Asymptotics of work distributions in a stochastically driven system

We determine the asymptotic forms of work distributions at arbitrary times $T$, in a class of driven stochastic systems using a theory developed by Engel and Nickelsen (EN theory) (arXiv:1102.4505v1 [cond-mat.stat-mech]), which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in the path integral form, are characterised by having quadratic actions. We first illustrate EN theory, for a deterministically driven system - the breathing parabola model, and show that within its framework, the Crooks flucutation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial function. We then extend our analysis to a stochastically driven system, studied in ( arXiv:1212.0704v2 [cond-mat.stat-mech], arXiv:1402.5777v1 [cond-mat.stat-mech]) using a moment-generating-function method, for both equilibrium and non - equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary $T$. For dissipated work in the steady state, we compare the large $T$ asymptotic behaviour of our solution to that already obtained in ( arXiv:1402.5777v1 [cond-mat.stat-mech]). In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with the numerical simulations. Our solutions are exact in the low noise limit.Comment: 26 pages, 8 figures. Changes from version 1: Several typos and equations corrected, references added, pictures modified. Version to appear in EPJ

Quasi-universal transient behavior of a nonequilibrium Mott insulator driven by an electric field

We use a self-consistent strong-coupling expansion for the self-energy (perturbation theory in the hopping) to describe the nonequilibrium dynamics of strongly correlated lattice fermions. We study the three-dimensional homogeneous Fermi-Hubbard model driven by an external electric field showing that the damping of the ensuing Bloch oscillations depends on the direction of the field, and that for a broad range of field strengths, a long-lived transient prethermalized state emerges. This long-lived transient regime implies that thermal equilibrium may be out of reach of the time scales accessible in present cold atom experiments, but shows that an interesting new quasi-universal transient state exists in nonequilibrium governed by a thermalized kinetic energy but not a thermalized potential energy. In addition, when the field strength is equal in magnitude to the interaction between atoms, the system undergoes a rapid thermalization, characterized by a different quasi-universal behavior of the current and spectral function for different values of the hopping.Comment: (5 pages, 5 figures, ReVTeX

Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory

We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse $10^d\times 10^d$ matrix, with $d > 6$. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in non-equilibrium setups without mass transport.Comment: 14 pages, 9 figure

When is electromagnetic spectrum fungible?

Fungibility is a common assumption for market-based spectrum management. In this paper, we explore the dimensions of practical fungibility of frequency bands from the point of view of the spectrum buyer who intends to use it. The exploration shows that fungibility is a complex, multidimensional concept that cannot casually be assumed. We develop two ideas for quantifying fungibility-(i) of a fungibility space in which the 'distance' between two slices of spectrum provides score of fungibility and (ii) a probabilistic score of fungibility. © 2012 IEEE

Detection of selfish manipulation of carrier sensing in 802.11 networks

Recently, tuning the clear channel assessment (CCA) threshold in conjunction with power control has been considered for improving the performance of WLANs. However, we show that, CCA tuning can be exploited by selfish nodes to obtain an unfair share of the available bandwidth. Specifically, a selfish entity can manipulate the CCA threshold to ignore ongoing transmissions; this increases the probability of accessing the medium and provides the entity a higher, unfair share of the bandwidth. We experiment on our 802.11 testbed to characterize the effects of CCA tuning on both isolated links and in 802.11 WLAN configurations. We focus on AP-client(s) configurations, proposing a novel approach to detect this misbehavior. A misbehaving client is unlikely to recognize low power receptions as legitimate packets; by intelligently sending low power probe messages, an AP can efficiently detect a misbehaving node. Our key contributions are: 1) We are the first to quantify the impact of selfish CCA tuning via extensive experimentation on various 802.11 configurations. 2) We propose a lightweight scheme for detecting selfish nodes that inappropriately increase their CCAs. 3) We extensively evaluate our system on our testbed; its accuracy is 95 percent while the false positive rate is less than 5 percent. © 2012 IEEE

A Framework of Efficient Hybrid Model and Optimal Control for Multihop Wireless Networks

The performance of multihop wireless networks (MWN) is normally studied via simulation over a fixed time horizon using a steady-state type of statistical analysis procedure. However, due to the dynamic nature of network connectivi- ty and nonstationary traffic, such an approach may be inap- propriate as the network may spend most time in a transien- t/nonstationary state. Moreover, the majority of the simu- lators suffer from scalability issues. In this work, we presents a performance modeling framework for analyzing the time varying behavior of MWN. Our framework is a hybrid mod- el of time varying connectivity matrix and nonstationary network queues. Network connectivity is captured using s- tochastic modeling of adjacency matrix by considering both wireless link quality and node mobility. Nonstationary net- work queues behavior are modeled using fluid flow based differential equations. In terms of the computational time, the hybrid fluid-based model is a more scalable tool than the standard simulator. Furthermore, an optimal control strategy is proposed on the basis of the hybrid model

Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

We develop a strong-coupling ($t \ll U$) expansion technique for calculating the density profile for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperature and finite on site interaction in the presence of superfluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We also show that the superfluid order parameter never vanishes in the trap due to proximity effect. Our calculations for the scaled density in the vacuum to superfluid transition agree well with the experimental data for appropriate temperatures. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments.Comment: 11 pages, 9 figure