Wigner distributions for finite-state systems without redundant phase-point operators

We set up Wigner distributions for N-state quantum systems following a Dirac-inspired approach. In contrast to much of the work in this study, requiring a 2N x 2N phase space, particularly when N is even, our approach is uniformly based on an N x N phase-space grid and thereby avoids the necessity of having to invoke a `quadrupled' phase space and hence the attendant redundance. Both N odd and even cases are analysed in detail and it is found that there are striking differences between the two. While the N odd case permits full implementation of the marginal property, the even case does so only in a restricted sense. This has the consequence that in the even case one is led to several equally good definitions of the Wigner distributions as opposed to the odd case where the choice turns out to be unique.

Exact static polarizabilities of correlated finite model systems

A finite-field method for calculating exact polarizabilities of correlated conjugated model systems within the valence bond (VB) framework is presented. The correlations reduce the polarizabilities from their noninteracting values and extend the range of linearity to higher external fields. The large nonlinear polarizabilities observed in strongly correlated conjugated organic molecules cannot be directly attributed to electron correlations. The method described can be employed to calculate static polarizabilities for any desired state of a correlated system.

Statistical theory of finite Fermi systems with chaotic excited eigenstates

A theory of strongly interacting Fermi systems of a few particles is developed. At high excit at ion energies (a few times the single-parti cle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-part icle basis st at es by the residual two- body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-part icle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without diagonalization of the Hamiltonian matrix. We show how to use this approach to calculate mean orbital occupation numbers and matrix elements between chaotic eigenstates and introduce typically statistical variable s such as t emperature in an isolated microscopic Fermi system of a few particles.

Correlation approach to work extraction from finite quantum systems

Reversible work extraction from identical quantum systems via collective operations was shown to be possible even without producing entanglement among the sub-parts. Here, we show that implementing such global operations necessarily imply the creation of quantum correlations, as measured by quantum discord. We also reanalyze the conditions under which global transformations outperform local gates as far as maximal work extraction is considered by deriving a necessary and sufficient condition that is based on classical correlations.

Average ground-state energy of finite Fermi systems

Semiclassical theories such as the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard-wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.

Back-to-back correlations in finite expanding systems

Back-to-Back Correlations (BBC) of particle-antiparticle pairs are predicted to appear if hot and dense hadronic matter is formed in high energy nucleus-nucleus collisions. The BBC are related to in-medium mass-modification and squeezing of the quanta involved. Although the suppression of finite emission times were already known, the effects of finite system sizes and of collective phenomena had not been studied yet. Thus, for testing the survival and magnitude of the effect in more realistic situations, we study the BBC when mass-modification occurs in a finite sized, thermalized medium, considering a non-relativistically expanding fireball with finite emission time, and evaluating the width of the back-to-back correlation function. We show that the BBC signal indeed survives the expansion and flow effects, with sufficient magnitude to be observed at RHIC.

Strong Local Passivity in Finite Quantum Systems

Passive states of quantum systems are states from which no system energy can be extracted by any cyclic (unitary) process. Gibbs states of all temperatures are passive. Strong local (SL) passive states are defined to allow any general quantum operation, but the operation is required to be local, being applied only to a specific subsystem. Any mixture of eigenstates in a system-dependent neighborhood of a nondegenerate entangled ground state is found to be SL passive. In particular, Gibbs states are SL passive with respect to a subsystem only at or below a critical system-dependent temperature. SL passivity is associated in many-body systems with the presence of ground state entanglement in a way suggestive of collective quantum phenomena such as quantum phase transitions, superconductivity, and the quantum Hall effect. The presence of SL passivity is detailed for some simple spin systems where it is found that SL passivity is neither confined to systems of only a few particles nor limited to the near vicinity of the ground state.

Block envelope solution of finite difference systems /

"November, 1975."--T.p.

Finite connectivity systems as error-correcting codes

We investigate the performance of parity check codes using the mapping onto spin glasses proposed by Sourlas. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C parity checks per message bit. We show, using the replica method, that these codes saturate Shannon's coding bound for K?8 when the code rate K/C is finite. We then examine the finite temperature case to asses the use of simulated annealing methods for decoding, study the performance of the finite K case and extend the analysis to accommodate different types of noisy channels. The analogy between statistical physics methods and decoding by belief propagation is also discussed.

Study of Queuing Systems with a Generalized Departure Process

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.

On the Busy Period in One Finite Queue of M/G/1 Type with Inactive Orbit

The paper deals with a single server finite queuing system where the customers, who failed to get service, are temporarily blocked in the orbit of inactive customers. This model and its variants have many applications, especially for optimization of the corresponding models with retrials. We analyze the system in non-stationary regime and, using the discrete transformations method study, the busy period length and the number of successful calls made during it. ACM Computing Classification System (1998): G.3, J.7.

Representations and algorithms for finite-state bisimulations of linear discrete-time control systems

While a large amount of research over the past two decades has focused on discrete abstractions of infinite-state dynamical systems, many structural and algorithmic details of these abstractions remain unknown. To clarify the computational resources needed to perform discrete abstractions, this paper examines the algorithmic properties of an existing method for deriving finite-state systems that are bisimilar to linear discrete-time control systems. We explicitly find the structure of the finite-state system, show that it can be enormous compared to the original linear system, and give conditions to guarantee that the finite-state system is reasonably sized and efficiently computable. Though constructing the finite-state system is generally impractical, we see that special cases could be amenable to satisfiability based verification techniques. ©2009 IEEE.

Queue Length Simulations in a Finite Single-line Queueing System with Repeated Calls

2000 Mathematics Subject Classification: 60K25.

Impact of Residual Transmit RF Impairments on Training-Based MIMO Systems

Radio-frequency (RF) impairments, which intimately exist in wireless communication systems, can severely limit the performance of multiple-input-multiple-output (MIMO) systems. Although we can resort to compensation schemes to mitigate some of these impairments, a certain amount of residual impairments always persists. In this paper, we consider a training-based point-to-point MIMO system with residual transmit RF impairments (RTRI) using spatial multiplexing transmission. Specifically, we derive a new linear channel estimator for the proposed model, and show that RTRI create an estimation error floor in the high signal-to-noise ratio (SNR) regime. Moreover, we derive closed-form expressions for the signal-to-noise-plus-interference ratio (SINR) distributions, along with analytical expressions for the ergodic achievable rates of zero-forcing, maximum ratio combining, and minimum mean-squared error receivers, respectively. In addition, we optimize the ergodic achievable rates with respect to the training sequence length and demonstrate that finite dimensional systems with RTRI generally require more training at high SNRs than those with ideal hardware. Finally, we extend our analysis to large-scale MIMO configurations, and derive deterministic equivalents of the ergodic achievable rates. It is shown that, by deploying large receive antenna arrays, the extra training requirements due to RTRI can be eliminated. In fact, with a sufficiently large number of receive antennas, systems with RTRI may even need less training than systems with ideal hardware.

Accepting splicing systems with permitting and forbidding words

Abstract: In this paper we propose a generalization of the accepting splicingsystems introduced in Mitrana et al. (Theor Comput Sci 411:2414?2422,2010). More precisely, the input word is accepted as soon as a permittingword is obtained provided that no forbidding word has been obtained sofar, otherwise it is rejected. Note that in the new variant of acceptingsplicing system the input word is rejected if either no permitting word isever generated (like in Mitrana et al. in Theor Comput Sci 411:2414?2422,2010) or a forbidding word has been generated and no permitting wordhad been generated before. We investigate the computational power ofthe new variants of accepting splicing systems and the interrelationshipsamong them. We show that the new condition strictly increases thecomputational power of accepting splicing systems. Although there areregular languages that cannot be accepted by any of the splicing systemsconsidered here, the new variants can accept non-regular and even non-context-free languages, a situation that is not very common in the case of(extended) finite splicing systems without additional restrictions. We alsoshow that the smallest class of languages out of the four classes definedby accepting splicing systems is strictly included in the class of context-free languages. Solutions to a few decidability problems are immediatelyderived from the proof of this result.