Abstract:
The mapping between genotype and phenotype is encoded in the complex web of epistatic interaction between genetic loci. In this rugged fitness landscape, recombination processes, which tend to increase variation in the population, compete with selection processes that tend to reduce genetic variation. Here we show that the Bose-Einstein distribution describe the multiple stationary states of a diploid population under this multi-loci evolutionary dynamics. Moreover, the evolutionary process might undergo an interesting condensation phase transition in the universality class of a Bose-Einstein condensation when a finite fraction of pairs of linked loci, is fixed into given allelic states. Below this phase transition the genetic variation within a species is significantly reduced and only maintained by the remaining polymorphic loci.

Abstract:
It is shown, that Bose-Einstein statistical distributions can occur not only in quantum system, but in classical systems as well. The coherent dynamics of the system, or equivalently autocatalytic dynamics in momentum space of the system is the main reason for the Bose-Einstein condensation. A coherence is possible in both quantum and classical systems, and in both cases can lead to Bose-Einstein statistical distribution.

Abstract:
We have observed Bose-Einstein condensation of molecules. When a spin mixture of fermionic Li-6 atoms was evaporatively cooled in an optical dipole trap near a Feshbach resonance, the atomic gas was converted into Li_2 molecules. Below 600 nK, a Bose-Einstein condensate of up to 900,000 molecules was identified by the sudden onset of a bimodal density distribution. This condensate realizes the limit of tightly bound fermion pairs in the crossover between BCS superfluidity and Bose-Einstein condensation.

Abstract:
We discuss the properties of an ideal relativistic gas of events possessing Bose-Einstein statistics. We find that the mass spectrum of such a system is bounded by $\mu \leq m\leq 2M/\mu _K,$ where $\mu $ is the usual chemical potential, $M$ is an intrinsic dimensional scale parameter for the motion of an event in space-time, and $\mu _K$ is an additional mass potential of the ensemble. For the system including both particles and antiparticles, with nonzero chemical potential $\mu ,$ the mass spectrum is shown to be bounded by $|\mu |\leq m\leq 2M/\mu _K,$ and a special type of high-temperature Bose-Einstein condensation can occur. We study this Bose-Einstein condensation, and show that it corresponds to a phase transition from the sector of continuous relativistic mass distributions to a sector in which the boson mass distribution becomes sharp at a definite mass $M/\mu _K.$ This phenomenon provides a mechanism for the mass distribution of the particles to be sharp at some definite value.

Abstract:
We report on the generation of a Bose-Einstein condensate in a gas of chromium atoms, which will make studies of the effects of anisotropic long-range interactions in degenerate quantum gases possible. The preparation of the chromium condensate requires novel cooling strategies that are adapted to its special electronic and magnetic properties. The final step to reach quantum degeneracy is forced evaporative cooling of 52Cr atoms within a crossed optical dipole trap. At a critical temperature of T~700nK, we observe Bose-Einstein condensation by the appearance of a two-component velocity distribution. Released from an anisotropic trap, the condensate expands with an inversion of the aspect ratio. We observe critical behavior of the condensate fraction as a function of temperature and more than 50,000 condensed 52Cr atoms.

Abstract:
Bose-Einstein condensation of charged scalar and vector particles may actually occur in presence of a constant homogeneous magnetic field, but there is no critical temperature at which condensation starts. The condensate is described by the statistical distribution. The Meissner effect is possible in the scalar, but not in the vector field case, which exhibits a ferromagnetic behavior.

Abstract:
We study the thermalization of gluons far from thermal equilibrium in relativistic kinetic theory. The initial distribution of gluons is assumed to resemble that in the early stage of ultrarelativistic heavy ion collisions. Only elastic scatterings in static, nonexpanding gluonic matter are considered. At first we show that the occurrence of condensation in the limit of vanishing particle mass requires a general constraint for the scattering matrix element. Then the thermalization of gluons with Bose-Einstein condensation is demonstrated in a transport calculation. We see a continuously increasing overpopulation of low energy gluons, followed by a decrease to the equilibrium distribution, when the condensation occurs. The times of the completion of the gluon condensation and of the entropy production are calculated. These times scale inversely with the energy density.

Abstract:
The close analogy between cluster percolation and string proliferation in the context of critical phenomena is studied. Like clusters in percolation theory, closed strings, which can be either finite-temperature worldlines or topological line defects, are described by a distribution parametrized by only two exponents. On approaching the critical point, the string tension vanishes, and the loops proliferate thereby signalling the onset of Bose-Einstein condensation (in case of worldlines) or the disordering of the ordered state (in case of vortices). The ideal Bose gas with modified energy spectrum is used as a stepping stone to derive general expressions for the critical exponents in terms of the two exponents parameterizing the loop distribution near criticality.

Abstract:
We consider the phenomenon of Bose-Einstein condensation in a random growing directed network. The network grows by the addition of vertices and edges. At each time step the network gains a vertex with probabilty $p$ and an edge with probability $1-p$. The new vertex has a fitness $(a,b)$ with probability $f(a,b)$. A vertex with fitness $(a,b)$, in-degree $i$ and out-degree $j$ gains a new incoming edge with rate $a(i+1)$ and an outgoing edge with rate $b(j+1)$. The Bose-Einstein condensation occurs as a function of fitness distribution $f(a,b)$.