Nonequilibrium quantum meson gas: Dimensional reduction

A nonequilibrium quantum gas of interacting relativistic effective mesons, ressembling qualitatively those produced in a heavy-ion collision, is described by a scalar quantum field in (1 + 3) -dimensional Minkowski space. For high temperature and large temporal and spatial scales, we justify that classical statistical mechanics including quantum renormalization effects describe approximately the gas: nonequilibrium dimensional reduction (NEDR). As a source of hints, we treat the gas at equilibrium in real-time formalism and obtain simplifications for high temperature and large spatial scales, thereby extending a useful equilibrium dimensional reduction known for the imaginary-time formalism. By assumption, the nonequilibrium initial state of the gas, not far from thermal equilibrium, includes interactions and inhomogeneities. We use nonequilibrium real-time generating functionals and correlators at nonzero temperature. In the NEDR regime, our arguments yield: 1) renormalized correlators simplify, 2) the perturbative series for those simplified correlators can be resummed into a new nonequilibrium generating functional, Z’ _{r, dr} , which is super-renormalizable and includes renormalization effects (large position-dependent thermal self-energies and effective couplings). Z’ _{r, dr} could enable to study nonperturbatively changes in the phase structures of the field, by proceeding from the nonequilibrium quantum regime to the NEDR one.     

Non-linear scission/recombination kinetics of living polymerization

Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M ^* (M^* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M ^* ≪ M ≪ M ^*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t₁, t₂, t₃ and t^*; 2) there are transient regimes (t ₁ ≲ t ≲ t ₃) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t₂. The chain growth is auto-accelerated for t ₁ ≲ t ≲ t ₂ : the cut-off chain length (= polymerization degree 〈n〉_w N ₁ ∝ t ² in this regime. 4) For t ₂ < t < t ₃ the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N₁ is decreasing with time in this regime, while the length scale N₂ of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^*, shows a sharp maximum in the vicinity of M^*; the effective exponent is as high as ∼ σ^-1/3 just above M^*.     

ℵ0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO(N) symmetry. We call these ℵ₀ (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ℵ₀ supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ℵ₀ globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ℵ₀ supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.     

Nonequilibrium quasi-classical effective meson gas

We treat a gas of interacting relativistic effective mesons (similar to those produced in a heavy-ion collision), regarded as a nonequilibrium statistical system. The large number of degrees of freedom gives rise to statistical features. We suppose large occupation numbers, temperature somewhat below typical critical temperatures and the quasi-classical regime. At the initial time t0, the gas is off-equilibrium. We analyze the time evolution of the quasi-classical effective meson gas for t>t₀ by using a new moment method. Long-time approximations, which could yield the approach to global thermal equilibrium, are presented.     

Thermal dileptons from quark and hadron phases of an expanding fireball

A fireball model with time evolution based on transport calculations is used to examine the dilepton emission rate of an ultra-relativistic heavy-ion collision. A transition from hadronic matter to a quark-gluon plasma at a critical temperature T _C between 130-170 MeV is assumed. We also consider a possible mixed phase scenario. We include thermal corrections to the hadronic spectra below T _C and use perturbation theory above T _C. The sensitivity of the spectra with respect to the freeze-out temperature, the initial fireball temperature and the critical temperature is investigated. Received: 4 August 2000 / Accepted: 14 November 2000     

MD simulation of concentrated polymer solutions: Structural relaxation near the glass transition

We examine by molecular dynamics simulations the relaxation of polymer-solvent mixtures close to the glass transition. The simulations employ a coarse-grained model in which polymers are represented by bead-spring chains and solvent particles by monomers. The interaction parameters between polymer and solvent are adjusted such that mixing is favored. We find that the mixtures have one glass transition temperature T _g or critical temperature T _c of mode-coupling theory (MCT). Both T _g and T _c (> T _g decrease with increasing solvent concentration . The decrease is linear for the concentrations studied (up to = 25%. Above T _c we explore the structure and relaxation of the polymer-solvent mixtures on cooling. We find that, if the polymer solution is compared to the pure polymer melt at the same T, local spatial correlations on the length scale of the first peak of the static structure factor S(q) are reduced. This difference between melt and solution is largely removed when comparing the S(q) of both systems at similar distance to the respective T _c. Near T _c we investigate dynamic correlation functions, such as the incoherent intermediate scattering function (t), mean-square displacements of the monomers and solvent particles, two non-Gaussian parameters, and the probability distribution P(ln r;t) of the logarithm of single-particle displacements. In accordance with MCT we find, for instance, that (t) obeys the time-temperature superposition principle and has relaxation times which are compatible with a power law increase close (but not too close) to T _c. In divergence to MCT, however, the increase of depends on the wavelength q, small q values having weaker increase than large ones. This decoupling of local and large-length scale relaxation could be related to the emergence of dynamic heterogeneity at low T. In the time window of the relaxation an analysis of P(ln r;t) reveals a double-peak structure close to T _c. The first peak correponds to “slow” particles (monomer or solvent) which have not moved much farther than 10% of their diameter in time t, whereas the second occurs at distances of the order of the particle diameter. These “fast” particles have succeeded in leaving their nearest-neighbor cage in time t. The simulation thus demonstrates that large fluctuations in particle mobility accompany the final structural relaxation of the cold polymer solution in the vicinity of the extrapolated T _c.     

Macroscopic Determinism in Noninteracting Systems Using Large Deviation Theory

We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the particle microstates is then examined in the large-n limit. Using the theory of large deviations, we show that if the initial macroscopic average is constrained to be near a given value, y, then the macroscopic average at time t converges in probability as n to a value _t(y) given explicitly in terms of a canonical expectation. Some general features of the graph of _t(y) versus t are examined, particularly in regard to continuity, symmetry, and convergence.     

Compression properties of finite nuclei in a semi-classical relativistic approach

Skyrme type potentials are known to lead — in the framework of the scaling model — to a finite-nucleus incompressibility valueK _A where the volume coefficientK _v equals roughly the negative surface coefficient K_s. This is found for Skyrme interactions with K_v between 200 and 360 MeV. In a semi-classical relativistic approach on the basis of the — model (linear as well as non-linear) using in addition local density approximations, we findK _s to depend in particular on the surface energy coefficienta _s , and not so much on the value ofK _v . For a realistic value of a_s, both the linear and the non-linear — model (with NL1 parameter set) yield a ratio ¦K _s K _v ¦ of approximately 1. We discuss implications of this finding with a particular view on recent empirical results onK _v andK _s .Dedicated to Prof. Dr. H. J. Mang on the occasion of his 60th birthday     

Macroscopic Determinism in Interacting Systems Using Large Deviation Theory

We consider the quasi-deterministic behavior of systems with a large number, n, of deterministically interacting constituents. This work extends the results of a previous paper [J. Statist. Phys. 99:1225–1249 (2000)] to include vector-valued observables on interacting systems. The approach used here, however, differs markedly in that a level-1 large deviation principle (LDP) on joint observables, rather than a level-2 LDP on empirical distributions, is employed. As before, we seek a mapping _t on the set of (possibly vector-valued) macrostates such that, when the macrostate is given to be a ₀ at time zero, the macrostate at time t is _t (a ₀) with a probability approaching one as n tends to infinity. We show that such a map exists and derives from a generalized dynamic free energy function, provided the latter is everywhere well defined, finite, and differentiable. We discuss some general properties of _t relevant to issues of irreversibility and end with an example of a simple interacting lattice, for which an exact macroscopic solution is obtained.     

Schwinger mechanism for gluon-pair production in the presence of arbitrary time-dependent chromo-electric field

We study the Schwinger mechanism for gluon-pair production in the presence of an arbitrary time-dependent chromo-electric background field E ^a (t) with arbitrary color index a=1,2,…,8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon-pair production per unit time per unit volume and per unit transverse momentum, , from arbitrary E ^a (t). We show that the tadpole (or single-gluon) effective action does not contribute to the non-perturbative gluon-pair production rate, . We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives , where n=1,2,…,∞, and that it has the same functional dependence on the two Casimir invariants, [E ^a (t)E ^a (t)] and [d _abc E ^a (t)E ^b (t)E ^c (t)]², as the constant chromo-electric field E ^a result with the replacement: E ^a →E ^a (t). This result relies crucially on the validity of the shift conjecture, which has not yet been established. This result may be relevant to the study of the production of a non-perturbative quark–gluon plasma at RHIC and LHC.     

Unconventional photoluminescence effect of SrTiO3 thin film under UV-illumination

We find that PL intensity I(t) of SrTiO₃ thin film measured under UHV condition increases with UV-laser illumination over long time scale of ∼ 2 h. The intensity increase takes place at lower sample temperature as well, 200, 100 K, and 20 K. When O₂ and N₂ gas are introduced into the sample chamber the PL intensity decreases with the UV-illumination time, opposite to the UHV-case. We consider a quantitative thermal energy flow model of the laser-power and heat absorption by the sample, but find that temperature change of the sample is not large enough to account for the time dependent I(t). We propose photo-catalysis effect on STO surface as possible scenario of the PL intensity change.     

Temporal correlations and persistence in the kinetic Ising model: the role of temperature

We study the statistical properties of the sum S _t = dt'σ _t', that is the difference of time spent positive or negative by the spin σ _t, located at a given site of a D-dimensional Ising model evolving under Glauber dynamics from a random initial configuration. We investigate the distribution of S_t and the first-passage statistics (persistence) of this quantity. We discuss successively the three regimes of high temperature ( T > T _c), criticality ( T = T _c), and low temperature ( T < T _c). We discuss in particular the question of the temperature dependence of the persistence exponent , as well as that of the spectrum of exponents (x), in the low temperature phase. The probability that the temporal mean S _t/t was always larger than the equilibrium magnetization is found to decay as t ^{- - ?}. This yields a numerical determination of the persistence exponent in the whole low temperature phase, in two dimensions, and above the roughening transition, in the low-temperature phase of the three-dimensional Ising model. Received 4 December 2000     

Coexistence of color superconductivity and chiral symmetry breaking within the NJL model

The phase diagram for quark matter is investigated within a simple Nambu-Jona-Lasinio model without vector correlations. It is found that the phase structure in the temperature-density plane depends sensitively on the parametrization of the model. We present two schemes of parametrization of the model where, within the first one, a first-order phase transition from a phase with broken chiral symmetry to a color superconducting phase for temperatures below the triple point at T _t = 55 MeV occurs, whereas for the second one a second-order phase transition for temperatures below T _t = 7 MeV is found. In the latter case, there is also a coexistence phase of broken chiral symmetry with color superconductivity, which is a new finding within this class of models. Possible consequences for the phenomenology of the QCD phase transition at high baryon densities are discussed. Received: 3 January 2003 / Accepted: 21 February 2003 / Published online: 24 April 2003     

The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T₀ only affects the relaxation up to T₀ + T_Lag, where T_Lag is proportional to the logarithm of the annealing time t_A. A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E = (317 + 1.17ξ)×10³ J/mol, and therefore must have a characteristic relaxation time τ which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t) = N(ξ)e^-t/τ(T,ξ)dξ, in which both the relaxation time τ(T,ξ) and the distribution function N(ξ) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.     

Dephasing in two decoupled one-dimensional Bose-Einstein condensates and the subexponential decay of the interwell coherence

We provide a simple physical picture of the loss of coherence between two coherently split one-dimensional Bose-Einstein condensates. The source of the dephasing is identified with nonlinear corrections to the elementary excitation energies in either of the two independent condensates. We retrieve the result by Burkov, Lukin and Demler [Phys. Rev. Lett. 98, 200404 (2007)] on the subexponential decay of the coherence ∝exp [-(t/t₀)^2/3] for the large time t, however, the scaling of t₀ differs.     

Reaction kinetics in polymer melts

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi [#!doi:inter2!#], de Gennes [#!gennes:polreactionsiandii!#], and Friedman and O'Shaughnessy [#!ben:interdil_all_aip!#], to arbitrary initial reactive group density n₀ and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, .For high Q, a transition occurs to diffusion-controlled (DC) kinetics with (where x_t is rms monomer displacement in time t) leading to a density decay . If n₀ exceeds the chain overlap threshold, this behavior is followed by a regime where during which k has the same power law dependence in time, , but possibly different numerical coefficient. For unentangled melts this gives while for entangled cases one or more of the successive regimes ,t ^-3/8 and t ^-3/4 may be realized depending on the magnitudes of Q and n₀. Kinetics at times longer than the longest polymer relaxation time are always MF. If a DC regime has developed before then the long time rate constant is where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis. Received: 2 June 1998 / Revised: 9 July 1998 / Accepted: 10 July 1998     

Polarized spectral properties of Pr3+ ions in NaGd(MO4)2 crystal

A Pr³⁺:NaGd(MoO₄)₂ single crystal has been grown by the Czochralski method. The polarized absorption spectra, polarized fluorescence spectra, and fluorescence decay curves of the crystal were measured at room temperature. The Judd–Ofelt intensity parameters Ω _t,q (t=2,4,6) and the spectroscopic parameters related to the ³ P ₀ and ¹ D ₂ multiplets were obtained and analyzed. The decay mechanisms for the ³ P ₀ and ¹ D ₂ multiplets were also discussed.     

Dynamical Correlation Functions for an Impenetrable Bose Gas with Neumann or Dirichlet Boundary Conditions

Abstract

We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions ψ(x ₁, 0)ψ ^?(x ₂ , t) _±,T . We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special case x ₁ = 0, we express correlation functions with Neumann boundary conditions ψ(0, 0)ψ ^?(x ₂ , t) _+,T , in terms of solutions of nonlinear partial differential equations which were introduced in [1] as a generalization of the nonlinear Schrödinger equations. We generalize the Fredholm minor determinant formulae of ground state correlation functions ψ(x ₁)ψ ^?(x ₂) _±,0 in [2], to the Fredholm determinant formulae for the time and temperature dependent correlation functions ψ(x ₁, 0)ψ ^?(x ₂ , t) _±,T , t ∈ R, T ≥ 0.     

A quantum long time energy red shift: a contribution to varying <Emphasis Type="Italic">α</Emphasis> theories

By analyzing the survival probability amplitude of an unstable state we show that the energy corrections to this state in the long (t→∞) and relatively short (lifetime of the state) time regions are different. It is shown that in the considered model the above corrections decrease to zero as t→∞. It is hypothesized that this property could be detected by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of possible deviations of the fine structure constant α as well as other astrophysical and cosmological parameters.