Non-diffusive phase spreading of a Bose-Einstein condensate at finite temperature

We show that the phase of a condensate in a finite temperature gas spreads linearly in time at long times rather than in a diffusive way. This result is supported by classical field simulations, and analytical calculations which are generalized to the quantum case under the assumption of quantum ergodicity in the system. This super-diffusive behavior is intimately related to conservation of energy during the free evolution of the system and to fluctuations of energy in the prepared initial state.Comment: 16 pages, 7 figure

FREE-CARRIER PLASMONS AS A NOVEL TOOL IN SEMICONDUCTOR PHYSICS*

It is demonstrated that free-carrier plasmons, being well defined collective excitations of the electron gas in the range of small wave vectors, can serve as a sensitive tool to investigate the optical processes related to the small momentum transfers. As an example the system HgSe:Fe is analysed both experimentally and theoretically. It is well known that the excitation of the free-carrier plasma in the light absorption process is possible only in the presence of defects breaking the translational invariance of the system. Due to the overall momentum conservation requirement there must exist a momentum source to make the photon absorption *This work is supported in part by CPBP 01.06. (141

From a nonlinear string to a weakly interacting Bose gas

We investigate a real scalar field whose dynamics is governed by a nonlinear wave equation. We show that classical description can be applied to a quantum system of many interacting bosons provided that some quantum ingredients are included. An universal action has to be introduced in order to define particle number. The value of this action should be equal to the Planck constant. This constrain can be imposed by removing high frequency modes from the dynamics by introducing a cut-off. We show that the position of the cut-off has to be carefully adjusted. Finally, we show the proper choice of the cut-off ensures that all low frequency eigenenmodes which are taken into account are macroscopically occupied.Comment: 7 pages, 4 figure

Disturbed Expression of Splicing Factors in Renal Cancer Affects Alternative Splicing of Apoptosis Regulators, Oncogenes, and Tumor Suppressors

BACKGROUND: Clear cell renal cell carcinoma (ccRCC) is the most common type of renal cancer. One of the processes disturbed in this cancer type is alternative splicing, although phenomena underlying these disturbances remain unknown. Alternative splicing consists of selective removal of introns and joining of residual exons of the primary transcript, to produce mRNA molecules of different sequence. Splicing aberrations may lead to tumoral transformation due to synthesis of impaired splice variants with oncogenic potential. In this paper we hypothesized that disturbed alternative splicing in ccRCC may result from improper expression of splicing factors, mediators of splicing reactions. METHODOLOGY/PRINCIPAL FINDINGS: Using real-time PCR and Western-blot analysis we analyzed expression of seven splicing factors belonging to SR proteins family (SF2/ASF, SC35, SRp20, SRp75, SRp40, SRp55 and 9G8), and one non-SR factor, hnRNP A1 (heterogeneous nuclear ribonucleoprotein A1) in 38 pairs of tumor-control ccRCC samples. Moreover, we analyzed splicing patterns of five genes involved in carcinogenesis and partially regulated by analyzed splicing factors: RON, CEACAM1, Rac1, Caspase-9, and GLI1. CONCLUSIONS/SIGNIFICANCE: We found that the mRNA expression of splicing factors was disturbed in tumors when compared to paired controls, similarly as levels of SF2/ASF and hnRNP A1 proteins. The correlation coefficients between expression levels of specific splicing factors were increased in tumor samples. Moreover, alternative splicing of five analyzed genes was also disturbed in ccRCC samples and splicing pattern of two of them, Caspase-9 and CEACAM1 correlated with expression of SF2/ASF in tumors. We conclude that disturbed expression of splicing factors in ccRCC may possibly lead to impaired alternative splicing of genes regulating tumor growth and this way contribute to the process of carcinogenesis

Generalized Bose-Einstein Condensation

Generalized Bose-Einstein condensation (GBEC) involves condensates appearing simultaneously in multiple states. We review examples of the three types in an ideal Bose gas with different geometries. In Type I there is a discrete number of quantum states each having macroscopic occupation; Type II has condensation into a continuous band of states, with each state having macroscopic occupation; in Type III each state is microscopically occupied while the entire condensate band is macroscopically occupied. We begin by discussing Type I or "normal" BEC into a single state for an isotropic harmonic oscillator potential. Other geometries and external potentials are then considered: the {}"channel" potential (harmonic in one dimension and hard-wall in the other), which displays Type II, the {}"cigar trap" (anisotropic harmonic potential), and the "Casimir prism" (an elongated box), the latter two having Type III condensations. General box geometries are considered in an appendix. We particularly focus on the cigar trap, which Van Druten and Ketterle first showed had a two-step condensation: a GBEC into a band of states at a temperature $T_{c}$ and another "one-dimensional" transition at a lower temperature $T_{1}$ into the ground state. In a thermodynamic limit in which the ratio of the dimensions of the anisotropic harmonic trap is kept fixed, $T_{1}$ merges with the upper transition, which then becomes a normal BEC. However, in the thermodynamic limit of Beau and Zagrebnov, in which the ratio of the boundary lengths increases exponentially, $T_{1}$ becomes fixed at the temperature of a true Type I phase transition. The effects of interactions on GBEC are discussed and we show that there is evidence that Type III condensation may have been observed in the cigar trap.Comment: 17 pages; 6 figures. Intended for American Journal of Physic

Winding up superfluid in a torus via Bose Einstein condensation

Phase transitions are usually treated as equilibrium phenomena, which yields telltale universality classes with scaling behavior of relaxation time and healing length. However, in second-order phase transitions relaxation time diverges near the critical point (“critical slowing down”). Therefore, every such transition traversed at a finite rate is a non-equilibrium process. Kibble-Zurek mechanism (KZM) captures this basic physics, predicting sizes of domains – fragments of broken symmetry – and the density of topological defects, long-lived relics of symmetry breaking that can survive long after the transition. To test KZM we simulate Bose-Einstein condensation in a ring using stochastic Gross-Pitaevskii equation and show that BEC formation can spontaneously generate quantized circulation of the newborn condensate. The magnitude of the resulting winding numbers and the time-lag of BEC density growth – both experimentally measurable – follow scalings predicted by KZM. Our results may also facilitate measuring the dynamical critical exponent for the BEC transition