Comment on "Classical interventions in quantum systems II. Relativistic invariance"

In a recent paper [Phys. Rev. A 61, 022117 (2000)], quant-ph/9906034, A. Peres argued that quantum mechanics is consistent with special relativity by proposing that the operators that describe time evolution do not need to transform covariantly, although the measurable quantities need to transform covariantly. We discuss the weaknesses of this proposal.Comment: 4 pages, to appear in Phys. Rev.

Infinite matrices may violate the associative law

The momentum operator for a particle in a box is represented by an infinite order Hermitian matrix $P$. Its square $P^2$ is well defined (and diagonal), but its cube $P^3$ is ill defined, because $P P^2\neq P^2 P$. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.Comment: final version in J. Phys. A28 (1995) 1765-177

Revising Limits on Neutrino-Majoron Couplings

Any theory that have a global spontaneously broken symmetry will imply the existence of very light neutral bosons or massless bosons (sometimes called Majorons). For most of these models we have neutrino-Majoron couplings, that appear as additional branching ratios in decays of mesons and leptons. Here we present an updated limits on the couplings between the electron, muon and tau neutrinos and Majorons. For such we analyze the possible effects of Majoron emission in both meson and lepton decays. In the latter we also include an analysis of the muon decay spectrum. Our results are $|g_{e\alpha}|^{2}<5.5x10^{-6}$, $|g_{\mu\alpha}|^{2}<4.5x10^{-5}$ and $|g_{\tau\alpha}|^{2}<5.5x10^{-2}$ at 90 % C. L., where $\alpha=e,\mu,\tau$.Comment: 12 pages, 5 figure

Spacings and pair correlations for finite Bernoulli convolutions

We consider finite Bernoulli convolutions with a parameter $1/2 < r < 1$ supported on a discrete point set, generically of size $2^N$. These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure $\nu_r$, as $N$ tends to infinity. Numerical evidence suggests that for a generic $r$, the distribution of spacings between appropriately rescaled points is Poissonian. We obtain some partial results in this direction; for instance, we show that, on average, the pair correlations do not exhibit attraction or repulsion in the limit. On the other hand, for certain algebraic $r$ the behavior is totally different.Comment: 17 pages, 6 figure

Quantum mechanics explained

The physical motivation for the mathematical formalism of quantum mechanics is made clear and compelling by starting from an obvious fact - essentially, the stability of matter - and inquiring into its preconditions: what does it take to make this fact possible?Comment: 29 pages, 5 figures. v2: revised in response to referee comment

Bell's inequality with Dirac particles

We study Bell's inequality using the Bell states constructed from four component Dirac spinors. Spin operator is related to the Pauli-Lubanski pseudo vector which is relativistic invariant operator. By using Lorentz transformation, in both Bell states and spin operator, we obtain an observer independent Bell's inequality, so that it is maximally violated as long as it is violated maximally in the rest frame.Comment: 7 pages. arXiv admin note: text overlap with arXiv:quant-ph/0308156 by other author

Charge and Spin Transport in the One-dimensional Hubbard Model

In this paper we study the charge and spin currents transported by the elementary excitations of the one-dimensional Hubbard model. The corresponding current spectra are obtained by both analytic methods and numerical solution of the Bethe-ansatz equations. For the case of half-filling, we find that the spin-triplet excitations carry spin but no charge, while charge $\eta$-spin triplet excitations carry charge but no spin, and both spin-singlet and charge $\eta$-spin-singlet excitations carry neither spin nor charge currents.Comment: 24 pages, 14 figure