2,773 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
Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History
Decoherent histories quantum theory is reformulated with the assumption that
there is one "real" fine-grained history, specified in a preferred complete set
of sum-over-histories variables. This real history is described by embedding it
in an ensemble of comparable imagined fine-grained histories, not unlike the
familiar ensemble of statistical mechanics. These histories are assigned
extended probabilities, which can sometimes be negative or greater than one. As
we will show, this construction implies that the real history is not completely
accessible to experimental or other observational discovery. However,
sufficiently and appropriately coarse-grained sets of alternative histories
have standard probabilities providing information about the real fine-grained
history that can be compared with observation. We recover the probabilities of
decoherent histories quantum mechanics for sets of histories that are recorded
and therefore decohere. Quantum mechanics can be viewed as a classical
stochastic theory of histories with extended probabilities and a well-defined
notion of reality common to all decoherent sets of alternative coarse-grained
histories.Comment: 11 pages, one figure, expanded discussion and acknowledgment
How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems
The maximum entropy principle (MEP) is a method for obtaining the most likely
distribution functions of observables from statistical systems, by maximizing
entropy under constraints. The MEP has found hundreds of applications in
ergodic and Markovian systems in statistical mechanics, information theory, and
statistics. For several decades there exists an ongoing controversy whether the
notion of the maximum entropy principle can be extended in a meaningful way to
non-extensive, non-ergodic, and complex statistical systems and processes. In
this paper we start by reviewing how Boltzmann-Gibbs-Shannon entropy is related
to multiplicities of independent random processes. We then show how the
relaxation of independence naturally leads to the most general entropies that
are compatible with the first three Shannon-Khinchin axioms, the
(c,d)-entropies. We demonstrate that the MEP is a perfectly consistent concept
for non-ergodic and complex statistical systems if their relative entropy can
be factored into a generalized multiplicity and a constraint term. The problem
of finding such a factorization reduces to finding an appropriate
representation of relative entropy in a linear basis. In a particular example
we show that path-dependent random processes with memory naturally require
specific generalized entropies. The example is the first exact derivation of a
generalized entropy from the microscopic properties of a path-dependent random
process.Comment: 6 pages, 1 figure. To appear in PNA
The Symmetries of Nature
The study of the symmetries of nature has fascinated scientists for eons. The application of the formal mathematical description of
symmetries during the last century has produced many breakthroughs in
our understanding of the substructure of matter. In this talk, a number
of these advances are discussed, and the important role that George
Sudarshan played in their development is emphasize
Regenerating a Symmetry in Asymmetric Dark Matter
Asymmetric dark matter theories generically allow for mass terms that lead to
particle-antiparticle mixing. Over the age of the Universe, dark matter can
thus oscillate from a purely asymmetric configuration into a symmetric mix of
particles and antiparticles, allowing for pair-annihilation processes.
Additionally, requiring efficient depletion of the primordial thermal
(symmetric) component generically entails large annihilation rates. We show
that unless some symmetry completely forbids dark matter particle-antiparticle
mixing, asymmetric dark matter is effectively ruled out for a large range of
masses, for almost any oscillation time-scale shorter than the age of the
Universe.Comment: 5 pages, 2 figure
Singular Instantons Made Regular
The singularity present in cosmological instantons of the Hawking-Turok type
is resolved by a conformal transformation, where the conformal factor has a
linear zero of codimension one. We show that if the underlying regular manifold
is taken to have the topology of , and the conformal factor is taken to
be a twisted field so that the zero is enforced, then one obtains a
one-parameter family of solutions of the classical field equations, where the
minimal action solution has the conformal zero located on a minimal volume
noncontractible submanifold. For instantons with two singularities, the
corresponding topology is that of a cylinder with D=4
analogues of `cross-caps' at each of the endpoints.Comment: 23 pages, compressed and RevTex file, including nine postscript
figure files. Submitted versio
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.
On the Definition of Decoherence
We examine the relationship between the decoherence of quantum-mechanical
histories of a closed system (as discussed by Gell-Mann and Hartle) and
environmentally-induced diagonalization of the density operator for an open
system. We study a definition of decoherence which incorporates both of these
ideas, and show that it leads to a consistent probabilistic interpretation of
the reduced density operator.Comment: 10 pages, LaTeX, SJSU/TP-93-1
Fermion Mass Hierarchy in Lifshitz Type Gauge Theory
We study the origin of fermion mass hierarchy and flavor mixing in a Lifshitz
type extension of the standard model including an extra scalar field. We show
that the hierarchical structure can originate from renormalizable interactions.
In contrast to the Froggatt-Nielsen mechanism, the higher the dimension of
associated operators, the heavier the fermion masses. Tiny masses for
left-handed neutrinos are obtained without introducing right-handed neutrinos.Comment: 13 pages; clarifications of some point
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