Quasiclassical Equations of Motion for Nonlinear Brownian Systems

Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description. This is done explicitly for the case of a system interacting with a ``bath'' of harmonic oscillators whose individual motions are neglected. The results are compared to the equations derived from the purely classical theory. The case of linear interactions is treated exactly, and nonlinear interactions are compared using classical and quantum perturbation theory.Comment: 24 pages, CALT-68-1848 (RevTeX 2.0 macros

Quasiclassical Coarse Graining and Thermodynamic Entropy

Our everyday descriptions of the universe are highly coarse-grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited powers of observation and computation. But in the modern quantum mechanics of closed systems, some measure of coarse graining is inescapable because there are no non-trivial, probabilistic, fine-grained descriptions. This essay explores the consequences of that fact. Quantum theory allows for various coarse-grained descriptions some of which are mutually incompatible. For most purposes, however, we are interested in the small subset of ``quasiclassical descriptions'' defined by ranges of values of averages over small volumes of densities of conserved quantities such as energy and momentum and approximately conserved quantities such as baryon number. The near-conservation of these quasiclassical quantities results in approximate decoherence, predictability, and local equilibrium, leading to closed sets of equations of motion. In any description, information is sacrificed through the coarse graining that yields decoherence and gives rise to probabilities for histories. In quasiclassical descriptions, further information is sacrificed in exhibiting the emergent regularities summarized by classical equations of motion. An appropriate entropy measures the loss of information. For a ``quasiclassical realm'' this is connected with the usual thermodynamic entropy as obtained from statistical mechanics. It was low for the initial state of our universe and has been increasing since.Comment: 17 pages, 0 figures, revtex4, Dedicated to Rafael Sorkin on his 60th birthday, minor correction

Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive

Phase space can be constructed for $N$ equal and distinguishable subsystems that could be (probabilistically) either {\it weakly} (or {\it "locally"}) correlated (e.g., independent, i.e., uncorrelated), or {\it strongly} (or {\it globally}) correlated. If they are locally correlated, we expect the Boltzmann-Gibbs entropy $S_{BG} \equiv -k \sum_i p_i \ln p_i$ to be {\it extensive}, i.e., $S_{BG}(N)\propto N$ for $N \to\infty$. In particular, if they are independent, $S_{BG}$ is {\it strictly additive}, i.e., $S_{BG}(N)=N S_{BG}(1), \forall N$. However, if the subsystems are globally correlated, we expect, for a vast class of systems, the entropy $S_q\equiv k [1- \sum_i p_i^q]/(q-1)$ (with $S_1=S_{BG}$) for some special value of $q\ne1$ to be the one which extensive (i.e., $S_q(N)\propto N$ for $N \to\infty$).Comment: 15 pages, including 9 figures and 8 Tables. The new version is considerably enlarged with regard to the previous ones. New examples and new references have been include

A Note on the Topology of Space-time in Special Relativity

We show that a topology can be defined in the four dimensional space-time of special relativity so as to obtain a topological semigroup for time. The Minkowski 4-vector character of space-time elements as well as the key properties of special relativity are still the same as in the standard theory. However, the new topological structure allows the possibility of an intrinsic asymmetry in the time evolution of physical systems

Cold dark matter and primordial superheavy particles

The hypothesis that cold dark matter consists of primordial superheavy particles, the decay of short lifetime component of which led to the observable mass of matter while long living component survived up to modern times manifesting its presence in high energetic cosmic rays particles is investigated.Comment: LaTeX, 5 pages, no figure

The 1953 Cosmic Ray Conference at Bagneres de Bigorre

The cosmic ray conference at Bagn`eres de Bigorre in July, 1953 organized by Patrick Blackett and Louis Leprince-Ringuet was a seminal one. It marked the beginning of sub atomic physics and its shift from cosmic ray research to research at the new high energy accelerators. The knowledge of the heavy unstable particles found in the cosmic rays was essentially correct in fact and interpretation and defined the experiments that needed to be carried out with the new accelerators. A large fraction of the physicists who had been using cosmic rays for their research moved to the accelerators. This conference can be placed in importance in the same category as two other famous conferences, the Solvay congress of 1927 and the Shelter Island Conference of 1948

Probing minimal supergravity in the type-I seesaw mechanism with lepton flavour violation at the CERN LHC

The most general supersymmetric seesaw mechanism has too many parameters to be predictive and thus can not be excluded by any measurements of lepton flavour violating (LFV) processes. We focus on the simplest version of the type-I seesaw mechanism assuming minimal supergravity boundary conditions. We compute branching ratios for the LFV scalar tau decays, ${\tilde \tau}_2 \to (e,\mu) + \chi^0_1$, as well as loop-induced LFV decays at low energy, such as $l_i \to l_j + \gamma$ and $l_i \to 3 l_j$, exploring their sensitivity to the unknown seesaw parameters. We find some simple, extreme scenarios for the unknown right-handed parameters, where ratios of LFV branching ratios correlate with neutrino oscillation parameters. If the overall mass scale of the left neutrinos and the value of the reactor angle were known, the study of LFV allows, in principle, to extract information about the so far unknown right-handed neutrino parameters.Comment: 29 pages, 27 figures; added explanatory comments, corrected typos, final version for publicatio

Phase Space Localization and Approach to Thermal Equilibrium for a Class of Open Systems

We analyse the evolution of a quantum oscillator in a finite temperature environment using the quantum state diffusion (QSD) picture. Following a treatment similar to that of reference [7] we identify stationary solutions of the corresponding It\^o equation. We prove their global stability and compute typical time scales characterizing the localization process. The recovery of the density matrix in approximately diagonal form enables us to verify the approach to thermal equilibrium in the long time limit and we comment on the connection between QSD and the decoherent histories approach.Comment: 10 pages, Late

Neutrino Models of Dark Energy

I consider a scenario proposed by Fardon, Nelson and Weiner where dark energy and neutrinos are connected. As a result, neutrino masses are not constant but depend on the neutrino number density. By examining the full equation of state for the dark sector, I show that in this scenario the dark energy is equivalent to having a cosmological constant, but one that "runs" as the neutrino mass changes with temperature. Two examples are examined that illustrate the principal feautures of the dark sector of this scenario. In particular, the cosmological constant is seen to be negligible for most of the evolution of the Universe, becoming inportant only when neutrinos become non-relativistic. Some speculations on features of this scenario which might be present in a more realistic theory are also presented.Comment: 12 pages, 6 figures. Added comments on why FNW scenario always leads to a running cosmological constant and a few references. To be published in Phys. Rev.