48 research outputs found
Path Integral Approach to 't Hooft's Derivation of Quantum from Classical Physics
We present a path-integral formulation of 't Hooft's derivation of quantum
from classical physics. The crucial ingredient of this formulation is Gozzi et
al.'s supersymmetric path integral of classical mechanics. We quantize
explicitly two simple classical systems: the planar mathematical pendulum and
the Roessler dynamical system.Comment: 29 pages, RevTeX, revised version with minor changes, accepted to
Phys. Rev.
Deformation quantization of linear dissipative systems
A simple pseudo-Hamiltonian formulation is proposed for the linear
inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics,
our approach is based on the use of non-stationary Poisson brackets, i.e.
corresponding Poisson tensor is allowed to explicitly depend on time. Starting
from this pseudo-Hamiltonian formulation we develop a consistent deformation
quantization procedure involving a non-stationary star-product and an
``extended'' operator of time derivative , differentiating
the -product. As in the usual case, the -algebra of physical
observables is shown to admit an essentially unique (time dependent) trace
functional . Using these ingredients we construct a complete and
fully consistent quantum-mechanical description for any linear dynamical system
with or without dissipation. The general quantization method is exemplified by
the models of damped oscillator and radiating point charge.Comment: 14 pages, typos correcte
Some Properties of R\'{e}nyi Entropy over Countably Infinite Alphabets
In this paper we study certain properties of R\'{e}nyi entropy functionals
on the space of probability distributions over
. Primarily, continuity and convergence issues are addressed.
Some properties shown parallel those known in the finite alphabet case, while
others illustrate a quite different behaviour of R\'enyi entropy in the
infinite case. In particular, it is shown that, for any distribution and any , there exists a sequence of distributions
converging to with respect to the total variation
distance, such that .Comment: 13 pages (single-column
The emergence of Special and Doubly Special Relativity
Building on our previous work [Phys.Rev.D82,085016(2010)], we show in this
paper how a Brownian motion on a short scale can originate a relativistic
motion on scales that are larger than particle's Compton wavelength. This can
be described in terms of polycrystalline vacuum. Viewed in this way, special
relativity is not a primitive concept, but rather it statistically emerges when
a coarse graining average over distances of order, or longer than the Compton
wavelength is taken. By analyzing the robustness of such a special relativity
under small variations in the polycrystalline grain-size distribution we
naturally arrive at the notion of doubly-special relativistic dynamics. In this
way, a previously unsuspected, common statistical origin of the two frameworks
is brought to light. Salient issues such as the role of gauge fixing in
emergent relativity, generalized commutation relations, Hausdorff dimensions of
representative path-integral trajectories and a connection with Feynman
chessboard model are also discussed.Comment: 21 pages, 1 figure, RevTeX4, substantially revised version, accepted
in Phys. Rev.
Sub-Planckian black holes and the Generalized Uncertainty Principle
The Black Hole Uncertainty Principle correspondence suggests that there could
exist black holes with mass beneath the Planck scale but radius of order the
Compton scale rather than Schwarzschild scale. We present a modified, self-dual
Schwarzschild-like metric that reproduces desirable aspects of a variety of
disparate models in the sub-Planckian limit, while remaining Schwarzschild in
the large mass limit. The self-dual nature of this solution under naturally implies a Generalized Uncertainty Principle
with the linear form . We also
demonstrate a natural dimensional reduction feature, in that the gravitational
radius and thermodynamics of sub-Planckian objects resemble that of -D
gravity. The temperature of sub-Planckian black holes scales as rather than
but the evaporation of those smaller than g is suppressed by
the cosmic background radiation. This suggests that relics of this mass could
provide the dark matter.Comment: 12 pages, 9 figures, version published in J. High En. Phy
Neutrino damping rate at finite temperature and density
A first principle derivation is given of the neutrino damping rate in
real-time thermal field theory. Starting from the discontinuity of the neutrino
self energy at the two loop level, the damping rate can be expressed as
integrals over space phase of amplitudes squared, weighted with statistical
factors that account for the possibility of particle absorption or emission
from the medium. Specific results for a background composed of neutrinos,
leptons, protons and neutrons are given. Additionally, for the real part of the
dispersion relation we discuss the relation between the results obtained from
the thermal field theory, and those obtained by the thermal average of the
forward scattering amplitude.Comment: LaTex Document, 19 pages, 3 figure