261 research outputs found
Thermal Fields, Entropy, and Black Holes
In this review we describe statistical mechanics of quantum systems in the
presence of a Killing horizon and compare statistical-mechanical and one-loop
contributions to black hole entropy. Studying these questions was motivated by
attempts to explain the entropy of black holes as a statistical-mechanical
entropy of quantum fields propagating near the black hole horizon. We provide
an introduction to this field of research and review its results. In
particular, we discuss the relation between the statistical-mechanical entropy
of quantum fields and the Bekenstein-Hawking entropy in the standard scheme
with renormalization of gravitational coupling constants and in the theories of
induced gravity.Comment: 44 pages, LaTeX fil
Non-linear feedback effects in coupled Boson-Fermion systems
We address ourselves to a class of systems composed of two coupled subsystems
without any intra-subsystem interaction: itinerant Fermions and localized
Bosons on a lattice. Switching on an interaction between the two subsystems
leads to feedback effects which result in a rich dynamical structure in both of
them. Such feedback features are studied on the basis of the flow equation
technique - an infinite series of infinitesimal unitary transformations - which
leads to a gradual elimination of the inter-subsystem interaction. As a result
the two subsystems get decoupled but their renormalized kinetic energies become
mutually dependent on each other. Choosing for the inter - subsystem
interaction a charge exchange term (the Boson-Fermion model) the initially
localized Bosons acquire itinerancy through their dependence on the
renormalized Fermion dispersion. This latter evolves from a free particle
dispersion into one showing a pseudogap structure near the chemical potential.
Upon lowering the temperature both subsystems simultaneously enter a
macroscopic coherent quantum state. The Bosons become superfluid, exhibiting a
soundwave like dispersion while the Fermions develop a true gap in their
dispersion. The essential physical features described by this technique are
already contained in the renormalization of the kinetic terms in the respective
Hamiltonians of the two subsystems. The extra interaction terms resulting in
the process of iteration only strengthen this physics. We compare the results
with previous calculations based on selfconsistent perturbative approaches.Comment: 14 pages, 16 figures, accepted for publication in Phys. Rev.
Quantum Fields and Extended Objects in Space-Times with Constant Curvature Spatial Section
The heat-kernel expansion and -regularization techniques for quantum
field theory and extended objects on curved space-times are reviewed. In
particular, ultrastatic space-times with spatial section consisting in manifold
with constant curvature are discussed in detail. Several mathematical results,
relevant to physical applications are presented, including exact solutions of
the heat-kernel equation, a simple exposition of hyperbolic geometry and an
elementary derivation of the Selberg trace formula. With regards to the
physical applications, the vacuum energy for scalar fields, the one-loop
renormalization of a self-interacting scalar field theory on a hyperbolic
space-time, with a discussion on the topological symmetry breaking, the finite
temperature effects and the Bose-Einstein condensation, are considered. Some
attempts to generalize the results to extended objects are also presented,
including some remarks on path integral quantization, asymptotic properties of
extended objects and a novel representation for the one-loop (super)string free
energy.Comment: Latex file, 122 page
Quantum gravity: unification of principles and interactions, and promises of spectral geometry
Quantum gravity was born as that branch of modern theoretical physics that
tries to unify its guiding principles, i.e., quantum mechanics and general
relativity. Nowadays it is providing new insight into the unification of all
fundamental interactions, while giving rise to new developments in modern
mathematics. It is however unclear whether it will ever become a falsifiable
physical theory, since it deals with Planck-scale physics. Reviewing a wide
range of spectral geometry from index theory to spectral triples, we hope to
dismiss the general opinion that the mere mathematical complexity of the
unification programme will obstruct that programme.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Non-stationary Spectra of Local Wave Turbulence
The evolution of the Kolmogorov-Zakharov (K-Z) spectrum of weak turbulence is
studied in the limit of strongly local interactions where the usual kinetic
equation, describing the time evolution of the spectral wave-action density,
can be approximated by a PDE. If the wave action is initially compactly
supported in frequency space, it is then redistributed by resonant interactions
producing the usual direct and inverse cascades, leading to the formation of
the K-Z spectra. The emphasis here is on the direct cascade. The evolution
proceeds by the formation of a self-similar front which propagates to the right
leaving a quasi-stationary state in its wake. This front is sharp in the sense
that the solution remains compactly supported until it reaches infinity. If the
energy spectrum has infinite capacity, the front takes infinite time to reach
infinite frequency and leaves the K-Z spectrum in its wake. On the other hand,
if the energy spectrum has finite capacity, the front reaches infinity within a
finite time, t*, and the wake is steeper than the K-Z spectrum. For this case,
the K-Z spectrum is set up from the right after the front reaches infinity. The
slope of the solution in the wake can be related to the speed of propagation of
the front. It is shown that the anomalous slope in the finite capacity case
corresponds to the unique front speed which ensures that the front tip contains
a finite amount of energy as the connection to infinity is made. We also
introduce, for the first time, the notion of entropy production in wave
turbulence and show how it evolves as the system approaches the stationary K-Z
spectrum.Comment: revtex4, 19 pages, 10 figure
Nonequilibrium relaxation in neutral BCS superconductors: Ginzburg-Landau approach with Landau damping in real time
We present a field-theoretical method to obtain consistently the equations of
motion for small amplitude fluctuations of the order parameter directly in real
time for a homogeneous, neutral BCS superconductor. This method allows to study
the nonequilibrium relaxation of the order parameter as an initial value
problem. We obtain the Ward identities and the effective actions for small
phase the amplitude fluctuations to one-loop order. Focusing on the
long-wavelength, low-frequency limit near the critical point, we obtain the
time-dependent Ginzburg-Landau effective action to one-loop order, which is
nonlocal as a consequence of Landau damping. The nonequilibrium relaxation of
the phase and amplitude fluctuations is studied directly in real time. The
long-wavelength phase fluctuation (Bogoliubov-Anderson-Goldstone mode) is
overdamped by Landau damping and the relaxation time scale diverges at the
critical point, revealing critical slowing down.Comment: 31 pages 14 figs, revised version, to appear in Phys. Rev.
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