Stability of atomic condensed systems with attractive two-body interactions

In the present report, we review recent investigations that we have conducted on the stability of atomic condensed systems, when the two-body interaction is attractive. In particular, the dynamics that occurs in the condensate due to nonconservative terms is considered in the context of an extension of the mean-field Gross-Pitaevskii approximation. Considering the relative intensity of the nonconservative parameters, chaotic and solitonic solutions are verified. Also discussed is the possibility of a liquid-gas phase transition in the presence of positive three-body elastic collisions.

Atomic Bose-Einstein condensation with three-body interactions and collective excitations

The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schrodinger equation is extended to include an effective potential dependent on the square of the density and solved numerically for the s-wave. The lowest collective mode excitations are determined and their dependences on the number of atoms and on the strength of the three-body force are studied. The addition of three-body dynamics can allow the number of condensed atoms to increase considerably, even when the strength of the three-body force is very small compared with the strength of the two-body force. We study in detail the first-order liquid-gas phase transition for the condensed state, which can happen in a critical range of the effective three-body force parameter.

Quantum state density and critical temperature in M-theory

We discuss the asymptotic properties of quantum states density for fundamental p-branes which can yield a microscopic interpretation of the thermodynamic quantities in M-theory. The matching of the BPS part of spectrum for superstring and supermembrane gives the possibility of getting membrane's results via string calculations. In the weak coupling limit of M-theory, the critical behavior coincides with the first-order phase transition in the standard string theory at temperature less than the Hagedorn's temperature T-H. The critical temperature at large coupling constant is computed by considering M-theory on manifold with topology R-9 circle times T-2. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.

Can dissipation prevent explosive decomposition in high-energy heavy ion collisions?

We discuss the role of dissipation in the explosive spinodal decomposition scenario of hadron production during the chiral transition after a high-energy heavy ion collision. We use a Langevin description inspired by microscopic nonequilibrium field theory results to perform real-time lattice simulations of the behavior of the chiral fields. We show that the effect of dissipation can be dramatic. Analytic results for the short-time dynamics are also presented. (c) 2005 Elsevier B.V. All rights reserved.

Nonlinear Schrodinger equation with power-law confining potential

Critical limits of a stationary nonlinear three-dimensional Schrodinger equation with confining power-law potentials (similar to r(alpha)) are obtained using spherical symmetry. When the nonlinearity is given by an attractive two-body interaction (negative cubic term), it is shown how the maximum number of particles N-c in the trap increases as alpha decreases. With a negative cubic and positive quintic terms we study a first order phase transition, that occurs if the strength g(3) of the quintic term is less than a critical value g(3c). At the phase transition, the behavior of g(3c) with respect to alpha is given by g(3c)similar to 0.0036+0.0251/alpha+0.0088/alpha(2).

Short-time dynamics of percolation observables

We consider the critical short-time evolution of magnetic and droplet-percolation order parameters for the Ising model in two and three dimensions, through Monte Carlo simulations with the (local) heat-bath method. We find qualitatively different dynamic behaviors for the two types of order parameters. More precisely, we find that the percolation order parameter does not have a power-law behavior as encountered for the magnetization, but develops a scale (related to the relaxation time to equilibrium) in the Monte Carlo time. We argue that this difference is due to the difficulty in forming large clusters at the early stages of the evolution. Our results show that, although the descriptions in terms of magnetic and percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interpret percolation observables at short times. In particular, this concerns the attempts to describe the dynamics of the deconfinement phase transition in QCD using cluster observables.

Semiclassical particle spectrum of double sine-Gordon model

We present new theoretical results on the spectrum of the quantum field theory of the double sine-Gordon model. This non-integrable model displays different varieties of kink excitations and bound states thereof. Their mass can be obtained by using a semiclassical expression of the matrix elements of the local fields. In certain regions of the coupling-constants space the semiclassical method provides a picture which is complementary to the one of the form factor perturbation theory, since the two techniques give information about the mass of different types of excitations. In other regions the two methods are comparable, since they describe the same kind of particles. Furthermore, the semiclassical picture is particularly suited to describe the phenomenon of false vacuum decay, and it also accounts in a natural way the presence of resonance states and the occurrence of a phase transition. (C) 2004 Elsevier B.V. All rights reserved.

Dynamic critical behavior of percolation observables in the 2d Ising model

We present preliminary results of our numerical study of the critical dynamics of percolation observables for the two-dimensional Ising model. We consider the (Monte-Carlo) short-time evolution of the system obtained with a local heat-bath method and with the global Swendsen-Wang algorithm. In both cases, we find qualitatively different dynamic behaviors for the magnetization and Omega, the order parameter of the percolation transition. This may have implications for the recent attempts to describe the dynamics of the QCD phase transition using cluster observables.

A path integral approach to the full Dicke model with dipole-dipole interaction

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Applicability of the linear delta expansion for the lambda phi(4) field theory at finite temperature in the symmetric and broken phases

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Cubic interactions and quantum criticality in dimerized antiferromagnets

In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.

Finite-momentum condensate of magnetic excitons in a bilayer quantum Hall system

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Noise and ultraviolet divergences in the dynamics of the chiral condensate in QCD

The time evolution of the matter produced in high energy heavy-ion collisions seems to be well described by relativistic viscous hydrodynamics. In addition to the hydrodynamic degrees of freedom related to energy-momentum conservation, degrees of freedom associated with order parameters of broken continuous symmetries must be considered because they are all coupled to each other. of particular interest is the coupling of degrees of freedom associated with the chiral symmetry of QCD. Quantum and thermal fluctuations of the chiral fields act as noise sources in the classical equations of motion, turning them into stochastic differential equations in the form of Ginzburg-Landau-Langevin (GLL) equations. Analytic solutions of GLL equations are attainable only in very special circumstances and extensive numerical simulations are necessary, usually by discretizing the equations on a spatial lattice. However, a not much appreciated issue in the numerical simulations of GLL equations is that ultraviolet divergences in the form of lattice-spacing dependence plague the solutions. The divergences are related to the well-known Rayleigh-Jeans catastrophe in classical field theory. In the present communication we present a systematic lattice renormalization method to control the catastrophe. We discuss the implementation of the method for a GLL equation derived in the context of a model for the QCD chiral phase transition and consider the nonequilibrium evolution of the chiral condensate during the hydrodynamic flow of the quark-gluon plasma.

Memory effect and fast spinodal decomposition

We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. We then study the process of spinodal decomposition in fast phase transitions associated with a conserved order parameter. The introduced memory effect plays an important role to obtain a finite group velocity. Then, we discuss the constraint for the parameters to satisfy causality. The memory effect is seen to affect the dynamics of phase transition at short times and have the effect of delaying, in a significant way, the process of rapid growth of the order parameter that follows a quench into the spinodal region.

Anomalous diffusion of pions at RHIC

After pointing out the difference between normal and anomalous diffusion, we consider a hadron resonance cascade (HRC) model simulation for particle emission at RHIC and point out that rescattering in an expanding hadron resonance gas leads to a heavy tail in the source distribution. The results are compared to recent PHENIX measurements of the tail of the particle emitting source in Au+Au collisions at RHIC. In this context, we show how can one distinguish experimentally the anomalous diffusion of hadrons from a second order QCD phase transition.