Bose-Einstein condensation in relativistic field theories far from equilibrium

The formation of Bose condensates far from equilibrium can play an important role in our understanding of collision experiments of heavy nuclei or for the evolution of the early Universe. In the relativistic quantum world particle number changing processes can counteract Bose condensation, and there is a considerable debate about the relevance of this phenomenon in this context. We show that the involved question of Bose condensation from initial overpopulation can be answered for the example of scalar field theories. Condensate formation occurs as a consequence of an inverse particle cascade with a universal power-law spectrum. This particle transport towards low momenta is part of a dual cascade, in which energy is also transferred by weak wave turbulence towards higher momenta. To highlight the importance of number changing processes for the subsequent decay of the condensate, we also compare to nonrelativistic theories with exact number conservation. We discuss the relevance of these results for non-Abelian gauge theories.     

A thermodynamic variational principle in nonlinear systems far from equilibrium

The simplest viewpoint of nonlinear systems far from equilibrium suggests that the state of maximum entropy production is most stable among various possible metastable states under external perturbation for immobile boundaries, and that the shape with maximum increasing rate of entropy production is stabilized for mobile boundaries. Examples of computer simulation are demonstrated for a chemical structure and a growing random pattern.     

A model for symmetries in nonlinear transport

A model for a Rayleigh particle suspended in a rarefied gas in internal equilibrium is constructed. It is shown that the macroscopic evolution of this system can be described by using nonlinear unilateral transfer flows which are gradients of particular scalar functions. These functions are constructed according to a general theory of nonlinear irreversible processes proposed previously by van Kampen.     

The universe: A birth far from equilibrium?

The scientific world is, as I have often repeated, a shadow world, shadowing a world familiar to our consciousness. Just how much do we expect it to shadow? We do not expect it to shadow all that is in our mind, emotions, memory, etc. In the main we expect it to shadow impressions which can be traced to external sense organs. But time makes a dual entry and thus forms an intermediate link between the internal and the external. This is shadowed partially by the scientific world of primary physics (which excludes time's arrow), but fully when we enlarge the scheme to include entropy. Therefore by the momentous departure in the nineteenth century the scientific world is not confined to a static extension around which the mind may spin a romance of activity and evolution; it shadows that dynamic quality of the familiar world which cannot be parted from it without disaster to its significance.—Arthur Eddington,The Nature of the Physical World.     

Anomalous nucleation far from equilibrium

We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process, involving two species of particles driven in opposite directions on a 2xL lattice. To resolve a stark discrepancy between earlier simulation data and an analytic conjecture, we argue that the presence of a single macroscopic cluster is an intermediate stage of a complex nucleation process: in smaller systems, this cluster is destabilized while larger systems form multiple clusters. Both limits lead to exponential cluster size distributions, controlled by very different length scales.     

Anisotropic flow far from equilibrium

We compute analytically the anisotropic flow in an expanding mixture of several species of relativistic massive particles. We find that a single collision per particle on average already leads to sizable elliptic flow, with mass ordering between the species.     

Brownian particles far from equilibrium

We study a model of Brownian particles which are pumped with energy by means of a non-linear friction function, for which different types are discussed. A suitable expression for a non-linear, velocity-dependent friction function is derived by considering an internal energy depot of the Brownian particles. In this case, the friction function describes the pumping of energy in the range of small velocities, while in the range of large velocities the known limit of dissipative friction is reached. In order to investigate the influence of additional energy supply, we discuss the velocity distribution function for different cases. Analytical solutions of the corresponding Fokker-Planck equation in 2d are presented and compared with computer simulations. Different to the case of passive Brownian motion, we find several new features of the dynamics, such as the formation of limit cycles in the four-dimensional phase-space, a large mean squared displacement which increases quadratically with the energy supply, or non-equilibrium velocity distributions with crater-like form. Further, we point to some generalizations and possible applications of the model. Received 24 November 1999     

Interfacial pattern formation far from equilibrium

Over the past few years diffusion-controlled systems have been shown to share a common set of interfacial morphologies. The singular nature of the microscopic dynamics of surface tension and kinetic growth far from equilibrium are critical to morphology selection, with special importance attributed to the anisotropy of these effects. The morphologies which develop can be organized via a morphology diagram according to the driving force and the effective anisotropy. We focus on the properties of the dense-branching morphology (DBM) which appears for sufficiently weak effective anisotropy, and the nature of morphology transitions between the DBM and dendritic growth stabilized by either surface tension or kinetic effects. The DBM is studied in the Hele-Shaw cell, and its structure analyzed by linear stability analysis. A comparison is made between the power spectrum of the structure and the stability analysis. We then provide a detailed account of the morphology diagram and morphology transitions in an anisotropic Hele-Shaw cell. Theoretically the question of morphology transitions is addressed within the boundary-layer model by computing selected velocities as a function of the undercooling for different values of the surface tension and the kinetic term. We argue that the fastest growing morphology is selected whether it is the DBM, surface tension dendrites, or kinetic dendrites. A comparison is made with our experimental results in electrochemical deposition for the correspondence between growth velocities and morphology transitions.     

Anomalous polymer sedimentation far from equilibrium

A single flexible polymer in strong sedimentation fields is investigated using hydrodynamic simulations and scaling arguments. For short chains and small fields compaction is observed. For elevated fields or long chains the chain stretches and the sedimentation coefficient decreases, in agreement with ultracentrifuge experiments on linear as well as circular DNA. For very large fields a tadpole forms consisting of a compact leading head and a trailing stretched tail.     

An observation on the effect of fluctuations far from equilibrium: The Lotka-Volterra model

Spontaneous fluctuations in the Lotka-Volterra model of chemical reactions are known to grow in an unbounded way when species held in excess are neglected. This result is obtained in a simple way using generalized fluctuation-dissipation principles but appears to be an artifact of ignoring fluctuations in the variables that are held fixed. When fluctuations in the other concentrations are included in the model, the spontaneous fluctuations become bounded.This work was supported by the National Science Foundation through Research Grant No. MPS 74-00483 AO1.     

Traffic jams and ordering far from thermal equilibrium

The recently suggested correspondence between domain dynamics of traffic models and the asymmetric chipping model is reviewed. It is observed that in many cases traffic domains perform the two characteristic dynamical processes of the chipping model, namely chipping and diffusion. This correspondence indicates that jamming in traffic models in which all dynamical rates are non-deterministic takes place as a broad crossover phenomenon, rather than a sharp transition. Two traffic models are studied in detail and analyzed within this picture.     

Pattern formation in liquid crystals far from equilibrium

We have theoretically investigated the growth of the droplets of the nematic phase from supercooled isotropic phase of a liquid crystal. We have also suggested new experiments for testing our predictions in the early time regime.     

Field-theoretic approach to critical dynamics far from equilibrium

The field-theoretic approach to critical phenomena is extended to deal with critical dynamics far from equilibrium. In particular, the macroscopic evolution equation for the average order parameter is derived in a manner parallel to the derivation of the equation of state. The method is illustrated by deriving the scaled macroscopic equation of motion for the timedependent Ginzburg-Landau model near the critical point for dimensionality near four.