204002791
Phase transitions in the early universe: geometric effects.
11606437
Fluctuation-dissipation relation for semiclassical cosmology.
Using the concept of open systems where the classical geometry is treated as the system and the quantum matter field as the environment, we derive a fluctuation-dissipation theorem for semiclassical cosmology. This theorem, which exists under very general conditions for dissipations in the dynamics of the system, and the noise and fluctuations in the environment, can be traced to the formal mathematical relation between the dissipation and noise kernels of the influence functional depicting the open system, and is ultimately a consequence of the unitarity of the closed system. In particular, for semiclassical gravity, it embodies the back reaction effect of matter fields on the dynamics of spacetime. The back reaction equation derivable from the influence action is in the form of an Einstein-Langevin equation. It contains a dissipative term in the equation of motion for the dynamics of spacetime and a noise term related to the fluctuations of particle creation in the matter field. Using the well-studied model of a quantum scalar field in a Bianchi type-I universe we illustrate how this Langevin equation and the noise term are derived and show how the creation of particles and the dissipation of anisotropy during the expansion of the Universe can be understood as a manifestation of this fluctuation-dissipation relation.
117521319
Gauge-invariant effective action for the dynamics of Bose-Einstein condensates with a fixed number of atoms
In this paper we present a particle-number-conserving (PNC) functional formalism to describe the dynamics of a cold bosonic gas. Treating the total number of particles as a constraint, whereby the phase invariance of the theory becomes local in time, we study this U(1) gauge theory using DeWitt's "gauge invariant effective action" techniques. Our functional formulation and earlier PNC proposals are shown to yield equivalent results to next-to-leading order in an expansion in the inverse powers of the total number of particles. In this more general framework we also show that earlier PNC proposals can be seen as different gauge (and gauge fixing condition) choices within the same physical theory.
16659491
Worldline Influence Functional: Abraham-Lorentz-Dirac-Langevin Equation from QED
We present a stochastic theory of charges moving in an electromagnetic field using nonequilibrium quantum field theory. We give a first principles' derivation of the Abraham-Lorentz-Dirac-Langevin equation which depicts the quantum expectation value for a particle's trajectory and its stochastic fluctuations by combining the worldline path integral quantization with the Feynman-Vernon influence functional or closed-time-path effective action methods. At lowest order, the equations of motion are approximated by a stochastic Lorentz-Dirac equation.
18511662
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.
118352317
GRAVITY AND NONEQUILIBRIUM THERMODYNAMICS OF CLASSICAL MATTER
Happy Birthday Mario, the philosopher, the king and the philosopher king! — This was explained in the first few slides of my talk at Mariofest. In an earlier, different occasion I had compared Mario, in his capacity of an inspiring mentor and a chief architect, in building up an eminent school of theoretical physics and astrophysics in Argentina, to my own Ph.D. advisor, the late Professor John Archibald Wheeler, in the USA. The nature of this meeting could perhaps allow me to also relate some of my past experience with Wheeler, and to pay homage to his influence on me in the same capacity as is done here by many young researchers, leaders in their own rights in different fields of physics and astrophysics, with Mario. So please forgive me if you find me delving at times into the past, referring to what I was thinking when I was a graduate student, some 40 years ago, on certain topics, some still of current interest. One of these ideas bears on the present theme of gravity in relation to thermodynamics, another on the philosophy I use for understanding it.
123376658
Power spectra of higher period multiplings in area-preserving maps
Abstract We have studied the power spectra of higher period p -multiplings for p = 3, 4, 5 and 6 in area-preserving maps. The ratio of the successive average heights of the peaks of the spectrum for each p -multiplying is found to approach a universal scaling limit that increases with p .
123516619
Nonanalytic twist maps and Frenkel-Kontorova models
We give a review of our recent works on a class of twist maps and Frenkel-Kontorova (FK) models in which the external potential function is nonanalytic (C1) and endowed with a variable degree of inflection z. When z > 3, recurrence of invariant curves has been observed. An “inverse residue criterion” for the reappearance of an invariant curve — complementary to the “residue criterion” for the disappearance of an invariant curve — is introduced to make a precise determination of the reappearance point. We have also studied the local and global scaling behaviors of these curves. The critical exponents, the singularity spectrum, and the generalized dimensions are found to vary with z when 2 ⩽ z < 3, but remain the same for z ⩾ 3. The degree of inflection thus plays a role reminiscent of that of dimensionality in phase transitions with z = 2 and 3 corresponding respectively to the lower and upper critical dimensions. When the same nonanalytic function is substituted for the sinusoidal external potential in the standard FK model, the same conclusions are reached: there exists a sequence of pinning-depinning transitions, and the critical exponents of the phonon gap, the coherence length, and the Peierls-Nabarro barrier all show the same dependence on z.
119185851
Timelike vector field dynamics in the early universe
We study the dynamics of a timelike vector field when the background spacetime is in an accelerating phase in the early universe. With a timelike vector field, an inflationary phase is shown to be difficult to realize, so we investigate the evolution of a vector field within a scalar field-driven inflation model. Also, we calculate the power spectrum of the vector field without considering the metric perturbations. While the time component of the vector field perturbations provides a scale invariant spectrum when ζ = 0, where ζ is a nonminimal coupling parameter, both the longitudinal and the transverse perturbations give a scale invariant spectrum when ζ = 1/6 in the absence of the coupling terms. The deviation of the power spectrum due to the coupling terms is calculated by use of the Greens’ function.
119229309
Non-Gaussian features from the inverse volume corrections in loop quantum cosmology
In this paper we study the non-Gaussian features of the primordial fluctuations in loop quantum cosmology with the inverse volume corrections. The detailed analysis is performed in the single field slow-roll inflationary models. However, our results reflect the universal characteristics of bispectrum in loop quantum cosmology. The main corrections to the scalar bispectrum come from two aspects: one is the modifications to the standard Bunch-Davies vacuum, and the other is the corrections to the background dependent variables, such as slow-roll parameters. Our calculations show that the loop quantum corrections make f(NL) of the inflationary models increase 0.1%. Moreover, we find that two new shapes of non-Gaussian signal arise, which we name F-1 and F-2. The former gives a unique loop quantum feature, which is less correlated with the local, equilateral, and single types, while the latter is highly correlated with the local one.
121564578
A two-dimensional scaling theory of intermittency
Abstract A two-dimensional scaling theory of intermittency in the presence of noise is modeled on tangent bifurcation of general area-preserving maps incorporating different universality classes. The two-dimensional functional renormalization group equations, and the associated eigenvalue equations describing deterministic and stochastic perturbations are derived. The complete eigenvalue spectra are found, and the scaling behavior of the length of laminarity is discussed.