A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix

In time reversal symmetric systems with half integral spins (or more concretely, systems with an antiunitary symmetry that squares to -1 and commutes with the Hamiltonian) the transmission eigenvalues of the scattering matrix come in pairs. We present a proof of this fact that is valid both for even and odd number of modes and relies solely on the antisymmetry of the scattering matrix imposed by time reversal symmetry.Comment: 2 page

Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics

It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way, the ergodic theorem and the H-theorem are formulated and proven (without "assumptions of disorder"), followed by a discussion of the physical meaning of the mathematical conditions characterizing their domain of validity.Comment: English translation by Roderich Tumulka of J. von Neumann: Beweis des Ergodensatzes und des H-Theorems. 41 pages LaTeX, no figures; v2: typos corrected. See also the accompanying commentary by S. Goldstein, J. L. Lebowitz, R. Tumulka, N. Zanghi, arXiv:1003.212

A model for the condensation of a dusty plasma

A model for the condensation of a dusty plasma is constructed by considering the spherical shielding layers surrounding a dust grain test particle. The collisionless region less than a collision mean free path from the test particle is shown to separate into three concentric layers, each having distinct physics. The method of matched asymptotic expansions is invoked at the interfaces between these layers and provides equations which determine the radii of the interfaces. Despite being much smaller than the Wigner-Seitz radius, the dust Debye length is found to be physically significant because it gives the scale length of a precipitous cut-off of the shielded electrostatic potential at the interface between the second and third layers. Condensation is predicted to occur when the ratio of this cut-off radius to the Wigner-Seitz radius exceeds unity and this prediction is shown to be in good agreement with experiments.Comment: 29 pages, 4 figures, 1 table, to appear in Physics of Plasmas. Manuscript revised on May 1, 2004 to take into account accuracy of Mie scattering dust grain diameter measurement method used in Hayashi/Tachibana experiment. Model now compared to Hayashi/Tachibana experiment using measured rather than fitted dust grain diameter and using higher estimate for Te/Ti (two new references added; revisions made to two paragraphs in Sec. VII, to bottom plot of Fig. 3, and to right-most column of Table 1

What is tested when experiments test that quantum dynamics is linear

Experiments that look for nonlinear quantum dynamics test the fundamental premise of physics that one of two separate systems can influence the physical behavior of the other only if there is a force between them, an interaction that involves momentum and energy. The premise is tested because it is the assumption of a proof that quantum dynamics must be linear. Here variations of a familiar example are used to show how results of nonlinear dynamics in one system can depend on correlations with the other. Effects of one system on the other, influence without interaction between separate systems, not previously considered possible, would be expected with nonlinear quantum dynamics. Whether it is possible or not is subject to experimental tests together with the linearity of quantum dynamics. Concluding comments and questions consider directions our thinking might take in response to this surprising unprecedented situation.Comment: 14 pages, Title changed, sentences adde

Dark matter: A spin one half fermion field with mass dimension one?

We report an unexpected theoretical discovery of a spin one half matter field with mass dimension one. It is based on a complete set of eigenspinors of the charge conjugation operator. Due to its unusual properties with respect to charge conjugation and parity it belongs to a non standard Wigner class. Consequently, the theory exhibits non-locality with (CPT)^2 = - I. Its dominant interaction with known forms of matter is via Higgs, and with gravity. This aspect leads us to contemplate it as a first-principle candidate for dark matter.Comment: 5 pages, RevTex, v2: slightly extended discussion, new refs. and note adde

Wigner-Araki-Yanase theorem on Distinguishability

The presence of an additive conserved quantity imposes a limitation on the measurement process. According to the Wigner-Araki-Yanase theorem, the perfect repeatability and the distinguishability on the apparatus cannot be attained simultaneously. Instead of the repeatability, in this paper, the distinguishability on both systems is examined. We derive a trade-off inequality between the distinguishability of the final states on the system and the one on the apparatus. The inequality shows that the perfect distinguishability of both systems cannot be attained simultaneously.Comment: To be published in Phys.Rev.

Excitations and Quantum Fluctuations in Site Diluted Two-Dimensional Antiferromagnets

We study the effect of site dilution and quantum fluctuations in an antiferromagnetic spin system on a square lattice within the linear spin-wave approximation. By performing numerical diagonalization in real space and finite-size scaling, we characterize the nature of the low-energy spin excitations for different dilution fractions up to the classical percolation threshold. We find nontrivial signatures of fractonlike excitations at high frequencies. Our simulations also confirm the existence of an upper bound for the amount of quantum fluctuations in the ground state of the system, leading to the persistence of long-range order up to the percolation threshold. This result is in agreement with recent neutron-scattering experimental data and quantum Monte Carlo numerical calculations. We also show that the absence of a quantum critical point below the classical percolation threshold holds for a large class of systems whose Hamiltonians can be mapped onto a system of coupled noninteracting massless bosons.Comment: RevTex 4, 16 pages, 8 EPS figures, typos corrected, data from Ref. 9 added, few minor changes in the text, to appear in Phys. Rev.

Instabilities in complex mixtures with a large number of components

Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterise all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the conditions under which the mixtures phase separate. The approach approximates the matrix of second virial coefficients of the mixture by a random matrix, and determines the stability of the mixture from the spectrum of such random matrices.Comment: 4 pages, uses RevTeX 4.