A homogenization theorem for Langevin systems with an application to Hamiltonian dynamics

This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role of detailed balance and presenting the heuristics based on a multiscale expansion. This is used to propose a physical interpretation of recent results by the authors, as well as to motivate a new theorem proven here. Its main content is a sufficient condition, expressed in terms of solvability of an associated partial differential equation ("the cell problem"), under which the homogenization limit of an SDE is calculated explicitly. The general theorem is applied to a class of systems, satisfying a generalized detailed balance condition with a position-dependent temperature.Comment: 32 page

Quantum Dynamics for de Sitter Radiation

We revisit the Hamiltonian formalism for a massive scalar field and study the particle production in a de Sitter space. In the invariant-operator picture the time-dependent annihilation and creation operators are constructed in terms of a complex solution to the classical equation of motion for the field and the Gaussian wave function for each Fourier mode is found which is an exact solution to the Schr\"odinger equation. The in-out formalism is reformulated by the annihilation and creation operators and the Gaussian wave functions. The de Sitter radiation from the in-out formalism differs from the Gibbons-Hawking radiation in the planar coordinates, and we discuss the discrepancy of the particle production by the two methodComment: LaTex 12 pages, no figure; CosPA2011, Peking Univ., Oct. 28-31, 2011; references added; to be published in International Journal of Modern Physics: Conference Serie

Generalized modified gravity with the second order acceleration equation

In the theories of generalized modified gravity, the acceleration equation is generally fourth order. So it is hard to analyze the evolution of the Universe. In this paper, we present a class of generalized modified gravity theories which have the acceleration equation of second order derivative. Then both the cosmic evolution and the weak-field limit of the theories are easily investigated. We find that not only the Big-bang singularity problem but also the current cosmic acceleration problem could be easily dealt with.Comment: 8 pages, 2 figures. To appear in Phys. Rev.

Quantum Larmor radiation in conformally flat universe

We investigate the quantum effect on the Larmor radiation from a moving charge in an expanding universe based on the framework of the scalar quantum electrodynamics (SQED). A theoretical formula for the radiation energy is derived at the lowest order of the perturbation theory with respect to the coupling constant of the SQED. We evaluate the radiation energy on the background universe so that the Minkowski spacetime transits to the Milne universe, in which the equation of motion for the mode function of the free complex scalar field can be exactly solved in an analytic way. Then, the result is compared with the WKB approach, in which the equation of motion of the mode function is constructed with the WKB approximation which is valid as long as the Compton wavelength is shorter than the Hubble horizon length. This demonstrates that the quantum effect on the Larmor radiation of the order e^2\hbar is determined by a non-local integration in time depending on the background expansion. We also compare our result with a recent work by Higuchi and Walker [Phys. Rev. D80 105019 (2009)], which investigated the quantum correction to the Larmor radiation from a charged particle in a non-relativistic motion in a homogeneous electric field.Comment: 12 pages, 4 figure, accepted for publication in Physical Review

Matter density perturbations in modified gravity models with arbitrary coupling between matter and geometry

We consider theories with an arbitrary coupling between matter and gravity and obtain the perturbation equation of matter on subhorizon scales. Also, we derive the effective gravitational constant $G_{eff}$ and two parameters $\Sigma$ and $\eta$, which along with the perturbation equation of the matter density are useful to constrain the theory from growth factor and weak lensing observations. Finally, we use a completely solvable toy model which exhibits nontrivial phenomenology to investigate specific features of the theory. We obtain the analytic solution of the modified Friedmann equation for the scale factor $a$ in terms of time $t$ and use the age of the oldest star clusters and the primordial nucleosynthesis bounds in order to constrain the parameters of our toy model.Comment: 9 pages, 3 figures, uses revtex4, added Appendix and references, minor changes, accepted in Phys. Rev. D (to appear

Detection of acceleration radiation in a Bose-Einstein condensate

We propose and study methods for detecting the Unruh effect in a Bose-Einstein condensate. The Bogoliubov vacuum of a Bose-Einstein condensate is used here to simulate a scalar field-theory, and accelerated atom dots or optical lattices as means for detecting phonon radiation due to acceleration effects. We study Unruh's effect for linear acceleration and circular acceleration. In particular, we study the dispersive effects of the Bogoliubov spectrum on the ideal case of exact thermalization. Our results suggest that Unruh's acceleration radiation can be tested using current accessible experimental methods.Comment: 5 pages, 3 figure

Hawking Radiation from Fluctuating Black Holes

Classically, black Holes have the rigid event horizon. However, quantum mechanically, the event horizon of black holes becomes fuzzy due to quantum fluctuations. We study Hawking radiation of a real scalar field from a fluctuating black hole. To quantize metric perturbations, we derive the quadratic action for those in the black hole background. Then, we calculate the cubic interaction terms in the action for the scalar field. Using these results, we obtain the spectrum of Hawking radiation in the presence of interaction between the scalar field and the metric. It turns out that the spectrum deviates from the Planck spectrum due to quantum fluctuations of the metric.Comment: 35pages, 4 figure

Black hole collapse simulated by vacuum fluctuations with a moving semi-transparent mirror

Creation of scalar massless particles in two-dimensional Minkowski space-time--as predicted by the dynamical Casimir effect--is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a trajectory that simulates a black hole collapse (defined by Walker, and Carlitz and Willey), and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [r(w)=-i\alpha/(\w+i\alpha) and s(w)=\w/(\w+i\alpha), with $\alpha\geq 0$], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when $\alpha$ is very large (case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a black body radiation), in accordance with results previously obtained in the literature. However, when $\alpha$ is finite (semitransparent mirror, a physically realistic situation) the striking result is obtained that the thermal emission of scalar massless particles obeys Fermi-Dirac statistics. We also show here that the reverse change of statistics takes place in a bidimensional fermionic model for massless particles, namely that the Fermi-Dirac statistics for the completely reflecting situation will turn into the Bose-Einstein statistics for a partially reflecting, physical mirror.Comment: 13 pages, no figures, version to appear in Physical Review

Classical and quantum radiation from a moving charge in an expanding universe

We investigate photon emission from a moving particle in an expanding universe. This process is analogous to the radiation from an accelerated charge in the classical electromagnetic theory. Using the framework of quantum field theory in curved spacetime, we demonstrate that the Wentzel-Kramers-Brillouin (WKB) approximation leads to the Larmor formula for the rate of the radiation energy from a moving charge in an expanding universe. Using exactly solvable models in a radiation-dominated universe and in a Milne universe, we examine the validity of the WKB formula. It is shown that the quantum effect suppresses the radiation energy in comparison with the WKB formula.Comment: 16 pages, JCAP in pres

The Gauge Fields and Ghosts in Rindler Space

We consider 2d Maxwell system defined on the Rindler space with metric ds^2=\exp(2a\xi)\cdot(d\eta^2-d\xi^2) with the goal to study the dynamics of the ghosts. We find an extra contribution to the vacuum energy in comparison with Minkowski space time with metric ds^2= dt^2-dx^2. This extra contribution can be traced to the unphysical degrees of freedom (in Minkowski space). The technical reason for this effect to occur is the property of Bogolubov's coefficients which mix the positive and negative frequencies modes. The corresponding mixture can not be avoided because the projections to positive -frequency modes with respect to Minkowski time t and positive -frequency modes with respect to the Rindler observer's proper time \eta are not equivalent. The exact cancellation of unphysical degrees of freedom which is maintained in Minkowski space can not hold in the Rindler space. In BRST approach this effect manifests itself as the presence of BRST charge density in L and R parts. An inertial observer in Minkowski vacuum |0> observes a universe with no net BRST charge only as a result of cancellation between the two. However, the Rindler observers who do not ever have access to the entire space time would see a net BRST charge. In this respect the effect resembles the Unruh effect. The effect is infrared (IR) in nature, and sensitive to the horizon and/or boundaries. We interpret the extra energy as the formation of the "ghost condensate" when the ghost degrees of freedom can not propagate, but nevertheless do contribute to the vacuum energy. Exact computations in this simple 2d model support the claim made in [1] that the ghost contribution might be responsible for the observed dark energy in 4d FLRW universe.Comment: Final version to appear in Phys. Rev. D. Comments on relation with energy momentum computations and few new refs are adde