6,553 research outputs found
Models for Chronology Selection
In this paper, we derive an expression for the grand canonical partition
function for a fluid of hot, rotating massless scalar field particles in the
Einstein universe. We consider the number of states with a given energy as one
increases the angular momentum so that the fluid rotates with an increasing
angular velocity. We find that at the critical value when the velocity of the
particles furthest from the origin reaches the speed of light, the number of
states tends to zero. We illustrate how one can also interpret this partition
function as the effective action for a boosted scalar field configuration in
the product of three dimensional de Sitter space and . In this case, we
consider the number of states with a fixed linear momentum around the as
the particles are given more and more boost momentum. At the critical point
when the spacetime is about to develop closed timelike curves, the number of
states again tends to zero. Thus it seems that quantum mechanics naturally
enforces the chronology protection conjecture by superselecting the causality
violating field configurations from the quantum mechanical phase space.Comment: 20 pages, Late
Hamiltonian thermodynamics of the Reissner-Nordstr\"om-anti-de Sitter black hole
We consider the Hamiltonian dynamics and thermodynamics of spherically
symmetric Einstein-Maxwell spacetimes with a negative cosmological constant. We
impose boundary conditions that enforce every classical solution to be an
exterior region of a Reissner-Nordstr\"om-anti-de Sitter black hole with a
nondegenerate Killing horizon, with the spacelike hypersurfaces extending from
the horizon bifurcation two-sphere to the asymptotically anti-de Sitter
infinity. The constraints are simplified by a canonical transformation, which
generalizes that given by Kucha\v{r} in the spherically symmetric vacuum
Einstein theory, and the theory is reduced to its true dynamical degrees of
freedom. After quantization, the grand partition function of a thermodynamical
grand canonical ensemble is obtained by analytically continuing the Lorentzian
time evolution operator to imaginary time and taking the trace. A~similar
analysis under slightly modified boundary conditions leads to the partition
function of a thermodynamical canonical ensemble. The thermodynamics in each
ensemble is analyzed, and the conditions that the (grand) partition function be
dominated by a classical Euclidean black hole solution are found. When these
conditions are satisfied, we recover in particular the Bekenstein-Hawking
entropy. The limit of a vanishing cosmological constant is briefly discussed.
(This paper is dedicated to Karel Kucha\v{r} on the occasion of his sixtieth
birthday.)Comment: 34 pages, REVTeX v3.0. (Minor corrections and presentational
revisions; added references.
Hamiltonian dynamics and geometry of phase transitions in classical XY models
The Hamiltonian dynamics associated to classical, planar, Heisenberg XY
models is investigated for two- and three-dimensional lattices. Besides the
conventional signatures of phase transitions, here obtained through time
averages of thermodynamical observables in place of ensemble averages,
qualitatively new information is derived from the temperature dependence of
Lyapunov exponents. A Riemannian geometrization of newtonian dynamics suggests
to consider other observables of geometric meaning tightly related with the
largest Lyapunov exponent. The numerical computation of these observables -
unusual in the study of phase transitions - sheds a new light on the
microscopic dynamical counterpart of thermodynamics also pointing to the
existence of some major change in the geometry of the mechanical manifolds at
the thermodynamical transition. Through the microcanonical definition of the
entropy, a relationship between thermodynamics and the extrinsic geometry of
the constant energy surfaces of phase space can be naturally
established. In this framework, an approximate formula is worked out,
determining a highly non-trivial relationship between temperature and topology
of the . Whence it can be understood that the appearance of a phase
transition must be tightly related to a suitable major topology change of the
. This contributes to the understanding of the origin of phase
transitions in the microcanonical ensemble.Comment: in press on Physical Review E, 43 pages, LaTeX (uses revtex), 22
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