28,851 research outputs found
Holographic Algorithm with Matchgates Is Universal for Planar CSP Over Boolean Domain
We prove a complexity classification theorem that classifies all counting
constraint satisfaction problems (CSP) over Boolean variables into exactly
three categories: (1) Polynomial-time tractable; (2) P-hard for general
instances, but solvable in polynomial-time over planar graphs; and (3)
P-hard over planar graphs. The classification applies to all sets of local,
not necessarily symmetric, constraint functions on Boolean variables that take
complex values. It is shown that Valiant's holographic algorithm with
matchgates is a universal strategy for all problems in category (2).Comment: 94 page
Measure Factors, Tension, and Correlations of Fluid Membranes
We study two geometrical factors needed for the correct construction of
statistical ensembles of surfaces. Such ensembles appear in the study of fluid
bilayer membranes, though our results are more generally applicable. The naive
functional measure over height fluctuations must be corrected by these factors
in order to give correct, self-consistent formulas for the free energy and
correlation functions of the height. While one of these corrections -- the
Faddeev-Popov determinant -- has been studied extensively, our derivation
proceeds from very simple geometrical ideas, which we hope removes some of its
mystery. The other factor is similar to the Liouville correction in string
theory. Since our formulas differ from those of previous authors, we include
some explicit calculations of the effective frame tension and two-point
function to show that our version indeed secures coordinate-invariance and
consistency to lowest nontrivial order in a temperature expansion.Comment: 24 pp; plain Te
The Cardy-Verlinde formula and entropy of Topological Reissner-Nordstr\"om black holes in de Sitter spaces
In this paper we discuss the question of whether the entropy of cosmological
horizon in Topological Reissner-Nordstr\"om- de Sitter spaces can be described
by the Cardy-Verlinde formula, which is supposed to be an entropy formula of
conformal field theory in any dimension. Furthermore, we find that the entropy
of black hole horizon can also be rewritten in terms of the Cardy-Verlinde
formula for these black holes in de Sitter spaces, if we use the definition due
to Abbott and Deser for conserved charges in asymptotically de Sitter spaces.
Our result is in favour of the dS/CFT correspondence.Comment: 6 pages, accepted for publication in IJMP
Quantum Decoherence Modulated by Special Relativity
By investigating the evolution of a moving spin-1/2 Dirac electron coupled
with a background magnetic noise, we demonstrate that the effects of special
relativity will significantly modify the decoherence properties of the spin
state. The dephasing could be much suppressed, and for a sufficiently long time
the decoherence even seems to halt. This interesting phenomenon stems from the
dressed environment induced by special relativity
Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model
Infinite hierarchy of exact equations are derived for the newly-observed
f-avalanche in the Bak-Sneppen evolution model. By solving the first order
exact equation, we found that the critical exponent which governs the
divergence of the average avalanche size, is exactly 1 (for all dimensions),
confirmed by the simulations. Solution of the gap equation yields another
universal exponent, denoting the the relaxation to the attractor, is exactly 1.
We also establish some scaling relations among the critical exponents of the
new avalanche.Comment: 5 pages, 1 figur
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