arXiv subjects

H. J. de Vega

Publications and source records attributed to H. J. de Vega.

At least 109 records · Page 6Linked to original sources

arXiv1999

Dynamics of Symmetry Breaking in FRW Cosmologies: Emergence of Scaling

The dynamics of a symmetry breaking phase transition is studied in a radiation and matter dominated spatially flat FRW cosmology in the large N limit of a scalar field theory.The quantum density matrix is evolved from an initial state of quasiparticles in thermal equilibrium at a temperature higher than the critical. The cosmological expansion decreases the temperature and triggers the phase transition. We identify three different time scales: an early regime dominated by linear instabilities and the exponential growth of long-wavelength fluctuations,an intermediate scale when the field fluctuations probe the broken symmetry states and an asymptotic scale wherein a scaling regime emerges for modes of wavelength comparable to or larger than the horizon.The scaling regime is characterized by a dynamical physical correlation length xi_{phys} = d_H(t) with d_H(t) the size of the causal horizon, thus there is one correlated region per causal horizon. Inside these correlated regions the field fluctuations sample the broken symmetry states. The amplitude of the long-wavelength fluctuations becomes non-perturbatively large due to the early times instabilities and a semiclassical but stochastic description emerges in the asymptotic regime. In the scaling regime, the power spectrum is peaked at zero momentum revealing the onset of a Bose-Einstein condensate.The scaling solution results in that the equation of state of the scalar fields is the same as that of the background fluid. This implies a Harrison-Zeldovich spectrum of scalar density perturbations for long-wavelengths. We discuss the corrections to scaling as well as the universality of the scaling solution and the differences and similarities with the classical non-linear sigma model.

hep-ph↗

arXiv1999

Dynamics of Symmetry Breaking Out of Equilibrium: From Condensed Matter to QCD and the Early Universe

The dynamics of symmetry breaking during out of equilibrium phase transitions is a topic of great importance in many disciplines, from condensed matter to particle physics and early Universe cosmology with definite experimental impact. In these notes we provide a summary of the relevant aspects of the dynamics of symmetry breaking in many different fields with emphasis on the experimental realizations. In condensed matter we address the dynamics of phase ordering, the emergence of condensates, coarsening and dynamical scaling. In QCD the possibility of disoriented chiral condensates of pions emerging during a strongly out of equilibrium phase transition is discussed. We elaborate on the dynamics of phase ordering in phase transitions in the Early Universe, in particular the emergence of condensates and scaling in FRW cosmologies. We mention some experimental efforts in different fields that study this wide ranging phenomena and offer a quantitative theoretical description both at the phenomenological level in condensed matter, introducing the scaling hypothesis as well as at a microscopic level in quantum field theories. The emergence of semiclassical condensates and a dynamical length scale is shown in detail, in quantum field theory this length scale is constrained by causality. The large N limit provides a natural bridge to compare the solutions in different settings and to establish similarities and differences.

hep-ph↗

arXiv1999

Initial Time Singularities in Non-Equilibrium Evolution of Condensates and Their Resolution in the Linearized Approximation

The real time non-equilibrium evolution of condensates in field theory requires an initial value problem specifying an initial quantum state or density matrix. Arbitrary specifications of the initial quantum state (pure or mixed) results in initial time singularities which are not removed by the usual renormalization counterterms. We study the initial time singularities in the linearized equation of motion for the scalar condensate in a renormalizable Yukawa theory in 3+1 dimensions. In this renormalizable theory the initial time singularities are enhanced. We present a consistent method for removing these initial time singularities by specifying initial states where the distribution of high energy quanta is determined by the initial conditions and the interaction effects. This is done through a Bogoliubov transformation which is consistently obtained in a perturbative expansion.The usual renormalization counterterms and the proper choice of the Bogoliubov coefficients lead to a singularity free evolution equation. We establish the relationship between the evolution equations in the linearized approximation and linear response theory. It is found that only a very specific form of the external source for linear response leads to a real time evolution equation which is singularity free. We focus on the evolution of spatially inhomogeneous scalar condensates by implementing the initial state preparation via a Bogoliubov transformation up to one-loop. As a concrete application, the evolution equation for an inhomogenous condensate is solved analytically and the results are carefully analyzed. Symmetry breaking by initial quantum states is discussed.

hep-ph↗

arXiv1999

Non-Singular String-Cosmologies From Exact Conformal Field Theories

Non-singular two and three dimensional string cosmologies are constructed using the exact conformal field theories corresponding to SO(2,1)/SO(1,1) and SO(2,2)/SO(2,1). All semi-classical curvature singularities are canceled in the exact theories for both of these cosets, but some new quantum curvature singularities emerge. However, considering different patches of the global manifolds, allows the construction of non-singular spacetimes with cosmological interpretation. In both two and three dimensions, we construct non-singular oscillating cosmologies, non-singular expanding and inflationary cosmologies including a de Sitter (exponential) stage with positive scalar curvature as well as non-singular contracting and deflationary cosmologies. We analyse these cosmologies in detail with respect to the behaviour of the scale factors, the scalar curvature and the string-coupling. The sign of the scalar curvature is changed by the quantum corrections in oscillating cosmologies and evolves with time in the non-oscillating cases. Similarities between the two and three dimensional cases suggest a general picture for higher dimensional coset cosmologies: Anisotropy seems to be a generic unavoidable feature, cosmological singularities are generically avoided and it is possible to construct non-singular cosmologies where some spatial dimensions are experiencing inflation while the others experience deflation.

hep-th↗

arXiv1999

Dynamical renormalization group resummation of finite temperature infrared divergences

We introduce the method of dynamical renormalization group to study relaxation and damping out of equilibrium directly in real time and applied it to the study of infrared divergences in scalar QED. This method allows a consistent resummation of infrared effects associated with the exchange of quasistatic transverse photons and leads to anomalous logarithmic relaxation of the form $e^{-αT t \ln[t/t_0]}$ which prevents a quasiparticle interpretation of charged collective excitations at finite temperature. The hard thermal loop resummation program is incorporated consistently into the dynamical renormalization group yielding a picture of relaxation and damping phenomena in a plasma in real time that trascends the conceptual limitations of the quasiparticle picture and other type of resummation schemes. We derive a simple criterion for establishing the validity of the quasiparticle picture to lowest order.

hep-ph↗

arXiv1999

Non-equilibrium phase transitions in condensed matter and cosmology: spinodal decomposition, condensates and defects

These lectures address the dynamics of phase ordering out of equilibrium in condensed matter and in quantum field theory in cosmological settings, emphasizing their similarities and differences. In condensed matter we describe the phenomenological approach based on the Time Dependent Ginzburg-Landau (TDGL) description. After a general discussion of the main experimental and theoretical features of phase ordering kinetics and the description of linear (spinodal) instabilities we introduce the scaling hypothesis and show how a dynamical correlation length emerges in the large N limit in condensed matter systems. The large N approximation is a powerful tool in quantum field theory that allows the study of non-perturbative phenomena in a consistent manner. We study the exact solution to the dynamics after a quench in this limit in Minkowski space time and in radiation dominated Friedman-Robertson-Walker Cosmology. There are some remarkable similarities between these very different settings such as the emergence of a scaling regime and of a dynamical correlation length at late times that describe the formation and growth of ordered regions. In quantum field theory and cosmology this length scale is constrained by causality and its growth in time is also associated with coarsening and the onset of a condensate. We provide a density matrix interpretation of the formation of defects and the classicalization of quantum fluctuations.

hep-ph↗

arXiv1999

Non-Equilibrium Bose-Einstein Condensates, Dynamical Scaling and Symmetric Evolution in large N Phi^4 theory

We analyze the non-equilibrium dynamics of the O(N) Phi^4 model in the large N limit and for states of large energy density. The dynamics is dramatically different when the energy density is above the top of the tree level potential V_0 than when it is below it.When the energy density is below V_0, we find that non-perturbative particle production through spinodal instabilities provides a dynamical mechanism for the Maxwell construction. The asymptotic values of the order parameter only depend on the initial energy density and all values between the minima of the tree level potential are available, the asymptotic dynamical `effective potential' is flat between the minima. When the energy density is larger than V_0, the evolution samples ergodically the broken symmetry states, as a consequence of non-perturbative particle production via parametric amplification. Furthermore, we examine the quantum dynamics of phase ordering into the broken symmetry phase and find novel scaling behavior of the correlation function. There is a crossover in the dynamical correlation length at a time scale t_s \sim \ln(1/lambda). For t < t_s the dynamical correlation length ξ(t) \propto \sqrt{t} and the evolution is dominated by spinodal instabilities, whereas for t>t_s the evolution is non-linear and dominated by the onset of non-equilibrium Bose-Einstein condensation of long-wavelength Goldstone bosons.In this regime a true scaling solution emerges with a non- perturbative anomalous scaling length dimension z=1/2 and a dynamical correlation length ξ(t) \propto (t-t_s). The equal time correlation function in this scaling regime vanishes for r>2(t-t_s) by causality. For t > t_s the equal time correlation function falls of as 1/r. A semiclassical but stochastic description emerges for time scales t > t_s.

hep-ph↗

arXiv1999

Fermion Damping in a Fermion-Scalar Plasma

In this article we study the dynamics of fermions in a fermion-scalar plasma. We begin by obtaining the effective in-medium Dirac equation in real time which is fully renormalized and causal and leads to the initial value problem. For a heavy scalar we find the novel result that the decay of the scalar into fermion pairs in the medium leads to damping of the fermionic excitations and their in-medium propagation as quasiparticles. That is, the fermions acquire a width due to the decay of the heavier scalar in the medium. We find the damping rate to lowest order in the Yukawa coupling for arbitrary values of scalar and fermion masses, temperature and fermion momentum. An all-order expression for the damping rate in terms of the exact quasiparticle wave functions is established. A kinetic Boltzmann approach to the relaxation of the fermionic distribution function confirms the damping of fermionic excitations as a consequence of the induced decay of heavy scalars in the medium. A linearization of the Boltzmann equation near equilibrium clearly displays the relationship between the damping rate of fermionic mean fields and the fermion interaction rate to lowest order in the Yukawa coupling directly in real time.

hep-ph↗

arXiv1998

Renormalization Group Flow and Fragmentation in the Self-Gravitating Thermal Gas

The self-gravitating thermal gas (non-relativistic particles of mass m at temperature T) is exactly equivalent to a field theory with a single scalar field phi(x) and exponential self-interaction. We build up perturbation theory around a space dependent stationary point phi_0(r) in a finite size domain delta \leq r \leq R ,(delta << R), which is relevant for astrophysical applica- tions (interstellar medium,galaxy distributions).We compute the correlations of the gravitational potential (phi) and of the density and find that they scale; the latter scales as 1/r^2. A rich structure emerges in the two-point correl- tors from the phi fluctuations around phi_0(r). The n-point correlators are explicitly computed to the one-loop level.The relevant effective coupling turns out to be lambda=4 pi G m^2 / (T R). The renormalization group equations (RGE) for the n-point correlator are derived and the RG flow for the effective coupling lambda(tau) [tau = ln(R/delta), explicitly obtained.A novel dependence on tau emerges here.lambda(tau) vanishes each time tau approaches discrete values tau=tau_n = 2 pi n/sqrt7-0, n=0,1,2, ...Such RG infrared stable behavior [lambda(tau) decreasing with increasing tau] is here connected with low density self-similar fractal structures fitting one into another.For scales smaller than the points tau_n, ultraviolet unstable behaviour appears which we connect to Jeans' unstable behaviour, growing density and fragmentation. Remarkably, we get a hierarchy of scales and Jeans lengths following the geometric progression R_n=R_0 e^{2 pi n /sqrt7} = R_0 [10.749087...]^n . A hierarchy of this type is expected for non-spherical geometries,with a rate different from e^{2 n/sqrt7}.

astro-ph↗

arXiv1998

Generation of gravitational waves by generic sources in de Sitter space-time

We study the generation of gravitational radiation by sources moving in the de Sitter background. Exploiting the maximal symmetry and the conformal flatness of de Sitter space-time we prove that the derivation of this gravitational radiation can be done along the same lines as in Minkowski space-time. A gauge is chosen in which all the physical and unphysical modes of the graviton are those of a minimally coupled massless scalar field in de Sitter space-time and a massless field in Minkowski space-time. The graviton retarded Green's function and the Schwinger commutator function are computed in this gauge using Quantum Field Theory techniques. We obtain closed formulae for the spectral decomposition in frequencies of the linaearized gravitational field produced by the source, in terms of a suitable spectral decomposition of the source energy-momentum tensor. This spectral decomposition is dictated by the free (sourceless) gravitational wave modes in the de Sitter background

astro-ph↗

arXiv1998

Anomalous Kinetics of Hard Charged Particles: Dynamical Renormalization Group Resummation

We study the kinetics of the distribution function for charged particles of hard momentum in scalar QED. The goal is to understand the effects of infrared divergences associated with the exchange of quasistatic magnetic photons in the relaxation of the distribution function. We begin by obtaining a kinetic transport equation for the distribution function for hard charged scalars in a perturbative expansion that includes hard thermal loop resummation. Solving this transport equation, the infrared divergences arising from absorption and emission of soft quasi-static magnetic photons are manifest in logarithmic secular terms. We then implement the dynamical renormalization group resummation of these secular terms in the relaxation time approximation. The distribution function (in the linearized regime) is found to approach equilibrium as $δn_k(t) =δn_k(t_o) e^{-2αT (t-t_o) \ln[(t-t_o)\barμ]}$, with $\barμ\approx ω_p$ the plasma frequency and $α=e^2/4π$. This anomalous relaxation is recognized to be the square of the relaxation of the single particle propagator, providing a generalization of the usual relation between the damping and the interaction rate. The renormalization group approach to kinetics reveals clearly the time scale $t_{rel} \approx (αT \ln[1/α])^{-1}$ arising from infrared physics and hinges upon the separation of scales $t_{rel} >>ω_p^{-1}$.

hep-ph↗

arXiv1998

Quantum kinetics and thermalization in a particle bath model

We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and Non-Markovian quantum kinetics. There are two different cases that are studied in detail: i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and ii) a stable renormalized `particle' state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.

cond-mat↗

arXiv1998

Non-Equilibrium Real-Time Dynamics of Quantum Fields: Linear and Non-Linear Relaxation in Scalar and Gauge Theories

The real time evolution of field condensates is solved for small and large field amplitudes in scalar theories.For small amplitudes,the quantum equations of motion for the condensate can be linearized and solved by Laplace transform. The late time evolution turns to be determined by the singularities in the complex plane (one-particle poles, two- and multi- particle cuts, Landau cuts for non-zero initial temperature). In hot scalar electrodynamics, we solve the real time evolution of field condensates with soft length scales \sim k^{-1}>(eT)^{-1}. Transverse gauge invariant condensates relax as 1/t^2 to amplitudes determined by the quasiparticle poles. We rederive the HTL action using the non-equilibrium field theory techniques.In the nonlinear regime (for large initial energy densities) we analyze the dynamics of dissipation and relaxation in scalar theory after linear unstabilities are shut-off by the quantum back-reaction. A new time scale emerges that separates the linear from the non-linear regimes. This scale is non-perturbative in the coupling and initial amplitude. A combination of numerical analysis and the implementation of a dynamical renormalization group resummation via multi-time scale analysis reveals the presence of unstable bands in the nonlinear regime. These are associated with power law growth of quantum fluctuations, that result in power law relaxation and dissipation with {\bf non-universal and non-perturbative dynamical anomalous exponents.

hep-ph↗

arXiv1998

Fractal Structures and Scaling Laws in the Universe: Statistical Mechanics of the Self-Gravitating Gas

Fractal structures are observed in the universe in two very different ways. Firstly, in the gas forming the cold interstellar medium in scales from 10^{-4} pc till 100 pc. Secondly, the galaxy distribution has been observed to be fractal in scales up to hundreds of Mpc. We give here a short review of the statistical mechanical (and field theoretical) approach developed by us. We consider a non-relativistic self-gravitating gas in thermal equilibrium at temperature T inside a volume V. The statistical mechanics of such system has special features and, as is known, the thermodynamical limit does not exist in its customary form. Moreover, the treatments through microcanonical, canonical and grand canonical ensembles yield different results.We present here for the first time the equation of state for the self-gravitating gas in the canonical ensemble. We find that it has the form p = [N T/ V] f(eta), where p is the pressure, N is the number of particles and η\equiv {G m^2 N \over V^{1/3} T}. The N \to\infty and V \to\infty limit exists keeping ηfixed. We compute the function f(η) using Monte Carlo simulations and for small eta analytically. We compute the thermodynamic quantities of the system as free energy, entropy, chemical potential, specific heat, compressibility and speed of sound. We reproduce the well-known gravitational phase transition associated to the Jeans' instability. Namely, a gaseous phase for eta < eta_c and a condensed phase for eta > eta_c. Moreover, we derive the precise behaviour of the physical quantities near the transition. In particular, the pressure vanishes as p \sim(eta_c-eta)^B with B \sim 0.2 and eta_c \sim 1.6 and the energy fluctuations diverge as \sim(eta_c-eta)^{B-1}. The speed of sound decreases monotonically and approaches the value sqrt{T/6} at the transition.

astro-ph↗

arXiv1998

Quantum kinetics and thermalization in an exactly solvable model

We study the dynamics of relaxation and thermalization in an exactly solvable model with the goal of understanding the effects of off-shell processes. The focus is to compare the exact evolution of the distribution function with different approximations to the relaxational dynamics: Boltzmann, non-Markovian and Markovian quantum kinetics. The time evolution of the distribution function is evaluated exactly using two methods: time evolution of an initially prepared density matrix and by solving the Heisenberg equations of motion. There are two different cases that are studied in detail: i) no stable particle states below threshold of the bath and a quasiparticle resonance above it and ii) a stable discrete exact `particle' state below threshold. For the case of quasiparticles in the continuum (resonances) the exact quasiparticle distribution asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes. In the case ii), the distribution of particles does not thermalize with the bath. We study the kinetics of thermalization and relaxation by deriving a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian and Boltzmann approximations are compared to the exact result of the model. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.

hep-ph↗

arXiv1998

Evolution of Inhomogeneous Condensates: Self-consistent Variational Approach

We establish a self-consistent variational framework that allows us to study numerically the non-equilibrium evolution of non-perturbative inhomogeneous field configurations including quantum backreaction effects. After discussing the practical merits and disadvantages of different approaches we provide a closed set of local and renormalizable update equations that determine the dynamical evolution of inhomogeneous condensates and can be implemented numerically. These incorporate self-consistently the backreaction of quantum fluctuations and particle production. This program requires the solution of a self-consistent inhomogeneous problem to provide initial Cauchy data for the inhomogeneous condensates and Green's functions. We provide a simple solvable ansatz for such an initial value problem for the Sine-Gordon and phi^4 quantum field theories in one spatial dimension. We compare exact known results of the Sine Gordon model to this simple ansatz. We also study the linear sigma model in the large N limit in three spatial dimensions as a microscopic model for pion production in ultrarelativistic collisions. We provide a solvable self- consistent ansatz for the initial value problem with cylindrical symmetry. For this case we also obtain a closed set of local and renormalized update equations that can be numerically implemented. A novel phenomenon of spinodal instabilities and pion production arises as a result of a Klein paradox for large amplitude inhomogeneous condensate configurations.

hep-ph↗

arXiv1998

Quantum String Dynamics in the conformal invariant SL(2,R) WZWN Background: Anti-de Sitter Space with Torsion

We consider classical and quantum strings in the conformally invariant background corresponding to the SL(2,R) WZWN model. This background is locally anti-de Sitter spacetime with non-vanishing torsion. Conformal invariance is expressed as the torsion being parallelized. The precise effect of the conformal invariance on the dynamics of both circular and generic classical strings is extracted. In particular, the conformal invariance gives rise to a repulsive interaction of the string with the background which precisely cancels the dominant attractive term arising from gravity. We perform both semi-classical and canonical string-quantization, in order to see the effect of the conformal invariance of the background on the string mass spectrum. Both approaches yield that the high-mass states are governed by m sim HN (N,`large integer'), where m is the string mass and H is the Hubble constant. It follows that the level spacing grows proportionally to N: d(m^2 alpha')/dN sim N, while the entropy goes like: S sim sqrt{m}. Moreover, it follows that there is no Hagedorn temperature,so that the partition function is well defined at any positive temperature. All results are compared with the analogue results in Anti- de Sitter spacetime, which is a non conformal invariant background. Conformal invariance simplifies the mathematics of the problem but the physics remains mainly unchanged. Differences between conformal and non-conformal backgrounds only appear in the intermediate region of the string spectrum, but these differences are minor. For low and high masses, the string mass spectra in conformal and non-conformal backgrounds are identical. Interestingly enough, conformal invariance fixes the value of the spacetime curvature to be -69/(26 alpha').

hep-th↗

arXiv1998

Fractal Dimensions and Scaling Laws in the Interstellar Medium and Galaxy Distributions: a new Field Theory Approach

We develop a field theoretical approach to the cold interstellar medium (ISM) and large structure of the universe. We show that a non-relativistic self- gravitating gas in thermal equilibrium with variable number of atoms or fragments is exactly equivalent to a field theory of a scalar field phi(x) with exponential self-interaction. We analyze this field theory perturbatively and non-perturbatively through the renormalization group(RG).We show scaling behaviour (critical) for a continuous range of the physical parameters as the temperature. We derive in this framework the scaling relation M(R) \sim R^{d_H} for the mass on a region of size R, and Delta v \sim R^\frac12(d_H -1) for the velocity dispersion. For the density-density correlations we find a power-law behaviour for large distances \sim |r_1 - r_2|^{2D - 6}.The fractal dimension D turns to be related with the critical exponent νby D = 1/ ν. Mean field theory yields ν= 1/2, D = 2. Both the Ising and the mean field values are compatible with the present ISM observational data:1.4\leq D \leq 2. We develop a field theoretical approach to the galaxy distribution considering a gas of self-gravitating masses on the FRW background, in quasi-thermal equi- librium. We show that it exhibits scaling behaviour by RG methods. The galaxy correlations are computed without assuming homogeneity. We find <ρ({\vec r_0})ρ({\vec r_0} + {\vec r}) > \sim r^{D-3} $. The theory allows to compute the three and higher density correlators without any assumption.We find that the connected N-points density scales as r_1^{N(D-3)}, when $ r_1 >> r_i, 2\leq i \leq N $. There are no free parameters in this theory.

astro-ph↗