Noninteracting Fermions in infinite dimensions

Usually, we study the statistical behaviours of noninteracting Fermions in finite (mainly two and three) dimensions. For a fixed number of fermions, the average energy per fermion is calculated in two and in three dimensions and it becomes equal to 50 and 60 per cent of the fermi energy respectively. However, in the higher dimensions this percentage increases as the dimensionality increases and in infinite dimensions it becomes 100 per cent. This is an intersting result, at least pedagogically. Which implies all fermions are moving with Fermi momentum. This result is not yet discussed in standard text books of quantum statistics. In this paper, this fact is discussed and explained. I hope, this article will be helpful for graduate students to study the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010

Quantum Dissipation and Decoherence via Interaction with Low-Dimensional Chaos: a Feynman-Vernon Approach

We study the effects of dissipation and decoherence induced on a harmonic oscillator by the coupling to a chaotic system with two degrees of freedom. Using the Feynman-Vernon approach and treating the chaotic system semiclassically we show that the effects of the low dimensional chaotic environment are in many ways similar to those produced by thermal baths. The classical correlation and response functions play important roles in both classical and quantum formulations. Our results are qualitatively similar to the high temperature regime of the Caldeira-Leggett model.Comment: 31 pages, 4 figure

Statistical Theory of Finite Fermi-Systems Based on the Structure of Chaotic Eigenstates

The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by the interaction between particles. New type of ``microcanonical'' partition function is introduced and expressed in terms of the average shape of eigenstates $F(E_k,E)$ where $E$ is the total energy of the system. This partition function plays the same role as the canonical expression $exp(-E^{(i)}/T)$ for open systems in thermal bath. The approach allows to calculate mean values and non-diagonal matrix elements of different operators. In particular, the following problems have been considered: distribution of occupation numbers and its relevance to the canonical and Fermi-Dirac distributions; criteria of equilibrium and thermalization; thermodynamical equation of state and the meaning of temperature, entropy and heat capacity, increase of effective temperature due to the interaction. The problems of spreading widths and shape of the eigenstates are also studied.Comment: 17 pages in RevTex and 5 Postscript figures. Changes are RevTex format (instead of plain LaTeX), minor misprint corrections plus additional references. To appear in Phys. Rev.

Fluctuating and dissipative dynamics of dark solitons in quasi-condensates

The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long lived soliton trajectories within each ensemble of numerical realizations (S.P. Cockburn {\it et al.}, Phys. Rev. Lett. 104, 174101 (2010)). Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon the dissipative Gross-Pitaevskii model (with the same {\it ab initio} damping). Probing the regime for which $0.8 k_{B}T < \mu < 1.6 k_{B}T$, we find average soliton lifetimes to scale with temperature as $\tau\sim T^{-4}$, in agreement with predictions previously made for the low-temperature regime $k_{B}T\ll\mu$. The model is also shown to capture the experimentally-relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations.Comment: 17 pages, 14 figure

Qualitative Analysis of Partially-observable Markov Decision Processes

We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with omega-regular objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider the qualitative analysis problem: given a POMDP with an omega-regular objective, whether there is an observation-based strategy to achieve the objective with probability~1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis of POMDP s with parity objectives (a canonical form to express omega-regular objectives) and its subclasses. Our contribution consists in establishing several upper and lower bounds that were not known in literature. Second, we present optimal bounds (matching upper and lower bounds) on the memory required by pure and randomized observation-based strategies for the qualitative analysis of POMDP s with parity objectives and its subclasses

Adiabatic Domain Wall Motion and Landau-Lifshitz Damping

Recent theory and measurements of the velocity of current-driven domain walls in magnetic nanowires have re-opened the unresolved question of whether Landau-Lifshitz damping or Gilbert damping provides the more natural description of dissipative magnetization dynamics. In this paper, we argue that (as in the past) experiment cannot distinguish the two, but that Landau-Lifshitz damping nevertheless provides the most physically sensible interpretation of the equation of motion. From this perspective, (i) adiabatic spin-transfer torque dominates the dynamics with small corrections from non-adiabatic effects; (ii) the damping always decreases the magnetic free energy, and (iii) microscopic calculations of damping become consistent with general statistical and thermodynamic considerations

Field Theoretic Description of Ultrarelativistic Electron-Positron Plasmas

Ultrarelativistic electron-positron plasmas can be produced in high-intensity laser fields and play a role in various astrophysical situations. Their properties can be calculated using QED at finite temperature. Here we will use perturbative QED at finite temperature for calculating various important properties, such as the equation of state, dispersion relations of collective plasma modes of photons and electrons, Debye screening, damping rates, mean free paths, collision times, transport coefficients, and particle production rates, of ultrarelativistic electron-positron plasmas. In particular, we will focus on electron-positron plasmas produced with ultra-strong lasers.Comment: 13 pages, 7 figures, 1 table, published versio

Phase transition in the bounded one-dimensional multitrap system

We have previously discussed the diffusion limited problem of the bounded one-dimensional multitrap system where no external fiel is included and pay special attention to the transmission of the diffusing particles through the system of imperfect traps. We discuss here the case in which an external field is included to each trap and find not only the transmission but also the energy associated with the diffusing particles in the presence and absence of such fields. From the energy we find the specific heat $C_h$ and show that for certain values of the parameters associated with the multitrap system it behaves in a manner which is suggestive of phase transition. Moreover, this phase transition is demonstrated not only through the conventional single peak at which the specific heat function is undifferentiable but also through the less frequent phenomenon of double peaks.Comment: 25 pages, 6 PS Figures, there have been introduced many changes including the remove of two figure

A hybrid kinetic Monte Carlo method for simulating silicon films grown by plasma-enhanced chemical vapor deposition

We present a powerful kinetic Monte Carlo (KMC) algorithm that allows one to simulate the growth of nanocrystalline silicon by plasma enhanced chemical vapor deposition (PECVD) for film thicknesses as large as several hundreds of monolayers. Our method combines a standard n-fold KMC algorithm with an efficient Markovian random walk scheme accounting for the surface diffusive processes of the species involved in PECVD. These processes are extremely fast compared to chemical reactions, thus in a brute application of the KMC method more than 99% of the computational time is spent in monitoring them. Our method decouples the treatment of these events from the rest of the reactions in a systematic way, thereby dramatically increasing the efficiency of the corresponding KMC algorithm. It is also making use of a very rich kinetic model which includes 5 species (H, SiH3, SiH2, SiH, and Si 2H5) that participate in 29 reactions. We have applied the new method in simulations of silicon growth under several conditions (in particular, silane fraction in the gas mixture), including those usually realized in actual PECVD technologies. This has allowed us to directly compare against available experimental data for the growth rate, the mesoscale morphology, and the chemical composition of the deposited film as a function of dilution ratio.open1

Principle of Maximum Entropy Applied to Rayleigh-B\'enard Convection

A statistical-mechanical investigation is performed on Rayleigh-B\'enard convection of a dilute classical gas starting from the Boltzmann equation. We first present a microscopic derivation of basic hydrodynamic equations and an expression of entropy appropriate for the convection. This includes an alternative justification for the Oberbeck-Boussinesq approximation. We then calculate entropy change through the convective transition choosing mechanical quantities as independent variables. Above the critical Rayleigh number, the system is found to evolve from the heat-conducting uniform state towards the convective roll state with monotonic increase of entropy on the average. Thus, the principle of maximum entropy proposed for nonequilibrium steady states in a preceding paper is indeed obeyed in this prototype example. The principle also provides a natural explanation for the enhancement of the Nusselt number in convection.Comment: 13 pages, 4 figures; typos corrected; Eq. (66a) corrected to remove a double counting for $k_{\perp}=0$; Figs. 1-4 replace