harmonic pulses from positively or negatively chirped input pulses. In particular, compressed second-harmonic pulses can be obtained. A brief summary of the underlying theory is presented, followed by a detailed discussion of our experimental results. We experimentally demonstrate quasi-phase-matching pulse compression in the sub-10-fs regime by generating few-cycle pulses in the blue to near-ultraviolet spectral range. Using this new frequency conversion technique, we generate sub-6-fs pulses centered at 405nm by second-harmonic generation from a 8.6fs Ti:sapphire laser pulse. The generated spectrum spans a bandwidth of 220THz. To our knowledge, these are the shortest pulses ever obtained by second-harmonic generatio
Ergodic properties of a model for turbulent dispersion of inertial particles
We study a simple stochastic differential equation that models the dispersion
of close heavy particles moving in a turbulent flow. In one and two dimensions,
the model is closely related to the one-dimensional stationary Schroedinger
equation in a random delta-correlated potential. The ergodic properties of the
dispersion process are investigated by proving that its generator is
hypoelliptic and using control theory
Exponential Mixing for a Stochastic PDE Driven by Degenerate Noise
We study stochastic partial differential equations of the reaction-diffusion
type. We show that, even if the forcing is very degenerate (i.e. has not full
rank), one has exponential convergence towards the invariant measure. The
convergence takes place in the topology induced by a weighted variation norm
and uses a kind of (uniform) Doeblin condition.Comment: 10 pages, 1 figur
Ergodicity, Decisions, and Partial Information
In the simplest sequential decision problem for an ergodic stochastic process
X, at each time n a decision u_n is made as a function of past observations
X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is
known that one may choose (under a mild integrability assumption) a decision
strategy whose pathwise time-average loss is asymptotically smaller than that
of any other strategy. The corresponding problem in the case of partial
information proves to be much more delicate, however: if the process X is not
observable, but decisions must be based on the observation of a different
process Y, the existence of pathwise optimal strategies is not guaranteed.
The aim of this paper is to exhibit connections between pathwise optimal
strategies and notions from ergodic theory. The sequential decision problem is
developed in the general setting of an ergodic dynamical system (\Omega,B,P,T)
with partial information Y\subseteq B. The existence of pathwise optimal
strategies grounded in two basic properties: the conditional ergodic theory of
the dynamical system, and the complexity of the loss function. When the loss
function is not too complex, a general sufficient condition for the existence
of pathwise optimal strategies is that the dynamical system is a conditional
K-automorphism relative to the past observations \bigvee_n T^n Y. If the
conditional ergodicity assumption is strengthened, the complexity assumption
can be weakened. Several examples demonstrate the interplay between complexity
and ergodicity, which does not arise in the case of full information. Our
results also yield a decision-theoretic characterization of weak mixing in
ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page
Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force
We discuss the ergodic properties of quasi-Markovian stochastic differential
equations, providing general conditions that ensure existence and uniqueness of
a smooth invariant distribution and exponential convergence of the evolution
operator in suitably weighted spaces, which implies the validity
of central limit theorem for the respective solution processes. The main new
result is an ergodicity condition for the generalized Langevin equation with
configuration-dependent noise and (non-)conservative force
Detection Strategies for Extreme Mass Ratio Inspirals
The capture of compact stellar remnants by galactic black holes provides a
unique laboratory for exploring the near horizon geometry of the Kerr
spacetime, or possible departures from general relativity if the central cores
prove not to be black holes. The gravitational radiation produced by these
Extreme Mass Ratio Inspirals (EMRIs) encodes a detailed map of the black hole
geometry, and the detection and characterization of these signals is a major
scientific goal for the LISA mission. The waveforms produced are very complex,
and the signals need to be coherently tracked for hundreds to thousands of
cycles to produce a detection, making EMRI signals one of the most challenging
data analysis problems in all of gravitational wave astronomy. Estimates for
the number of templates required to perform an exhaustive grid-based
matched-filter search for these signals are astronomically large, and far out
of reach of current computational resources. Here I describe an alternative
approach that employs a hybrid between Genetic Algorithms and Markov Chain
Monte Carlo techniques, along with several time saving techniques for computing
the likelihood function. This approach has proven effective at the blind
extraction of relatively weak EMRI signals from simulated LISA data sets.Comment: 10 pages, 4 figures, Updated for LISA 8 Symposium Proceeding
Asymptotic analysis for the generalized langevin equation
Various qualitative properties of solutions to the generalized Langevin
equation (GLE) in a periodic or a confining potential are studied in this
paper. We consider a class of quasi-Markovian GLEs, similar to the model that
was introduced in \cite{EPR99}. Geometric ergodicity, a homogenization theorem
(invariance principle), short time asymptotics and the white noise limit are
studied. Our proofs are based on a careful analysis of a hypoelliptic operator
which is the generator of an auxiliary Markov process. Systematic use of the
recently developed theory of hypocoercivity \cite{Vil04HPI} is made.Comment: 27 pages, no figures. Submitted to Nonlinearity
CLTs and asymptotic variance of time-sampled Markov chains
For a Markov transition kernel P and a probability distribution
μ on nonnegative integers, a time-sampled Markov chain evolves according
to the transition kernel Pμ = Σkμ(k)Pk. In this note we obtain CLT
conditions for time-sampled Markov chains and derive a spectral formula
for the asymptotic variance. Using these results we compare efficiency of
Barker's and Metropolis algorithms in terms of asymptotic variance
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