We study the dynamics of phase transitions out of equilibrium in weakly coupled scalar field theories. We consider the case in which there is a rapid supercooling from an initial symmetric phase in thermal equilibrium at temperature T i > T c to a final state at low temperature T f ≈ 0. In particular we study the formation and growth of correlated domains out of equilibrium. It is shown that the dynamics of the process of domain formation and growth (spinodal decomposition) cannot be studied in perturbation theory, and a non-perturbative self-consistent Hartree approximation is used to study the long time evolution. We find in weakly coupled theories that the size of domains grow at long times as ξ D (t) ≈ tξ(0). The size of the domains and the amplitude of the fluctuations grow up to a maximum time t s which in weakly coupled theories is estimated to bewith ξ(0) the zero temperature correlation length. For very weakly coupled the-1 ories, their final size is several times the zero temperature correlation length. For strongly coupled theories the final size of the domains is comparable to the zero temperature correlation length and the transition proceeds faster.

We apply the many-particle Schrödinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency -with a difference that depends on the internal structure of the object, and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot transferred from one object to another. Introduction and summary.-Testing non-relativistic quantum mechanics on macroscopic objects has has been a minor approach towards the search for effects of quantum gravity. Apart from the standard formulation of linearized quantum gravity [1], which seems rather implausible to test in the lab, several signatures have been conjectured: (i) gravity decoherence [2][3][4][5][6][7][8][9][10][11][12], where gravity introduces decoherence to macroscopic quantum superpositions; (ii) modifications to canonical quantization motivated by the existence of a minimum length scale [13][14][15], and (iii) semiclassical gravity [16][17][18], which will be the subject of this paper. As originally suggested by Møller [16] and Rosenfeld [17], spacetime structure might still remain classical even if it is sourced by matters of quantum nature, if we impose (G = c = 1):

Using the nonequilibrium quantum field theory, photon production from the coherently oscillating axion field in a flat Robertson-Walker cosmology is reexamined. First neglecting the Debye screening of the baryon plasma to photons, we find that the axions will dissipate into photons via spinodal instability in addition to parametric resonance. As a result of the pseudoscalar nature of the axion-photon coupling, we observe a circular polarization asymmetry in the photons produced. However, these effects are suppressed to an insignificant level in the expanding universe. We then briefly discuss a systematic way of including the plasma effect which can further suppress the photon production. We note that the formalism of the problem can be applied to any pseudoscalar field coupled to a photon in a thermal background in a general curved spacetime.PACS number͑s͒: 14.80. Mz, 95.35.ϩd, 98.80.Cq

We derive generalized two-superfluid continuity equations for the BEC-BCS crossover in the presence of a Feshbach resonance at T=0. In addition, we calculate the velocity of sound throughout both BCS and Bose-Einstein condensation (BEC) regimes.