143 research outputs found
An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem
Let (lambda_d)(p) be the p monomer-dimer entropy on the d-dimensional integer
lattice Z^d, where p in [0,1] is the dimer density. We give upper and lower
bounds for (lambda_d)(p) in terms of expressions involving (lambda_(d-1))(q).
The upper bound is based on a conjecture claiming that the p monomer-dimer
entropy of an infinite subset of Z^d is bounded above by (lambda_d)(p). We
compute the first three terms in the formal asymptotic expansion of
(lambda_d)(p) in powers of 1/d. We prove that the lower asymptotic matching
conjecture is satisfied for (lambda_d)(p).Comment: 15 pages, much more about d=1,2,
Vacuum Energy Density for Massless Scalar Fields in Flat Homogeneous Spacetime Manifolds with Nontrivial Topology
Although the observed universe appears to be geometrically flat, it could
have one of 18 global topologies. A constant-time slice of the spacetime
manifold could be a torus, Mobius strip, Klein bottle, or others. This global
topology of the universe imposes boundary conditions on quantum fields and
affects the vacuum energy density via Casimir effect. In a spacetime with such
a nontrivial topology, the vacuum energy density is shifted from its value in a
simply-connected spacetime. In this paper, the vacuum expectation value of the
stress-energy tensor for a massless scalar field is calculated in all 17
multiply-connected, flat and homogeneous spacetimes with different global
topologies. It is found that the vacuum energy density is lowered relative to
the Minkowski vacuum level in all spacetimes and that the stress-energy tensor
becomes position-dependent in spacetimes that involve reflections and
rotations.Comment: 25 pages, 11 figure
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