Magnetic Properties of a Bose-Einstein Condensate

Three hyperfine states of Bose-condensed sodium atoms, recently optically trapped, can be described as a spin-1 Bose gas. We study the behaviour of this system in a magnetic field, and construct the phase diagram, where the temperature of the Bose condensation $T_{BEC}$ increases with magnetic field. In particular the system is ferromagnetic below $T_{BEC}$ and the magnetization is proportional to the condensate fraction in a vanishing magnetic field. Second derivatives of the magnetisation with regard to temperature or magnetic field are discontinuous along the phase boundary.Comment: 5 pages, 5 figures included, to appear in Phys. Rev.

The Importance of DNA Repair in Tumor Suppression

The transition from a normal to cancerous cell requires a number of highly specific mutations that affect cell cycle regulation, apoptosis, differentiation, and many other cell functions. One hallmark of cancerous genomes is genomic instability, with mutation rates far greater than those of normal cells. In microsatellite instability (MIN tumors), these are often caused by damage to mismatch repair genes, allowing further mutation of the genome and tumor progression. These mutation rates may lie near the error catastrophe found in the quasispecies model of adaptive RNA genomes, suggesting that further increasing mutation rates will destroy cancerous genomes. However, recent results have demonstrated that DNA genomes exhibit an error threshold at mutation rates far lower than their conservative counterparts. Furthermore, while the maximum viable mutation rate in conservative systems increases indefinitely with increasing master sequence fitness, the semiconservative threshold plateaus at a relatively low value. This implies a paradox, wherein inaccessible mutation rates are found in viable tumor cells. In this paper, we address this paradox, demonstrating an isomorphism between the conservatively replicating (RNA) quasispecies model and the semiconservative (DNA) model with post-methylation DNA repair mechanisms impaired. Thus, as DNA repair becomes inactivated, the maximum viable mutation rate increases smoothly to that of a conservatively replicating system on a transformed landscape, with an upper bound that is dependent on replication rates. We postulate that inactivation of post-methylation repair mechanisms are fundamental to the progression of a tumor cell and hence these mechanisms act as a method for prevention and destruction of cancerous genomes.Comment: 7 pages, 5 figures; Approximation replaced with exact calculation; Minor error corrected; Minor changes to model syste

Weyl group multiple Dirichlet series constructed from quadratic characters

We construct multiple Dirichlet series in several complex variables whose coefficients involve quadratic residue symbols. The series are shown to have an analytic continuation and satisfy a certain group of functional equations. These are the first examples of an infinite collection of unstable Weyl group multiple Dirichlet series in greater than two variables.Comment: incorporated referee's comment

Vortex solutions of a Maxwell-Chern-Simons field coupled to four-fermion theory

We find the static vortex solutions of the model of Maxwell-Chern-Simons gauge field coupled to a (2+1)-dimensional four-fermion theory. Especially, we introduce two matter currents coupled to the gauge field minimally: the electromagnetic current and a topological current associated with the electromagnetic current. Unlike other Chern-Simons solitons the N-soliton solution of this theory has binding energy and the stability of the solutions is maintained by the charge conservation laws.Comment: 7 pages, harvmac, To be published in Phys. Rev. D5

Bogomol'nyi Equations of Maxwell-Chern-Simons vortices from a generalized Abelian Higgs Model

We consider a generalization of the abelian Higgs model with a Chern-Simons term by modifying two terms of the usual Lagrangian. We multiply a dielectric function with the Maxwell kinetic energy term and incorporate nonminimal interaction by considering generalized covariant derivative. We show that for a particular choice of the dielectric function this model admits both topological as well as nontopological charged vortices satisfying Bogomol'nyi bound for which the magnetic flux, charge and angular momentum are not quantized. However the energy for the topolgical vortices is quantized and in each sector these topological vortex solutions are infinitely degenerate. In the nonrelativistic limit, this model admits static self-dual soliton solutions with nonzero finite energy configuration. For the whole class of dielectric function for which the nontopological vortices exists in the relativistic theory, the charge density satisfies the same Liouville equation in the nonrelativistic limit.Comment: 30 pages(4 figures not included), RevTeX, IP/BBSR/93-6

Modification of radiation pressure due to cooperative scattering of light

Cooperative spontaneous emission of a single photon from a cloud of N atoms modifies substantially the radiation pressure exerted by a far-detuned laser beam exciting the atoms. On one hand, the force induced by photon absorption depends on the collective decay rate of the excited atomic state. On the other hand, directional spontaneous emission counteracts the recoil induced by the absorption. We derive an analytical expression for the radiation pressure in steady-state. For a smooth extended atomic distribution we show that the radiation pressure depends on the atom number via cooperative scattering and that, for certain atom numbers, it can be suppressed or enhanced.Comment: 8 pages, 2 Figure

Oscillons: Resonant Configurations During Bubble Collapse

Oscillons are localized, non-singular, time-dependent, spherically-symmetric solutions of nonlinear scalar field theories which, although unstable, are extremely long-lived. We show that they naturally appear during the collapse of subcritical bubbles in models with symmetric and asymmetric double-well potentials. By a combination of analytical and numerical work we explain several of their properties, including the conditions for their existence, their longevity, and their final demise. We discuss several contexts in which we expect oscillons to be relevant. In particular, their nucleation during cosmological phase transitions may have wide-ranging consequences.Comment: 31 pages Revtex, 20 uufiles-encoded figures. Section "Possible Applications of Oscillons" slightly expande

In-medium Yang-Mills equations: a derivation and canonical quantization

The equations for Yang-Mills field in a medium are derived in a linear approximation with respect to the gauge coupling parameter and the external field. The obtained equations closely resemble the macroscopic Maxwell equations. A canonical quantization is performed for a family of Fermi-like gauges in the case of constant and diagonal (in the group indices) tensors of electric permittivity and magnetic permeability. The physical subspace is defined and the gauge field propagator is evaluated for a particular choice of the gauge. The propagator is applied for evaluation of the cross-section of ellastic quark scattering in the Born approximation. Possible applications to Cherenkov-type gluon radiation are commented briefly.Comment: 27 pages, references added, version extended with emphasis on non-Abelian gauge group impact on medium characteristics. To appear in J. Phys.

Flux tube dynamics in the dual superconductor

We study plasma oscillations in a flux tube of the dual superconductor model of 't Hooft and Mandelstam. A magnetic condensate is coupled to an electromagnetic field by its dual vector potential, and fixed electric charges set up a flux tube. An electrically charged fluid (a quark plasma) flows in the tube and screens the fixed charges via plasma oscillations. We investigate both Type I and Type II superconductors, with plasma frequencies both above and below the threshold for radiation into the Higgs vacuum. We find strong radiation of electric flux into the superconductor in all regimes, and argue that this invalidates the use of the simplest dual superconductor model for dynamical problems.Comment: 25 pages Revtex with 11 EPS figure

Quantum Kinks: Solitons at Strong Coupling

We examine solitons in theories with heavy fermions. These ``quantum'' solitons differ dramatically from semi-classical (perturbative) solitons because fermion loop effects are important when the Yukawa coupling is strong. We focus on kinks in a $(1+1)$--dimensional $\phi^4$ theory coupled to fermions; a large-$N$ expansion is employed to treat the Yukawa coupling $g$ nonperturbatively. A local expression for the fermion vacuum energy is derived using the WKB approximation for the Dirac eigenvalues. We find that fermion loop corrections increase the energy of the kink and (for large $g$) decrease its size. For large $g$, the energy of the quantum kink is proportional to $g$, and its size scales as $1/g$, unlike the classical kink; we argue that these features are generic to quantum solitons in theories with strong Yukawa couplings. We also discuss the possible instability of fermions to solitons.Comment: 21 pp. + 2 figs., phyzzx, JHU-TIPAC-92001