Based on statistical approach we described possible formation of spatially inhomogeneous distribution in the system of interacting Bose particles. The condition of cluster formation in both gas and condensed phases was obtained in this system. We studied the dynamics of cluster formation in the limit case of high temperatures. We compared the cluster-formation processes in the attractive system (with short-range interaction) and in the gravitational system at the low temperatures of Bose-Einstein condensate regime.
Based on statistical approach we described possible formation of spatially inhomogeneous distribution in the system of interacting Bose particles. The condition of cluster formation in both gas and condensed phases was obtained in this system. We studied the dynamics of cluster formation in the limit case of high temperatures. We compared the cluster-formation processes in the attractive system (with short-range interaction) and in the gravitational system at the low temperatures of Bose-Einstein condensate regime.
We consider the one-dimensional interacting Bose gas in the presence of time-dependent and spatially inhomogeneous contact interactions. Within its attractive phase, the gas allows for bound states of an arbitrary number of particles, which are eventually populated if the system is dynamically driven from the repulsive to the attractive regime. Building on the framework of generalized hydrodynamics, we analytically determine the formation of bound states in the limit of adiabatic changes in the interactions. Our results are valid for arbitrary initial thermal states and, more generally, generalized Gibbs ensembles.
The kinetics of the formation of coherent correlation properties associated with Bose condensation is studied in detail. The evolution of a nonequilibrium state with no “condensate-seed” is related to a hierarchy of relaxation times. At the first stage, a particle flux in energy space toward low energies sets in. The evolution in this case is described by a nonlinear Boltzmann equation, with a characteristic time given by interparticle collisions. When the particles which will later form the condensate have a kinetic energy which is less than the potential energy, a quasicondensate starts to form. In this stage, fluctuations of the density (but not of the phase) are suppressed and short-range coherent correlation properties are governed by the equation of motion for a quasiclassical complex field. The next stage is connected with the formation of the long-range order. The time for forming topological order and therefore genuine superfluidity proves to be dependent on the system size. The off-diagonal long-range order, arising after the attenuation of long-wave phase fluctuations, has a size-dependent relaxation time as well. Introduction The problem of Bose–Einstein Condensation (BEC) kinetics, being interesting in itself, has acquired a special significance in connection with experimental efforts to observe this condensation in a number of systems with particles with a finite lifetime. Such systems include spin-polarized atomic hydrogen [1], excitons [2] and biexcitons [3] in semiconductors and, more recently, laser-cooled atomic systems [4].
We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low temperature condensed regime to the high temperature classical regime. As we show, the non-condensed particles play a crucial role in determining the region of stability, even providing a mechanism for collapse in the non-condensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.
Two-component fermions are known to behave like a gas of molecules in the limit of Bose-Einstein condensation of diatomic pairs tightly bound with zero-range interactions. We discover that the formation of cluster states occurs when the effective range of two-body interaction exceeds roughly 0.46 times the scattering length, regardless of the details of the short-range interaction. Using an explicitly correlated Gaussian basis set expansion approach, we calculate the binding energy of cluster states in trapped few-body systems and show the difference of structural properties between cluster states and gaslike states. We identify the condition for cluster formation and discuss the potential observation of cluster states in experiments.
The problem of understanding how a coherent, macroscopic Bose- Einstein condensate (BEC) emerges from the cooling of a thermal Bose gas has attracted significant theoretical and experimental interest over several decades. The pioneering achievement of BEC in weakly interacting dilute atomic gases in 1995 was followed by a number of experimental studies examining the growth of the BEC number, as well as the development of its coherence. More recently, there has been interest in connecting such experiments to universal aspects of nonequilibrium phase transitions, in terms of both static and dynamical critical exponents. Here, the spontaneous formation of topological structures such as vortices and solitons in quenched cold-atom experiments has enabled the verification of the Kibble-Zurek mechanism predicting the density of topological defects in continuous phase transitions, first proposed in the context of the evolution of the early universe. This chapter reviews progress in the understanding of BEC formation and discusses open questions and future research directions in the dynamics of phase transitions in quantum gases. Introduction The equilibrium phase diagram of the dilute Bose gas exhibits a continuous phase transition between condensed and noncondensed phases. The order parameter characteristic of the condensed phase vanishes above some critical temperature T c and grows continuously with decreasing temperature below this critical point. However, the dynamical process of condensate formation has proved to be a challenging phenomenon to address both theoretically and experimentally. This formation process is a crucial aspect of Bose systems and of direct relevance to all condensates discussed in this book, despite their evident system-specific properties. Important questions leading to intense discussions in the early literature include the time scale for condensate formation and the role of inhomogeneities and finite-size effects in “closed” systems. These issues are related to the concept of spontaneous symmetry breaking, its causes, and implications for physical systems (see, for example, Chapter 5 by Snoke and Daley). In this chapter, we give an overview of the dynamics of condensate formation and describe the present understanding provided by increasingly well-controlled cold-atom experiments and corresponding theoretical advances over the past twenty years. We focus on the growth of BECs in cooled Bose gases, which, from a theoretical standpoint, requires a suitable nonequilibrium formalism.
We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low-temperature condensed regime to the high temperature classical regime. As we show, the noncondensed particles play a crucial role in determining the region of stability, including providing a mechanism for collapse in the noncondensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.