Cost of s-fold Decisions in Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics

The exact forms of the degenerate Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropy functions, derived by Boltzmann's principle without the Stirling approximation (Niven, Physics Letters A, 342(4) (2005) 286), are further examined. Firstly, an apparent paradox in quantisation effects is resolved using the Laplace-Jaynes interpretation of probability. The energy cost of learning that a system, distributed over s equiprobable states, is in one such state (an s-fold decision) is then calculated for each statistic. The analysis confirms that the cost depends on one's knowledge of the number of entities N and (for BE and FD statistics) the degeneracy, extending the findings of Niven (2005).Comment: 7 figures; 5 pages; REVTEX / TeXShop; paper from 2005 NEXT-Sigma-Ph

Electromagnetic energy and energy flows in photonic crystals made of arrays of parallel dielectric cylinders

We consider the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel dielectric cylinders embedded a uniform medium. The frequency band structure is computed using the standard plane-wave expansion method, and the corresponding eigne-modes are obtained subsequently. The optical flows of the eigen-modes are calculated by a direct computation approach, and several averaging schemes of the energy current are discussed. The results are compared to those obtained by the usual approach that employs the group velocity calculation. We consider both the case in which the frequency lies within passing band and the situation in which the frequency is in the range of a partial bandgap. The agreements and discrepancies between various averaging schemes and the group velocity approach are discussed in detail. The results indicate the group velocity can be obtained by appropriate averaging method.Comment: 23 pages, 5 figure

Causality in Propagation of a Pulse in a Nonlinear Dispersive Medium

We investigate the causal propagation of the pulse through dispersive media by very precise numerical solution of the coupled Maxwell-Bloch equations without any approximations about the strength of the input field. We study full nonlinear behavior of the pulse propagation through solid state media like ruby and alexandrite. We have demonstrated that the information carried by the discontinuity, {\it i.e}, front of the pulse, moves inside the media with velocity $c$ even though the peak of the pulse can travel either with sub-luminal or with super-luminal velocity. We extend the argument of Levi-Civita to prove that the discontinuity would travel with velocity $c$ even in a nonlinear medium.Comment: 4 pages, 4 figures, 2 table

Power loss and electromagnetic energy density in a dispersive metamaterial medium

The power loss and electromagnetic energy density of a metamaterial consisting of arrays of wires and split-ring resonators (SRRs) are investigated. We show that a field energy density formula can be derived consistently from both the electrodynamic (ED) approach and the equivalent circuit (EC) approach. The derivations are based on the knowledge of the dynamical equations of the electric and magnetic dipoles in the medium and the correct form of the power loss. We discuss the role of power loss in determining the form of energy density and explain why the power loss should be identified first in the ED derivation. When the power loss is negligible and the field is harmonic, our energy density formula reduces to the result of Landau's classical formula. For the general case with finite power loss, our investigation resolves the apparent contradiction between the previous results derived by the EC and ED approaches.Comment: 10 pages, 1 figure, Submitted to Phys. Rev.

Energy Requirement of Control: Comments on Szilard's Engine and Maxwell's Demon

In mathematical physical analyses of Szilard's engine and Maxwell's demon, a general assumption (explicit or implicit) is that one can neglect the energy needed for relocating the piston in Szilard's engine and for driving the trap door in Maxwell's demon. If this basic assumption is wrong, then the conclusions of a vast literature on the implications of the Second Law of Thermodynamics and of Landauer's erasure theorem are incorrect too. Our analyses of the fundamental information physical aspects of various type of control within Szilard's engine and Maxwell's demon indicate that the entropy production due to the necessary generation of information yield much greater energy dissipation than the energy Szilard's engine is able to produce even if all sources of dissipation in the rest of these demons (due to measurement, decision, memory, etc) are neglected.Comment: New, simpler and more fundamental approach utilizing the physical meaning of control-information and the related entropy production. Criticism of recent experiments adde

Semiclassical approximation with zero velocity trajectories

We present a new semiclassical method that yields an approximation to the quantum mechanical wavefunction at a fixed, predetermined position. In the approach, a hierarchy of ODEs are solved along a trajectory with zero velocity. The new approximation is local, both literally and from a quantum mechanical point of view, in the sense that neighboring trajectories do not communicate with each other. The approach is readily extended to imaginary time propagation and is particularly useful for the calculation of quantities where only local information is required. We present two applications: the calculation of tunneling probabilities and the calculation of low energy eigenvalues. In both applications we obtain excellent agrement with the exact quantum mechanics, with a single trajectory propagation.Comment: 16 pages, 7 figure

The refractive index and wave vector in passive or active media

Materials that exhibit loss or gain have a complex valued refractive index $n$. Nevertheless, when considering the propagation of optical pulses, using a complex $n$ is generally inconvenient -- hence the standard choice of real-valued refractive index, i.e. n_s = \RealPart (\sqrt{n^2}). However, an analysis of pulse propagation based on the second order wave equation shows that use of $n_s$ results in a wave vector \emph{different} to that actually exhibited by the propagating pulse. In contrast, an alternative definition n_c = \sqrt{\RealPart (n^2)}, always correctly provides the wave vector of the pulse. Although for small loss the difference between the two is negligible, in other cases it is significant; it follows that phase and group velocities are also altered. This result has implications for the description of pulse propagation in near resonant situations, such as those typical of metamaterials with negative (or otherwise exotic) refractive indices.Comment: Phys. Rev. A, to appear (2009

On rational boundary conditions for higher-order long-wave models

Higher-order corrections to classical long-wave theories enable simple and efficient modelling of the onset of wave dispersion and size effects produced by underlying micro-structure. Since such models feature higher spatial derivatives, one needs to formulate additional boundary conditions when confined to bounded domains. There is a certain controversy associated with these boundary conditions, because it does not seem possible to justify their choice by purely physical considerations. In this paper an asymptotic model for onedimensional chain of particles is chosen as an exemplary higher-order theory. We demonstrate how the presence of higher-order derivative terms results in the existence of non-physical “extraneous” boundary layer-type solutions and argue that the additional boundary conditions should generally be formulated to eliminate the contribution of these boundary layers into the averaged solution. Several new methods of deriving additional boundary conditions are presented for essential boundary. The results are illustrated by numerical examples featuring comparisons with an exact solution for the finite chain