26,351 research outputs found
The Statistical Mechanics of the Self-Gravitating Gas: Equation of State and Fractal Dimension
We provide a complete picture of the self-gravitating non-relativistic gas at
thermal equilibrium using Monte Carlo simulations (MC), analytic mean field
methods (MF) and low density expansions. The system is shown to possess an
infinite volume limit, both in the canonical (CE) and in the microcanonical
ensemble (MCE) when N, V \to \infty, keeping N/ V^{1/3} fixed. We {\bf compute}
the equation of state (we do not assume it as is customary), the entropy, the
free energy, the chemical potential, the specific heats, the compressibilities,
the speed of sound and analyze their properties, signs and singularities. The
MF equation of state obeys a {\bf first order} non-linear differential equation
of Abel type. The MF gives an accurate picture in agreement with the MC
simulations both in the CE and MCE. The inhomogeneous particle distribution in
the ground state suggest a fractal distribution with Haussdorf dimension D with
D slowly decreasing with increasing density, 1 \lesssim D < 3.Comment: LaTex, 7 pages, 2 .ps figures, minor improvements, to appear in
Physics Letters
Quantum Nernst engines
We theoretically propose Nernst engines based on quantum Hall edge states. We
identify a setup that exhibits an extreme asymmetry between the off-diagonal
Onsager coefficients for heat and charge transport. In terms of thermodynamic
efficiency, this engine outperforms a recently proposed classical Nernst
engine. A second setup using an anti-dot is found to be more efficient as
energy filtering becomes less strong.Comment: 6 pages, 3 figures, published versio
A Temporal Logic for Hyperproperties
Hyperproperties, as introduced by Clarkson and Schneider, characterize the
correctness of a computer program as a condition on its set of computation
paths. Standard temporal logics can only refer to a single path at a time, and
therefore cannot express many hyperproperties of interest, including
noninterference and other important properties in security and coding theory.
In this paper, we investigate an extension of temporal logic with explicit path
variables. We show that the quantification over paths naturally subsumes other
extensions of temporal logic with operators for information flow and knowledge.
The model checking problem for temporal logic with path quantification is
decidable. For alternation depth 1, the complexity is PSPACE in the length of
the formula and NLOGSPACE in the size of the system, as for linear-time
temporal logic
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