A semiclassical theory of quantum noise in open chaotic systems

We consider the quantum evolution of classically chaotic systems in contact with surroundings. Based on $\hbar$-scaling of an equation for time evolution of the Wigner's quasi-probability distribution function in presence of dissipation and thermal diffusion we derive a semiclassical equation for quantum fluctuations. This identifies an early regime of evolution dominated by fluctuations in the curvature of the potential due to classical chaos and dissipation. A stochastic treatment of this classical fluctuations leads us to a Fokker-Planck equation which is reminiscent of Kramers' equation for thermally activated processes. This reveals an interplay of three aspects of evolution of quantum noise in weakly dissipative open systems; the reversible Liouville flow, the irreversible chaotic diffusion which is characteristic of the system itself, and irreversible dissipation induced by the external reservoir. It has been demonstrated that in the dissipation-free case a competition between Liouville flow in the contracting direction of phase space and chaotic diffusion sets a critical width in the Wigner function for quantum fluctuations. We also show how the initial quantum noise gets amplified by classical chaos and ultimately equilibrated under the influence of dissipation. We establish that there exists a critical limit to the expansion of phase space. The limit is determined by chaotic diffusion and dissipation. Making use of appropriate quantum-classical correspondence we verify the semiclassical analysis by the fully quantum simulation in a chaotic quartic oscillator.Comment: Plain Latex, 27 pages, 6 ps figure, To appear in Physica

Low-Mass Dileptons at the CERN-SpS: Evidence for Chiral Restoration?

Using a rather complete description of the in-medium $\rho$ spectral function - being constrained by various independent experimental information - we calculate pertinent dilepton production rates from hot and dense hadronic matter. The strong broadening of the $\rho$ resonance entails a reminiscence to perturbative $q\bar q$ annihilation rates in the vicinity of the phase boundary. The application to dilepton observables in Pb(158AGeV)+Au collisions - incorporating recent information on the hadro-chemical composition at CERN-SpS energies - essentially supports the broadening scenario. Possible implications for the nature of chiral symmetry restoration are outlined.Comment: 6 pages ReVTeX including 5 eps-figure

Nonequilibrium fluctuation induced escape from a metastable state

Based on a simple microscopic model where the bath is in a non-equilibrium state we study the escape from a metastable state in the over-damped limit. Making use of Fokker-Planck-Smoluchowski description we derive the time dependent escape rate in the non-stationary regime in closed analytical form which brings on to fore a strong non-exponential kinetic of the system mode.Comment: 4 pages, no figures, EPJ class file include

Analytical and numerical investigation of escape rate for a noise driven bath

We consider a system-reservoir model where the reservoir is modulated by an external noise. Both the internal noise of the reservoir and the external noise are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. Based on a relation between the dissipation of the system and the response function of the reservoir driven by external noise we numerically examine the model using a full bistable potential to show that one can recover the turn-over features of the usual Kramers' dynamics when the external noise modulates the reservoir rather than the system directly. We derive the generalized Kramers' rate for this nonequilibrium open system. The theoretical results are verified by numerical simulation.Comment: Revtex, 25 pages, 5 figures. To appear in Phys. Rev.

MacWilliams Identities for mm-tuple Weight Enumerators

Since MacWilliams proved the original identity relating the Hamming weight enumerator of a linear code to the weight enumerator of its dual code there have been many different generalizations, leading to the development of $m$-tuple support enumerators. We prove a generalization of theorems of Britz and of Ray-Chaudhuri and Siap, which build on earlier work of Kl{\o}ve, Shiromoto, Wan, and others. We then give illustrations of these $m$-tuple weight enumerators.Comment: 17 pages. Accepted to SIAM Journal on Discrete Mathematic

Use of expert system software for life monitoring of power plant components

Life management of primarily high temperature components in power/process plants is a very involved task. Various components in a running power plant are subjected to different loading cycles, temperature, pressure and environmental conditions. The dependence of running power plant on various components as well as interdependence of various components on each other adds to the enormity of the task and requires different maintenance/ repair/ replacement schedules. A systematic and smooth functioning of the plant necessitates a step-by-step analysisfor each components based on its operating parameters, material. In present days, various commercial softwares are used for life monitoring, deciding different schedules in these plants. In the present paper an effort has been made to show the use ofALIAS (Advanced Life Assessment System) and its effectiveness in handling problems related to plant life monitoring, risk analysis, preparing maintenance/repair/replacement schedules

Quantum theory of dissipation of a harmonic oscillator coupled to a nonequilibrium bath; Wigner-Weisskopf decay and physical spectra

We extend the quantum theory of dissipation in the context of system-reservoir model, where the reservoir in question is kept in a nonequilibrium condition. Based on a systematic separation of time scales involved in the dynamics, appropriate generalizations of the fluctuation-dissipation and Einstein's relations have been pointed out. We show that the Wigner-Weisskopf decay of the system mode results in a rate constant which depending on the relaxation of nonequilibrium bath is dynamically modified. We also calculate the time-dependent spectra of a cavity mode with a suitable gain when the cavity is kept in contact with a nonequilibrium bath.Comment: Plain Latex, 28 pages, 2 PS figure

Time dependent current in a nonstationary environment: A microscopic approach

Based on a microscopic system reservoir model,where the associated bath is not in thermal equilibrium, we simulate the nonstationary Langevin dynamics and obtained the generalized nonstationary fluctuation dissipation relation (FDR) which asymptotically reduces to the traditional form. Our Langevin dynamics incorporates non-Markovian process also, the origin of which lies on the decaying term of the nonstationary FDR. We then follow the stochastic dynamics of the Langevin particle based on the Fokker-Planck-Smoluchowski description, in ratchet potential to obtain the steady and time dependent current in an analytic form. We also examine the influence of initial excitation and subsequent relaxation of bath modes on the transport of the Langevin particle to show that the nonequilibrium nature of the bath leads to both strong non-exponential dynamics as well as nonstationary current.Comment: 10 pages, RevTex4, references updated, final version to appear in Journal of Mathematical Physic