Stability of Bose-Einstein Condensates Confined in Traps

Bose-Einstein condensation has been realized in dilute atomic vapors. This achievement has generated immerse interest in this field. Presented is a review of recent theoretical research into the properties of trapped dilute-gas Bose-Einstein condensates. Among them, stability of Bose-Einstein condensates confined in traps is mainly discussed. Static properties of the ground state are investigated by use of the variational method. The anlysis is extended to the stability of two-component condensates. Time-development of the condensate is well-described by the Gross-Pitaevskii equation which is known in nonlinear physics as the nonlinear Schr\"odinger equation. For the case that the inter-atomic potential is effectively attractive, a singularity of the solution emerges in a finite time. This phenomenon which we call collapse explains the upper bound for the number of atoms in such condensates under traps.Comment: 74 pages with 12 figures, submitted to the review section of International Journal of Modern Physics

Exact results on the dynamics of multi-component Bose-Einstein condensate

We study the time-evolution of the two dimensional multi-component Bose-Einstein condensate in an external harmonic trap with arbitrary time-dependent frequency. We show analytically that the time-evolution of the total mean-square radius of the wave-packet is determined in terms of the same solvable equation as in the case of a single-component condensate. The dynamics of the total mean-square radius is also the same for the rotating as well as the non-rotating multi-component condensate. We determine the criteria for the collapse of the condensate at a finite time. Generalizing our previous work on a single-component condensate, we show explosion-implosion duality in the multi-component condensate.Comment: Two-column 6 pages, RevTeX, no figures(v1); Added an important reference, version to appear in Physical Review A (v2

Dynamical effects of the nanometer-sized polarized domains in Pb(Zn1/3Nb2/3)O3

Recent neutron scattering measurements performed on the relaxor ferroelectric Pb[(Zn1/3Nb2/3)0.92Ti0.08]O3 (PZN-8%PT) in its cubic phase at 500 K, have revealed an anomalous ridge of inelastic scattering centered ~0.2 A-1 from the zone center (Gehring et al., Phys. Rev. Lett. 84, 5216 (2000)). This ridge of scattering resembles a waterfall when plotted as a phonon dispersion diagram, and extends vertically from the transverse acoustic (TA) branch near 4 meV to the transverse optic (TO) branch near 9 meV. No zone center optic mode was found. We report new results from an extensive neutron scattering study of pure PZN that exhibits the same waterfall feature. We are able to model the dynamics of the waterfall using a simple coupled-mode model that assumes a strongly q-dependent optic mode linewidth Gamma1(q) that increases sharply near 0.2 A-1 as one approaches the zone center. This model was motivated by the results of Burns and Dacol in 1983, who observed the formation of a randomly-oriented local polarization in PZN at temperatures far above its ferroelectric phase transition temperature. The dramatic increase in Gamma1 is believed to occur when the wavelength of the optic mode becomes comparable to the size of the small polarized micro-regions (PMR) associated with this randomly-oriented local polarization, with the consequence that longer wavelength optic modes cannot propagate and become overdamped. Below Tc=410 K, the intensity of the waterfall diminishes. At lowest temperatures ~30 K the waterfall is absent, and we observe the recovery of a zone center transverse optic mode near 10.5 meV.Comment: 8 pages, 9 figures (one color). Submitted to Physical Review

Soft Phonon Anomalies in the Relaxor Ferroelectric Pb(Zn_1/3Nb_2/3)_0.92Ti_0.08O_3

Neutron inelastic scattering measurements of the polar TO phonon mode dispersion in the cubic relaxor Pb(Zn_1/3Nb_2/3)_0.92Ti_0.08O_3 at 500K reveal anomalous behavior in which the optic branch appears to drop precipitously into the acoustic branch at a finite value of the momentum transfer q=0.2 inverse Angstroms, measured from the zone center. We speculate this behavior is the result of nanometer-sized polar regions in the crystal.Comment: 4 pages, 4 figure

Nonlinear magnetoinductive transmission lines

Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent capacitance. Extended numerical simulations reveal that power transmission along the array is also possible in other than the linear frequency bands, which are located close to the nonlinear resonances of a single nonlinear RLC circuit. Moreover, the effectiveness of power transmission for driving frequencies in the nonlinear bands is comparable to that in the linear band. Power transmission in the nonlinear bands occurs through the linear modes of the system, and it is closely related to the instability of a mode that is localized at the driven site.Comment: 11 pages, 11 figures, submitted to International Journal of Bifurcation and Chao

Nonlocal interactions prevent collapse in negative scattering length Bose-Einstein gases

We study the effect of nonlocality on the collapse properties of a self-focusing Nonlinear Schr\"odinger system related to Bose-Einstein condensation problems. Using a combination of moment techniques, time dependent variational methods and numerical simulations we present evidences in support of the hypothesis that nonlocal attractively interacting condensates cannot collapse when the dominant interaction term is due to finite range interactions. Instead there apppear oscillations of the wave packet with a localized component whose size is of the order of the range of interactions. We discuss the implications of the results to collapse phenomena in negative scattering length Bose-Einstein condensates

Methylated DNA recognition during the reversal of epigenetic silencing is regulated by cysteine and cerine residues in the Epstein-Barr Virus lytic switch protein

Epstein-Barr virus (EBV) causes infectious mononucleosis and is associated with various malignancies, including Burkitt's lymphoma and nasopharyngeal carcinoma. Like all herpesviruses, the EBV life cycle alternates between latency and lytic replication. During latency, the viral genome is largely silenced by host-driven methylation of CpG motifs and, in the switch to the lytic cycle, this epigenetic silencing is overturned. A key event is the activation of the viral BRLF1 gene by the immediate-early protein Zta. Zta is a bZIP transcription factor that preferentially binds to specific response elements (ZREs) in the BRLF1 promoter (Rp) when these elements are methylated. Zta's ability to trigger lytic cycle activation is severely compromised when a cysteine residue in its bZIP domain is mutated to serine (C189S), but the molecular basis for this effect is unknown. Here we show that the C189S mutant is defective for activating Rp in a Burkitt's lymphoma cell line. The mutant is compromised both in vitro and in vivo for binding two methylated ZREs in Rp (ZRE2 and ZRE3), although the effect is striking only for ZRE3. Molecular modeling of Zta bound to methylated ZRE3, together with biochemical data, indicate that C189 directly contacts one of the two methyl cytosines within a specific CpG motif. The motif's second methyl cytosine (on the complementary DNA strand) is predicted to contact S186, a residue known to regulate methyl-ZRE recognition. Our results suggest that C189 regulates the enhanced interaction of Zta with methylated DNA in overturning the epigenetic control of viral latency. As C189 is conserved in many bZIP proteins, the selectivity of Zta for methylated DNA may be a paradigm for a more general phenomenon

Modulation Instability of Ultrashort Pulses in Quadratic Nonlinear Media beyond the Slowly Varying Envelope Approximation

We report a modulational instability (MI) analysis of a mathematical model appropriate for ultrashort pulses in cascaded quadratic-cubic nonlinear media beyond the so-called slowly varying envelope approximation. Theoretically predicted MI properties are found to be in good agreement with numerical simulation. The study shows the possibility of controlling the generation of MI and formation of solitons in a cascaded quadratic-cubic media in the few cycle regimes. We also find that stable propagation of soliton-like few-cycle pulses in the medium is subject to the fulfilment of the modulation instability criteria

Modulational instability of bright solitary waves in incoherently coupled nonlinear Schr\"odinger equations

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schr\"odinger equations. Varying the relative strength of cross-phase and self-phase effects we show existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group velocity dispersion (GVD) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.Comment: Physical Review E, July, 199

Mutual Inhibition between Kaposi's Sarcoma-Associated Herpesvirus and Epstein-Barr Virus Lytic Replication Initiators in Dually-Infected Primary Effusion Lymphoma

Background: Both Kaposi’s sarcoma-associated herpesvirus (KSHV) and Epstein-Barr virus (EBV) are members of the human gamma herpesvirus family: each is associated with various human cancers. The majority of AIDS-associated primary effusion lymphoma (PEL) are co-infected with both KSHV and EBV. Dually-infected PELs selectively switch from latency to lytic replication of either KSHV or EBV in response to chemical stimuli. KSHV replication and transcription activator (K-RTA) is necessary and sufficient for the switch from KSHV latency to lytic replication, while EBV BZLF1 gene product (EBV-Z) is a critical initiator for induction of EBV lytic replication. Methodology/Principal Findings: We show K-RTA and EBV-Z are co-localized and physically interact with each other in dually-infected PELs. K-RTA inhibits the EBV lytic replication by nullifying EBV-Z-mediated EBV lytic gene activation. EBV-Z inhibits KSHV lytic gene expression by blocking K-RTA-mediated transactivations. The physical interaction between K-RTA and EBV-Z are required for the mutual inhibition of the two molecules. The leucine heptapeptide repeat (LR) region in K-RTA and leucine zipper region in EBV-Z are involved in the physical interactions of the two molecules. Finally, initiation of KSHV lytic gene expression is correlated with the reduction of EBV lytic gene expression in the same PEL cells. Conclusions/Significance: In this report, how the two viruses interact with each other in dually infected PELs is addressed. Our data may provide a possible mechanism for maintaining viral latency and for selective lytic replication in dually infected PELs, i.e., through mutual inhibition of two critical lytic replication initiators. Our data about putative interactions between EBV and KSHV would be applicable to the majority of AIDS-associated PELs and may be relevant to the pathogenesis of PELs