Vibrating quantum billiards on Riemannian manifolds

Quantum billiards provide an excellent forum for the analysis of quantum chaos. Toward this end, we consider quantum billiards with time-varying surfaces, which provide an important example of quantum chaos that does not require the semiclassical ($\hbar \longrightarrow 0$) or high quantum-number limits. We analyze vibrating quantum billiards using the framework of Riemannian geometry. First, we derive a theorem detailing necessary conditions for the existence of chaos in vibrating quantum billiards on Riemannian manifolds. Numerical observations suggest that these conditions are also sufficient. We prove the aforementioned theorem in full generality for one degree-of-freedom boundary vibrations and briefly discuss a generalization to billiards with two or more degrees-of-vibrations. The requisite conditions are direct consequences of the separability of the Helmholtz equation in a given orthogonal coordinate frame, and they arise from orthogonality relations satisfied by solutions of the Helmholtz equation. We then state and prove a second theorem that provides a general form for the coupled ordinary differential equations that describe quantum billiards with one degree-of-vibration boundaries. This set of equations may be used to illustrate KAM theory and also provides a simple example of semiquantum chaos. Moreover, vibrating quantum billiards may be used as models for quantum-well nanostructures, so this study has both theoretical and practical applications.Comment: 23 pages, 6 figures, a few typos corrected. To appear in International Journal of Bifurcation and Chaos (9/01

Excess radiation from the large planets

An alternative model is proposed for the excess radiation emitted by the larger planets, each with a liquid metallic hydrogen annular domain about a central core of ice and rocks. This model is based on the mutual attraction between elements of an aggregate of charged bosons in a charge-neutralizing background, in equilibrium at very high pressure, and the property that spin-1 deuterons are bosons. Assuming valid parameters for Jupiter, it is derived that the deuteron density in Saturn is approximately equal to that in Jupiter and that particles emitted in reactions in the liquid metal domain are thermalized in the liquid hydrogen domain, resulting in infrared radiation, in accord with observed values. With corroborating properties of Neptune, it is proposed that this planet likewise contains a spherical shell of liquid metallic hydrogen outside and close to its rocky core. Whereas data are insufficient to support degenerate fusion, the known magnetic moment of Neptune is found to be consistent with positive charge components rotating in the frame of the liquid metallic hydrogen fluid with current density approximate to 8:4 x 10(-6) Am-2. It is proposed that the related coupling between current and magnetic field is supported by a dynamo effect. A brief description is included describing the influence of convective storms in the large planets

Minimum of η/s\eta/s and the phase transition of the Linear Sigma Model in the large-N limit

We reexamine the possibility of employing the viscosity over entropy density ratio as a diagnostic tool to identify a phase transition in hadron physics to the strongly coupled quark-gluon plasma and other circumstances where direct measurement of the order parameter or the free energy may be difficult. It has been conjectured that the minimum of eta/s does indeed occur at the phase transition. We now make a careful assessment in a controled theoretical framework, the Linear Sigma Model at large-N, and indeed find that the minimum of eta/s occurs near the second order phase transition of the model due to the rapid variation of the order parameter (here the sigma vacuum expectation value) at a temperature slightly smaller than the critical one.Comment: 22 pages, 19 figures, v2, some references and several figures added, typos corrected and certain arguments clarified, revised for PR

A Model for the Diffuse γ-Ray Spectrum

A model is proposed to describe the observed shelf in the cosmic diffuse radiation spectrum just above 1 MeV. This model is based on induced positronium annihilation, which at incident photon energy 2 mc^2 gives rise to enhancement of the radiative field. It is proposed that this amplification may occur in double radio sources or other accreting objects. Recent observation of γ-ray line emission from the double radio sources SS 433 at 1.2 and 1.5 MeV is in good agreement with the proposed model

Acoustic Analog to Quantum Mechanical Level Splitting

A simple physical system is discussed that mirrors the quantum mechanical infinite square well with a central delta well potential. The physical realization consists of a continuous sound wave traveling in a pair of tubes separated by an adjustable diaphragm. The equivalence between the quantum system and the acoustic system is explored. The analytic solution to the quantum system exhibits level splitting as does the acoustic system

Calculating and visualizing the density of states for simple quantum mechanical systems

We present a graphical approach to understanding the degeneracy, density of states, and cumulative state number for some simple quantum systems. By taking advantage of basic computing operations, we define a straightforward procedure for determining the relationship between discrete quantum energy levels and the corresponding density of states and cumulative level number. The density of states for a particle in a rigid box of various shapes and dimensions is examined and graphed. It is seen that the dimension of the box, rather than its shape, is the most important feature. In addition, we look at the density of states for a multi-particle system of identical bosons built on the single-particle spectra of those boxes. A simple model is used to explain how the N-particle density of states arises from the single particle system it is based on

Classical diamagnetism, magnetic interaction energies, and repulsive forces in magnetized plasmas

The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position dependent interactions but this is not required by classical physics. Since the work of Darwin in 1920 it has been known that the magnetism due to classical charged point particles can only be described by allowing velocity dependent interactions in the Lagrangian. Legendre transformation to an approximate Hamiltonian can give an estimate of the Darwin diamagnetism for a system of charged point particles. Comparison with experiment, however, requires knowledge of the number of classically behaving electrons in the sample. A new repulsive effective many-body force, which should be relevant in plasmas, is predicted by the Hamiltonian.Comment: added references, revise

Introductory quantum mechanics

Careful and detailed explanations of challenging concepts in Introductory Quantum Mechanics, Fourth Edition, and comprehensive and up-to-date coverage, continue to set the standard in physics education. In the new edition of this best-selling quantum mechanics book, a new chapter on the revolutionary topic of of quantum computing (not currently covered in any other book at this level) and thorough updates to the rest of the book bring it up to date