M. Revzen

Repulsive Casimir forces

We discuss repulsive Casimir forces between dielectric materials with nontrivial magnetic susceptibility. It is shown that considerations based on the naive pairwise summation of van der Waals and Casimir-Polder forces may not only give an incorrect estimate of the magnitude of the total Casimir force but even the wrong sign of the force when materials with high dielectric and magnetic responses are involved. Indeed repulsive Casimir forces may be found in a large range of parameters, and we suggest that the effect may be realized in known materials. The phenomenon of repulsive Casimir forces may be of importance both for experimental study and for nanomachinery applications.

Thermal coherent states

Abstract The formalism of thermo field dynamics is used to define a thermal coherent state, and thus calculate some correlation functions. The relation of the thermal coherent state so defined to earlier definitions is briefly discussed.

Relation Between Quantum and Thermal Fluctuations

Abstract A relation between quantum and thermal fluctuations, called the generalized uncertainty relation, is derived and discussed. It is given in the terminology of thermo field dynamics. The relation enables us to separate the purely thermal fluctuation from the total fluctuation.

Casimir effect: The Classical limit

Abstract We analyze the high temperature (or classical) limit of the Casimir effect. A useful quantity which arises naturally in our discussion is the “relative Casimir energy,” which we define for a configuration of disjoint conducting boundaries of arbitrary shapes, as the difference of Casimir energies between the given configuration and a configuration with the same boundaries infinitely far apart. Using path integration techniques, we show that the relative Casimir energy vanishes exponentially fast in temperature. This is consistent with a simple physical argument based on Kirchhoffs law. As a result the “relative Casimir entropy,” which we define in an obviously analogous manner, tends, in the classical limit, to a finite asymptotic value which depends only on the geometry of the boundaries. Thus the Casimir force between disjoint pieces of the boundary, in the classical limit, is entropy driven and is governed by a dimensionless number characterizing the geometry of the cavity. Contributions to the Casimir thermodynamical quantities due to each individual connected component of the boundary exhibit logarithmic deviations in temperature from the behavior just described. These logarithmic deviations seem to arise due to our difficulty to separate the Casimir energy (and the other thermodynamical quantities) from the “electromagnetic” self-energy of each of the connected components of the boundary in a well defined manner. Our approach to the Casimir effect is not to impose sharp boundary conditions on the fluctuating field, but rather take into consideration its interaction with the plasma of “charge carriers” in the boundary, with the plasma frequency playing the role of a physical UV cutoff. This also allows us to analyze deviations from a perfect conductor behavior.

Functional Integrals for Many‐Boson Systems

We express the grand canonical partition function (GCPF) for a system of interacting bosons as a functional integral over one complex function. Our derivation is based on the so‐called coherent‐state representation [R. J. Glauber, Phys. Rev. 136, 2766 (1963)]. We show how to extract the perturbative expansion of the GCPF and the various Greens functions from our functional‐integral representation and we indicate the relevance of our formalism to the theory of superfluidity.

Maximally entangled states via mutual unbiased collective bases

Relative and center-of-mass coordinates are used to generalize mutually unbiased bases (MUB) and define mutually unbiased collective bases (MUCB). Maximally entangled states are given as product states in the collective variables. These states are analyzed in terms of the Wigner representative function of the states and shown to display a discontinuous attribute of the entanglement. Finite Hilbert space dimensionality collective coordinates are introduced and provide a framework for the analysis.

Coherent and thermal coherent state

The characterization of coherent states as the quantum states that split into two uncorrelated beams is considered. The characterization leads to the study of coherent states at finite temperature—thermal coherent states (TCS’s). These TCS’s are defined within the formalism of thermo field dynamics (TFD). TFD allows a generalization of the uncertainty relation that accounts for both thermal and quantum fluctuations. The TCS is shown to be a minimal state for the generalized uncertainty relation.

Maximal entanglement, collective coordinates and tracking the King

Maximal entangled states provide a basis to two d-dimensional particles in Hilbert space, d = prime � 2. The maximally entangled states forming this basis are uniquely related to product states in the collective, center of mass and relative, coordinates. These states are associated (underpinned) with lines of finite geometry whose constituent points are associated with product states carrying mutual unbiased bases labels. This representation is shown to be convenient for the study of the mean King problem and a variant thereof, termed ‘tracking the King’, which proves to be a novel quantum communication channel. The main topics and notations used are reviewed in an attempt to keep the paper self contained.

Casimir effect for conducting and permeable plates at finite temperature

The effect of temperature for the Casimir force is calculated for a system of two different parallel plates, one being a perfect conductor and the other infinitely permeable. The analysis of high and low temperature is developed via the behaviour of the Casimir free energy and entropy. In particular, in the case of high-temperature limit, it is shown that the repulsive character of the Casimir force between the plates is purely entropic.

Casimir energy of a dilute dielectric ball with uniform velocity of light at finite temperature

The Casimir energy, free energy and Casimir force are evaluated, at arbitrary finite temperature, for a dilute dielectric ball with uniform velocity of light inside the ball and in the surrounding medium. In particular, we investigate the classical limit at high temperature. The Casimir force found is repulsive, as in previous calculations.