91,074 research outputs found
Chern-Weil homomorphism in twisted equivariant cohomology
AbstractWe describe the Cartan and Weil models of twisted equivariant cohomology together with the Cartan homomorphism among the two, and we extend the Chern–Weil homomorphism to the twisted equivariant cohomology. We clarify that in order to have a cohomology theory, the coefficients of the twisted equivariant cohomology must be taken in the completed polynomial algebra over the dual Lie algebra of G. We recall the relation between the equivariant cohomology of exact Courant algebroids and the twisted equivariant cohomology, and we show how to endow with a generalized complex structure the finite-dimensional approximations of the Borel construction M×GEGk, whenever the generalized complex manifold M possesses a Hamiltonian G-action
Fluctuations of the vacuum energy density of quantum fields in curved spacetime via generalized zeta functions
For quantum fields on a curved spacetime with an Euclidean section, we derive
a general expression for the stress energy tensor two-point function in terms
of the effective action. The renormalized two-point function is given in terms
of the second variation of the Mellin transform of the trace of the heat kernel
for the quantum fields. For systems for which a spectral decomposition of the
wave opearator is possible, we give an exact expression for this two-point
function. Explicit examples of the variance to the mean ratio of the vacuum energy density of a
massless scalar field are computed for the spatial topologies of and , with results of , and
respectively. The large variance signifies the importance
of quantum fluctuations and has important implications for the validity of
semiclassical gravity theories at sub-Planckian scales. The method presented
here can facilitate the calculation of stress-energy fluctuations for quantum
fields useful for the analysis of fluctuation effects and critical phenomena in
problems ranging from atom optics and mesoscopic physics to early universe and
black hole physics.Comment: Uses revte
Mode decomposition and renormalization in semiclassical gravity
We compute the influence action for a system perturbatively coupled to a
linear scalar field acting as the environment. Subtleties related to
divergences that appear when summing over all the modes are made explicit and
clarified. Being closely connected with models used in the literature, we show
how to completely reconcile the results obtained in the context of stochastic
semiclassical gravity when using mode decomposition with those obtained by
other standard functional techniques.Comment: 4 pages, RevTeX, no figure
Nonequilibrium Phase Transitions of Vortex Matter in Three-Dimensional Layered Superconductors
Large-scale simulations on three-dimensional (3D) frustrated anisotropic XY
model have been performed to study the nonequilibrium phase transitions of
vortex matter in weak random pinning potential in layered superconductors. The
first-order phase transition from the moving Bragg glass to the moving smectic
is clarified, based on thermodynamic quantities. A washboard noise is observed
in the moving Bragg glass in 3D simulations for the first time. It is found
that the activation of the vortex loops play the dominant role in the dynamical
melting at high drive.Comment: 3 pages,5 figure
Mode entanglement of electrons in the one-dimensional Frenkel-Kontorova model
We study the mode entanglement in the one-dimensional Frenkel-Kontorova
model, and found that behaviors of quantum entanglement are distinct before and
after the transition by breaking of analyticity. We show that the more extended
the electron is, the more entangled the corresponding state. Finally, a
quantitative relation is given between the average square of the concurrence
quantifying the degree of entanglement and the participation ratio
characterizing the degree of localization.Comment: 4 pages, 4 figures. V
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