16548163
Uniformly Accelerated Charge in a Quantum Field: From Radiation Reaction to Unruh Effect
We present a stochastic theory for the nonequilibriurn dynamics of charges moving in a quantum scalar field based on the worldline influence functional and the close-time-path (CTP or in-in) coarse-grained effective action method. We summarize (1) the steps leading to a derivation of a modified Abraham-Lorentz-Dirac equation whose solutions describe a causal semiclassical theory free of runaway solutions and without pre-acceleration patholigies, and (2) the transformation to a stochastic effective action, which generates Abraham-Lorentz-Dirac-Langevin equations depicting the fluctuations of a particle’s worldline around its semiclassical trajectory. We point out the misconceptions in trying to directly relate radiation reaction to vacuum fluctuations, and discuss how, in the framework that we have developed, an array of phenomena, from classical radiation and radiation reaction to the Unruh effect, are interrelated to each other as manifestations at the classical, stochastic and quantum levels. Using this method we give a derivation of the Unruh effect for the spacetime worldline coordinates of an accelerating charge. Our stochastic particle-field model, which was inspired by earlier work in cosmological backreaction, can be used as an analog to the black hole backreaction problem describing the stochastic dynamics of a black hole event horizon.
22366791
Noise kernel in stochastic gravity and stress energy bitensor of quantum fields in curved spacetimes
The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bi-tensor which describes the fluctuations of a quantum field in curved spacetimes. It plays the role in stochastic semiclassical gravity based on the Einstein-Langevin equation similar to the expectation value of the stress-energy tensor in semiclassical gravity based on the semiclassical Einstein equation. According to the stochastic gravity program, this two point function (and by extension the higher order correlations in a hierarchy) of the stress energy tensor possesses precious statistical mechanical information of quantum fields in curved spacetime and, by the self-consistency required of Einstein's equation, provides a probe into the coherence properties of the gravity sector (as measured by the higher order correlation functions of gravitons) and the quantum nature of spacetime. It reflects the low and medium energy (referring to Planck energy as high energy) behavior of any viable theory of quantum gravity, including string theory. It is also useful for calculating quantum fluctuations of fields in modern theories of structure formation and for backreaction problems in cosmological and black holes spacetimes. 
We discuss the properties of this bi-tensor with the method of point-separation, and derive a regularized expression of the noise-kernel for a scalar field in general curved spacetimes. One collorary of our finding is that for a massless conformal field the trace of the noise kernel identically vanishes. We outline how the general framework and results derived here can be used for the calculation of noise kernels for Robertson-Walker and Schwarzschild spacetimes.
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.
17830761
Correlation entropy of an interacting quantum field and H theorem for the O(N) model
Following the paradigm of Boltzmann-BBGKY we propose a correlation entropy (of the nth order) for an interacting quantum field, obtained by `slaving' (truncation with causal factorization) of the higher (n+1 th) order correlation functions in the Schwinger-Dyson system of equations. This renders an otherwise closed system effectively open where dissipation arises. The concept of correlation entropy is useful for addressing issues related to thermalization. As a small yet important step in that direction we prove an H-theorem for the correlation entropy of a quantum mechanical O(N) model with a Closed Time Path Two Particle Irreducible Effective Action at the level of Next-to-Leading-Order large N approximation. This model may be regarded as a field theory in $0$ space dimensions.
118267306
Cosmology as `Condensed Matter' Physics
We note that in general there exist two basic aspects in any branch of physics, including cosmology - one dealing with the attributes of basic constituents and forces of nature, the other dealing with how structures arise from them and how they evolve. Current research in quantum and superstring cosmology is directed mainly towards the first aspect, even though a viable theory of the underlying interactions is lacking. We call the attention to the development of the second aspect, i.e., on the organization and processing of the basic constituents of matter (in classical cosmology) and spacetime (in quantum cosmology). Many newly developed concepts and techniques in condensed matter physics stemming from the investigation of disordered, dynamical and complex systems can guide us in asking the right questions and formulating new solutions to existing and developing cosmological issues, thereby broadening our view of the universe both in its formative and present state.
119407258
Quantum statistical processes in the early universe
We show how the concept of quantum open system and the methods in non-equilibrium statistical mechanics can be usefully applied to studies of quantum statistical processes in the early universe. We first sketch how noise, fluctuation, dissipation and decoherence processes arise in a wide range of cosmological problems. We then focus on the origin and nature of noise in quantum fields and spacetime dynamics. We introduce the concept of geometrodynamic noise and suggest a statistical mechanical definition of gravitational entropy. We end with a brief discussion of the theoretical appropriateness to view the physical universe as an open system.
120701054
Renormalization group study of the one dimensional quantum mechanical XY model
The one dimensional quantum mechanical XY model is studied by the renormalization group method. To second order in the cumulant expansion, no non-trivial fixed points are found. The calculated free energy is in excellent agreement with that of the exact solution.
119199048
Effective field theory of cosmic acceleration : An implementation in CAMB
We implement the effective field theory (EFT) approach to dark energy and modified gravity in the public Einstein-Boltzmann solver CAMB. The resulting code, which we dub EFTCAMB, is a powerful and versatile tool that can be used for several objectives. It can be employed to evolve the full dynamics of linear scalar perturbations in any given single field dark energy or modified gravity model, once the latter is mapped into the EFT formalism. It offers a numerical implementation of EFT as a model-independent framework to test gravity on cosmological scales. EFTCAMB has a built-in check for the fulfillment of general stability conditions such as the absence of ghost and superluminal propagation of perturbations. It handles phantom-divide crossing models and does not contain any quasi-static approximation, but rather evolves the full dynamics of perturbations on linear scales. As we will show, the latter is an important feature in view of the accuracy and scale range of upcoming surveys. We show the reliability and applicability of our code by evolving the dynamics of linear perturbations and extracting predictions for power spectra in several models. In particular we perform a thorough analysis of f(R) theories, comparing our outputs with those of an existing code for LCDM backgrounds, and finding an agreement that can reach 0.1% for models with a Compton wavelength consistent with current cosmological data. We then showcase the flexibility of our code studying two different scenarios. First we produce new results for designer f(R) models with a time-varying dark energy equation of state. Second, we extract predictions for linear observables in some parametrized EFT models with a phantom-divide crossing equation of state for dark energy.
121822978
The classical Ising model: A quantum renormalization group approach☆
Abstract Proceeding from the equivalence between the d -dimentional classical Ising model and the ( d −1)-dimentional quantum mechanical Ising model in a transverse magnetic field, we study the critical properties of the classical model via the quantum mechanical model. Quantum renormalization group transformations based on the truncation method and the ground state projection operator method are used to calculate the critical exponents. They are found to agree well with the “exact” values.
120519307
Introduction to real-space renormalization-group methods in critical and chaotic phenomena
Abstract The methods of the real-space renormalization group, and their application to critical and chaotic phenomena are reviewed. The article consists of two parts: the first part deals with phase transitions and critical phenomena; the second part, bifurcations and transitions to chaos. We begin with an introduction to the phenomenology of phase transitions and critical phenomena. Seminal concepts such as scaling and universality, and their characterization by critical exponents are discussed. The basic ideas of the renormalization group are then explained. A survey of real-space renormalization-group methods: decimation, Migdal-Kadanoff approximation, cumulant and cluster expansions, is given. The Hamiltonian formulation of classical statistical systems into quantum mechanical systems by the method of the transfer matrix is introduced. Quantum renormalization-group methods of truncation and projection, and their application to the transcribed quantum mechanical Ising model in a transverse field are illustrated. Finally, the quantum cumulant-expansion method as applied to the one-dimensional quantum mechanical XY model is discussed. The second part of the article is devoted to the subject of bifurcations and transitions to chaos. The three most commonly discussed kinds of bifurcations: the pitchfork, tangent and Hopf bifurcations, and the associated routes to chaos: period doubling, intermittency and quasiperiodicity are discussed. Period doubling based on the logistic map is explained in detail. Universality and its expression in terms of functional renormalization-group equations is discussed. The Liapunov characteristic exponent and its analogy to the order parameter are introduced. The effect of external noise and its universal scaling feature are shown. The simplest characterizations of the Henon strange attractor are intuitively illustrated. The purpose of this article is primarily pedagogical. The similarity between critical and chaotic phenomena is a recurrent theme that underlines the importance and usefulness of such concepts as scaling, renormalization and universality.
118029650
Future CMB integrated-Sachs-Wolfe-lensing bispectrum constraints on modified gravity in the parametrized post-Friedmann formalism
We forecast the constraints on both Hu-Sawicki model and Bertschinger-Zukin model of modified gravity within the Parameterized Post-Friedmann (PPF) formalism for the Planck satellite experiment by performing the joint analysis of ISW-Lensing bispectrum and CMB power spectrum. We find that, even considering the temperature-temperature mode of CMB power spectrum only, Planck data are expected to reduce the error bars on the modified gravity parameter $B_0$ (related to the present value of Compton wavelength of the extra scalar degree of freedom) at least one order magnitude compared with WMAP. The spectrum-bispectrum joint analysis can further improve the results by a factor ranging from 1.14 to 5.32 depending on the specific modified gravity model. One of our main results is that the cross-correlation between ISW-Lensing bispectrum and power spectrum can be safely neglected when performing the joint analysis. For simplicity, we only investigate the likelihood of one parameter ({$B_0$}) and fix all other cosmological parameters to their best-fit values in WMAP7yr results.