83,090 research outputs found
Stress-energy Tensor Correlators in N-dim Hot Flat Spaces via the Generalized Zeta-Function Method
We calculate the expectation values of the stress-energy bitensor defined at
two different spacetime points of a massless, minimally coupled scalar
field with respect to a quantum state at finite temperature in a flat
-dimensional spacetime by means of the generalized zeta-function method.
These correlators, also known as the noise kernels, give the fluctuations of
energy and momentum density of a quantum field which are essential for the
investigation of the physical effects of negative energy density in certain
spacetimes or quantum states. They also act as the sources of the
Einstein-Langevin equations in stochastic gravity which one can solve for the
dynamics of metric fluctuations as in spacetime foams. In terms of
constitutions these correlators are one rung above (in the sense of the
correlation -- BBGKY or Schwinger-Dyson -- hierarchies) the mean (vacuum and
thermal expectation) values of the stress-energy tensor which drive the
semiclassical Einstein equation in semiclassical gravity. The low and the high
temperature expansions of these correlators are also given here: At low
temperatures, the leading order temperature dependence goes like while
at high temperatures they have a dependence with the subleading terms
exponentially suppressed by . We also discuss the singular behaviors of
the correlators in the coincident limit as was done before
for massless conformal quantum fields.Comment: 23 pages, no figures. Invited contribution to a Special Issue of
Journal of Physics A in honor of Prof. J. S. Dowke
Quantum Field Effects on Cosmological Phase Transition in Anisotropic Spacetimes
The one-loop renormalized effective potentials for the massive
theory on the spatially homogeneous models of Bianchi type I and
Kantowski-Sachs type are evaluated. It is used to see how the quantum field
affects the cosmological phase transition in the anisotropic spacetimes. For
reasons of the mathematical technique it is assumed that the spacetimes are
slowly varying or have specially metric forms. We obtain the analytic results
and present detailed discussions about the quantum field corrections to the
symmetry breaking or symmetry restoration in the model spacetimes.Comment: Latex 17 page
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
Gain-constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays
This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2013 IEEE.This paper is concerned with the gain-constrained recursive filtering problem for a class of time-varying nonlinear stochastic systems with probabilistic sensor delays and correlated noises. The stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case. The phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of Bernoulli distributed random variables taking values of 1 or 0, which means that the sensors may experience randomly occurring delays with individual delay characteristics. The process noise is finite-step autocorrelated. The purpose of the addressed gain-constrained filtering problem is to design a filter such that, for all probabilistic sensor delays, stochastic nonlinearities, gain constraint as well as correlated noises, the cost function concerning the filtering error is minimized at each sampling instant, where the filter gain satisfies a certain equality constraint. A new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre-specified filter gain constraint. A simulation example is provided to illustrate the effectiveness of the proposed filter design approach.This work was supported in part by the National Natural Science Foundation of China by Grants 61273156, 61028008, 60825303, 61104125, and 11271103, National 973 Project by Grant 2009CB320600, the Fok Ying Tung Education Fund by Grant 111064, the Special Fund for the Author of National Excellent Doctoral Dissertation of China by Grant 2007B4, the State Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. by Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany
Nonlinear analysis of dynamical complex networks
Copyright © 2013 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Complex networks are composed of a large number of highly interconnected dynamical units and therefore exhibit very complicated dynamics. Examples of such complex networks include the Internet, that is, a network of routers or domains, the World Wide Web (WWW), that is, a network of websites, the brain, that is, a network of neurons, and an organization, that is, a network of people. Since the introduction of the small-world network principle, a great deal of research has been focused on the dependence of the asymptotic behavior of interconnected oscillatory agents on the structural properties of complex networks. It has been found out that the general structure of the interaction network may play a crucial role in the emergence of synchronization phenomena in various fields such as physics, technology, and the life sciences
Quantum Brownian motion of multipartite systems and their entanglement dynamics
We solve the model of N quantum Brownian oscillators linearly coupled to an
environment of quantum oscillators at finite temperature, with no extra
assumptions about the structure of the system-environment coupling. Using a
compact phase-space formalism, we give a rather quick and direct derivation of
the master equation and its solutions for general spectral functions and
arbitrary temperatures. Since our framework is intrinsically nonperturbative,
we are able to analyze the entanglement dynamics of two oscillators coupled to
a common scalar field in previously unexplored regimes, such as off resonance
and strong coupling.Comment: 10 pages, 6 figure
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
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