4,684 research outputs found
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 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 to be {\it
extensive}, i.e., for . In particular, if
they are independent, is {\it strictly additive}, i.e., . However, if the subsystems are globally correlated, we
expect, for a vast class of systems, the entropy (with ) for some special value of to be the
one which extensive (i.e., for ).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, , as well as loop-induced LFV decays at low energy, such as
and , 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.
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