Derivation of Boltzmann Principle

We present a derivation of Boltzmann principle $S_{B}=k_{B}\ln \mathcal{W}$ based on classical mechanical models of thermodynamics. The argument is based on the heat theorem and can be traced back to the second half of the nineteenth century with the works of Helmholtz and Boltzmann. Despite its simplicity, this argument has remained almost unknown. We present it in a modern, self-contained and accessible form. The approach constitutes an important link between classical mechanics and statistical mechanics

Frustration - how it can be measured

A misfit parameter is used to characterize the degree of frustration of ordered and disordered systems. It measures the increase of the ground-state energy due to frustration in comparison with that of a relevant reference state. The misfit parameter is calculated for various spin-glass models. It allows one to compare these models with each other. The extension of this concept to other combinatorial optimization problems with frustration, e.g. p-state Potts glasses, graph-partitioning problems and coloring problems is given.Comment: 10 pages, 1 table, no figures, uses revtex.st

On the Quasiparticle Description of Lattice QCD Thermodynamics

We propose a novel quasiparticle interpretation of the equation of state of deconfined QCD at finite temperature. Using appropriate thermal masses, we introduce a phenomenological parametrization of the onset of confinement in the vicinity of the predicted phase transition. Lattice results of the energy density, the pressure and the interaction measure of pure SU(3) gauge theory are excellently reproduced. We find a relationship between the thermal energy density of the Yang-Mills vacuum and the chromomagnetic condensate _T. Finally, an extension to QCD with dynamical quarks is discussed. Good agreement with lattice data for 2, 2+1 and 3 flavour QCD is obtained. We also present the QCD equation of state for realistic quark masses.Comment: 20 pages, 10 eps figure

Larmor precession and tunneling time of a relativistic neutral spinning particle through an arbitrary potential barrier

The Larmor precession of a relativistic neutral spin-1/2 particle in a uniform constant magnetic field confined to the region of a one-dimensional arbitrary potential barrier is investigated. The spin precession serves as a clock to measure the time spent by a quantum particle traversing a potential barrier. With the help of general spin coherent state it is explicitly shown that the precession time is equal to the dwell time.Comment: 10 pages, 1 figure. To be published in Phys. Rev. A (01 February 2002

Shopping centre siting and modal choice in Belgium: a destination based analysis

Although modal split is only one of the elements considered in decision-making on new shopping malls, it remarkably often arises in arguments of both proponents and opponents. Today, this is also the case in the debate on the planned development of three major shopping malls in Belgium. Inspired by such debates, the present study focuses on the impact of the location of shopping centres on the travel mode choice of the customers. Our hypothesis is that destination-based variables such as embeddedness in the urban fabric, accessibility and mall size influence the travel mode choice of the visitors. Based on modal split data and location characteristics of seventeen existing shopping centres in Belgium, we develop a model for a more sustainable siting policy. The results show a major influence of the location of the shopping centre in relation to the urban form, and of the size of the mall. Shopping centres that are part of a dense urban fabric, measured through population density, are less car dependent. Smaller sites will attract more cyclists and pedestrians. Interestingly, our results deviate significantly from the figures that have been put forward in public debates on the shopping mall issue in Belgium

Time decay of the remanent magnetization in the ±J\pm J spin glass model at T=0

Using the zero-temperature Metropolis dynamics, the time decay of the remanent magnetization in the $\pm J$ Edward-Anderson spin glass model with a uniform random distribution of ferromagnetic and antiferromagnetic interactions has been investigated. Starting from the saturation, the magnetization per spin $m$ reveals a slow decrease with time, which can be approximated by a power law:$m(t)=m_{\infty}+ ({t\over a_{0}})^{a_{1}}$, $a_{1} < 0$. Moreover, its relaxation does not lead it into one of the ground states, and therefore the system is trapped in metastable isoenergetic microstates remaining magnetized. Such behaviour is discussed in terms of a random walk the system performs on its available configuration space.Comment: 9 pages, 3 figure

Microscopic Treatment of Binary Interactions in the Non-Equilibrium Dynamics of Partially Bose-condensed Trapped Gases

In this paper we use microscopic arguments to derive a nonlinear Schr\"{o}dinger equation for trapped Bose-condensed gases. This is made possible by considering the equations of motion of various anomalous averages. The resulting equation explicitly includes the effect of repeated binary interactions (in particular ladders) between the atoms. Moreover, under the conditions that dressing of the intermediate states of a collision can be ignored, this equation is shown to reduce to the conventional Gross-Pitaevskii equation in the pseudopotential limit. Extending the treatment, we show first how the occupation of excited (bare particle) states affects the collisions, and thus obtain the many-body T-matrix approximation in a trap. In addition, we discuss how the bare particle many-body T-matrix gets dressed by mean fields due to condensed and excited atoms. We conclude that the most commonly used version of the Gross-Pitaevskii equation can only be put on a microscopic basis for a restrictive range of conditions. For partial condensation, we need to take account of interactions between condensed and excited atoms, which, in a consistent formulation, should also be expressed in terms of the many-body T-matrix. This can be achieved by considering fluctuations around the condensate mean field beyond those included in the conventional finite temperature mean field, i.e. Hartree-Fock-Bogoliubov (HFB), theory.Comment: Resolved some problems with printing of figure

Time in Quantum Mechanics and Quantum Field Theory

W. Pauli pointed out that the existence of a self-adjoint time operator is incompatible with the semibounded character of the Hamiltonian spectrum. As a result, people have been arguing a lot about the time-energy uncertainty relation and other related issues. In this article, we show in details that Pauli's definition of time operator is erroneous in several respects.Comment: 20 page

Action Principle and Algebraic Approach to Gauge Transformations in Gauge Theories

The action principle is used to derive, by an entirely algebraic approach, gauge transformations of the full vacuum-to-vacuum transition amplitude (generating functional) from the Coulomb gauge to arbitrary covariant gauges and in turn to the celebrated Fock-Schwinger (FS) gauge for the abelian (QED) gauge theory without recourse to path integrals or to commutation rules and without making use of delta functionals. The interest in the FS gauge, in particular, is that it leads to Faddeev-Popov ghosts-free non-abelian gauge theories. This method is expected to be applicable to non-abelian gauge theories including supersymmetric ones.Comment: LaTeX, 12 pages, Corrected typo