1,254 research outputs found
Quantized fields and gravitational particle creation in f(R) expanding universes
The problem of cosmological particle creation for a spatially flat,
homogeneous and isotropic Universes is discussed in the context of f(R)
theories of gravity. Different from cosmological models based on general
relativity theory, it is found that a conformal invariant metric does not
forbid the creation of massless particles during the early stages (radiation
era) of the Universe.Comment: 14 pages, 2 figure
Generic dynamics of 4-dimensional C2 Hamiltonian systems
We study the dynamical behaviour of Hamiltonian flows defined on
4-dimensional compact symplectic manifolds. We find the existence of a
C2-residual set of Hamiltonians for which every regular energy surface is
either Anosov or it is in the closure of energy surfaces with zero Lyapunov
exponents a.e. This is in the spirit of the Bochi-Mane dichotomy for
area-preserving diffeomorphisms on compact surfaces and its continuous-time
version for 3-dimensional volume-preserving flows
The mean curvature of cylindrically bounded submanifolds
We give an estimate of the mean curvature of a complete submanifold lying
inside a closed cylinder in a product Riemannian manifold
. It follows that a complete hypersurface of given
constant mean curvature lying inside a closed circular cylinder in Euclidean
space cannot be proper if the circular base is of sufficiently small radius. In
particular, any possible counterexample to a conjecture of Calabion complete
minimal hypersurfaces cannot be proper. As another application of our method,
we derive a result about the stochastic incompleteness of submanifolds with
sufficiently small mean curvature.Comment: First version (December 2008). Final version, including new title
(February 2009). To appear in Mathematische Annale
Eigenvalue estimates for submanifolds of warped product spaces
We give lower bounds for the fundamental tone of open sets in minimal
submanifolds immersed into warped product spaces of type ,
where . We also study the essential spectrum of these
minimal submanifolds.Comment: 17 page
Quantum statistical correlations in thermal field theories: boundary effective theory
We show that the one-loop effective action at finite temperature for a scalar
field with quartic interaction has the same renormalized expression as at zero
temperature if written in terms of a certain classical field , and if
we trade free propagators at zero temperature for their finite-temperature
counterparts. The result follows if we write the partition function as an
integral over field eigenstates (boundary fields) of the density matrix element
in the functional Schr\"{o}dinger field-representation, and perform a
semiclassical expansion in two steps: first, we integrate around the
saddle-point for fixed boundary fields, which is the classical field ,
a functional of the boundary fields; then, we perform a saddle-point
integration over the boundary fields, whose correlations characterize the
thermal properties of the system. This procedure provides a
dimensionally-reduced effective theory for the thermal system. We calculate the
two-point correlation as an example.Comment: 13 pages, 1 figur
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