Esteban Calzetta

Noise and Fluctuations in Semiclassical Gravity

We continue our earlier investigation of the back reaction problem in semiclassical gravity with the Schwinger-Keldysh or closed-time-path (CTP) functional formalism using the language of the decoherent history formulation of quantum mechanics. Making use of its intimate relation with the Feynman-Vernon influence functional method, we examine the statistical mechanical meaning and show the interrelation of the many quantum processes involved in the back reaction problem, such as particle creation, decoherence, and dissipation. We show how noise and fluctuation arise naturally from the CTP formalism. We derive an expression for the CTP effective action in terms of the Bogoliubov coefficients and show how noise is related to the fluctuations in the number of particles created. In so doing we have extended the old framework of semiclassical gravity, based on the mean field theory of Einstein equation with a source given by the expectation value of the energy-momentum tensor, to that based on a Langevin-type equation, where the dynamics of the fluctuations of spacetime is driven by the quantum fluctuations of the matter field. This generalized framework is useful for the investigation of quantum processes in the early Universe involving fluctuations, vacuum instability, and phase transition phenomena as well as the nonequilibrium thermodynamics of black holes. It is also essential to an understanding of the transition from any quantum theory of gravity to classical general relativity.

Primordial magnetic fields induced by cosmological particle creation

We study the primordial magnetic field generated by stochastic currents produced by scalar charged particles created at the beginning of the radiation dominated epoch. We find that, for the mass range

Chaos around a black hole

{10}^{\ensuremath{-}6} \mathrm{GeV}\ensuremath{\lesssim}m\ensuremath{\lesssim}{10}^{2} \mathrm{GeV}

Nonequilibrium dynamics of optical-lattice-loaded Bose-Einstein-condensate atoms: Beyond the Hartree-Fock-Bogoliubov approximation

, a field of sufficient intensity to seed different mechanisms of galactic magnetic field generation, while still consistent with observational and theoretical constraints, is created coherently over a galactic scale.

Stochastic description for open quantum systems

The authors apply the Melnikov method for identifying chaos in near integrable systems to relativistic particle motion around a Schwarzschild black hole. They start by giving a self-contained introduction to the Melnikov method together with some relevant background on dynamical systems. Then they show that a relativistic particle was unstable circular orbits around a Schwarzschild black hole, and that each one of these gives rise to a homoclinic orbit in phase space, which tends to the unstable one for t to +or- infinity . Finally, the authors use the Melnikov method to conclude that, under most periodic perturbations of the black-hole metric, the homoclinic orbit becomes chaotic.

Coarse-grained effective action and renormalization group theory in semiclassical gravity and cosmology

In this work a two-particle irreducible (2PI) closed-time-path (CTP) effective action is used to describe the nonequilibrium dynamics of a Bose Einstein condensate (BEC) selectively loaded into every third site of a one-dimensional optical lattice. The motivation of this work is the recent experimental realization of this system at National Institute of Standards and Technology (NIST) where the placement of atoms in an optical lattice is controlled by using an intermediate superlattice. This patterned loading method is a useful technique for the proposed implementation of lattice-based AMO quantum computing. This system also serves to illustrate many basic issues in nonequilibrium quantum field theory pertaining to the dynamics of quantum correlations and fluctuations which goes beyond the capability of a mean field theory. By numerically evolving in time the initial state configuration using the Bose-Hubbard Hamiltonian an exact quantum solution is available for this system in the case of few atoms and wells. One can also use it to test out the various approximation methods constructed. Under the 2PI CTP scheme with this initial configuration, three different approximations are considered: a) the Hartree-Fock-Bogoliubov (HFB) approximation, b) the next-to-leading order 1/N expansion of the 2PI effective action up to second order in the interaction strength and c) a second order perturbative expansion in the interaction strength. We present detailed comparisons between these approximations and determine their range of validity by contrasting them with the exact many body solution for a moderate number of atoms and wells. As a general feature we observe that because the second order 2PI approximations include multi-particle scattering in a systematic way, they are able to capture damping effects exhibited in the exact solution that a mean field collisionless approach fails to produce. While the second order approximations show a clear improvement over the HFB approximation our numerical result shows that they do not work so well at late times, when interaction effects are significant. 1 Description of the Problem Bose-Einstein condensate (BEC) loaded into an optical lattice has provided an interesting arena for the study of quantum coherence and fluctuation phenomena in many body physics. Spectacular progress in experimental studies have been able to achieve regimes where standard mean field techniques used to describe weakly interacting atoms are not generally applicable. The description of the evolution of condensates far from equilibrium has also gained considerable importance in matter-wave physics, motivated by recent experimental realization of colliding and …

Stochastic dynamics of correlations in quantum field theory: From the Schwinger-Dyson to Boltzmann-Langevin equation

A linear quantum Brownian motion model with a general spectral density function is considered. In the framework of the influence functional formalism, a Langevin equation can be introduced to describe the systems fully quantum properties even beyond the semiclassical regime. In particular, we show that the reduced Wigner function for the system can be formally written as a double average over both the initial conditions and the stochastic source of the Langevin equation. This is exploited to provide a derivation of the master equation for the reduced density matrix alternative to those existing in the literature. Furthermore, we prove that all the correlation functions obtained in the context of the stochastic description associated to the Langevin equation actually correspond to quantum correlation functions for system observables. In doing so, we also compute the closed time path generating functional of the open system.

Cosmological magnetic fields from gauge-mediated supersymmetry-breaking models

In this report we introduce the basic techniques (of the closed-time-path (CTP) coarse-grained effective action (CGEA)) and ideas (scaling, coarse-graining and backreaction) behind the treatment of quantum processes in dynamical background spacetimes and fields. We show how they are useful for the construction of renormalization group (RG) theories for studying these nonequilibrium processes and discuss the underlying issues. Examples are drawn from quantum field processes in an inflationary universe, semiclassical cosmology and stochastic gravity. In Part I (Sections 2, 3) we begin by establishing a relation between scaling and inflation, and show how eternal inflation (where the scale factor of the universe grows exponentially) can be treated as static critical phenomena, while a ‘slow-roll’ or power-law inflation can be treated as dynamical critical phenomena. In Part II (Sections 4, 5) we introduce the key concepts in open systems and discuss the relation of coarse-graining and backreaction. We recount how the (in-out, or Schwinger–DeWitt) CGEA devised by Hu and Zhang can be used to treat some aspects of the effects of the environment on the system. This is illustrated by the stochastic inflation model where quantum fluctuations appearing as noise backreact on the inflaton field. We show how RG techniques can be usefully applied to obtain the running of coupling constants in the inflaton field, followed by a discussion of the cosmological and theoretical implications. In Part III (Sections 6–8) we present the CTP (in–in, or Schwinger–Keldysh) CGEA introduced by Hu and Sinha. We show how to calculate perturbatively the CTP CGEA for the λΦ4 model. We mention how it is useful for calculating the backreaction of environmental fields on the system field (e.g. light on heavy, fast on slow) or one sector of a field on another (e.g. high momentum modes on low, inhomogeneous modes on homogeneous), and problems in other areas of physics where this method can be usefully applied. This is followed by an introduction to the influence functional in the (Feynman–Vernon) formulation of quantum open systems, illustrated by the quantum Brownian motion models. We show its relation to the CTP CGEA, and indicate how to identify the noise and dissipation kernels therein. We derive the master and Langevin equations for interacting quantum fields, represented in the works of Lombardo and Mazzitelli and indicate how they can be applied to the problem of coarse-graining, decoherence and structure formation in de Sitter universe. We perform a nonperturbative evaluation of the CTP CGEA and show how to derive the renormalization group equations under an adiabatic approximation adopted for the modes by Dalvit and Mazzitelli. We assert that this approximation is incomplete as the effect of noise is suppressed. We then discuss why noise is expected in the RG equations for nonequilibrium processes. In Part IV (Sections 9, 10), following Lombardo and Mazzitelli, we use the RG equations to derive the Einstein–Langevin equation in stochastic semiclassical gravity. As an example, we calculate the quantum correction to the Newtonian potential. We end with a discussion on why a stochastic component of RG equations is expected for nonequilibrium processes.

Relativistic fluctuating hydrodynamics

The aim of this paper is twofold: to probe the statistical mechanical properties of interacting quantum fields, and to provide a field theoretical justification for a stochastic source term in the Boltzmann equation. We start with the formulation of quantum field theory in terms of the set of Schwinger-Dyson equations for the correlation functions, which we describe by a closed-time-path master

Semiclassical effects and the onset of inflation

(n=\ensuremath{\infty}\mathrm{PI})