Dimensional versus cut-off renormalization and the nucleon-nucleon interaction

The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.Comment: 19 pages + one postscript figur

The eigenspectra of Indian musical drums

In a family of drums used in the Indian subcontinent, the circular drum head is made of material of non-uniform density. Remarkably, and in contrast to a circular membrane of uniform density, the low eigenmodes of the non-uniform membrane are harmonic. In this work we model the drum head by a non-uniform membrane whose density varies smoothly between two prescribed values. Using a Fourier-Chebyshev spectral collocation method we obtain the eigenmodes and eigenvalues of the drum head. For a suitable choice of parameters, which we find by optimising a cost function, the eigenspectra obtained from our model are in excellent agreement with experimental values. Our model and the numerical method should find application in numerical sound synthesis

Performance of a prototype active veto system using liquid scintillator for a dark matter search experiment

We report the performance of an active veto system using a liquid scintillator with NaI(Tl) crystals for use in a dark matter search experiment. When a NaI(Tl) crystal is immersed in the prototype detector, the detector tags 48% of the internal K-40 background in the 0-10 keV energy region. We also determined the tagging efficiency for events at 6-20 keV as 26.5 +/- 1.7% of the total events, which corresponds to 0.76 +/- 0.04 events/keV/kg/day. According to a simulation, approximately 60% of the background events from U, Th, and K radioisotopes in photomultiplier tubes are tagged at energies of 0-10 keV. Full shielding with a 40-cm-thick liquid scintillator can increase the tagging efficiency for both the internal K-40 and external background to approximately 80%.Comment: Submitted to Nuclear Instruments and Methods in Physics Research Section

Effective Nonlinear Schr\"odinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity

In the case of tight transverse confinement (cigar-shaped trap) the three-dimensional (3D) nonlinear Schr\"odinger equation, describing superfluid Fermi atoms at unitarity (infinite scattering length $|a|\to \infty$), is reduced to an effective one-dimensional form by averaging over the transverse coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger equation, which produces results in good agreement with the original 3D one. In the limit of small and large fermion number $N$ the nonlinearity is of simple power-law type. A similar reduction of the 3D theory to a two-dimensional form is also performed for a tight axial confinement (disk-shaped trap). The resultant effective 2D nonpolynomial equation also produces results in agreement with the original 3D equation and has simple power-law nonlinearity for small and large $N$. For both cigar- and disk-shaped superfluids our nonpolynomial Schr\"odinger equations are quite attractive for phenomenological application.Comment: 22 pages, 5 figure

Lattice Discretization in Quantum Scattering

The utility of lattice discretization technique is demonstrated for solving nonrelativistic quantum scattering problems and specially for the treatment of ultraviolet divergences in these problems with some potentials singular at the origin in two and three space dimensions. This shows that lattice discretization technique could be a useful tool for the numerical solution of scattering problems in general. The approach is illustrated in the case of the Dirac delta function potential.Comment: 9 page

Endogenous Quasicycles and Stochastic Coherence in a Closed Endemic Model

We study the role of demographic fluctuations in typical endemics as exemplified by the stochastic SIRS model. The birth-death master equation of the model is simulated using exact numerics and analysed within the linear noise approximation. The endemic fixed point is unstable to internal demographic noise, and leads to sustained oscillations. This is ensured when the eigenvalues ($\lambda$) of the linearised drift matrix are complex, which in turn, is possible only if detailed balance is violated. In the oscillatory state, the phases decorrelate asymptotically, distinguishing such oscillations from those produced by external periodic forcing. These so-called quasicycles are of sufficient strength to be detected reliably only when the ratio $|Im(\lambda)/Re(\lambda)|$ is of order unity. The coherence or regularity of these oscillations show a maximum as a function of population size, an effect known variously as stochastic coherence or coherence resonance. We find that stochastic coherence can be simply understood as resulting from a non-monotonic variation of $|Im(\lambda)/Re(\lambda)|$ with population size. Thus, within the linear noise approximation, stochastic coherence can be predicted from a purely deterministic analysis. The non-normality of the linearised drift matrix, associated with the violation of detailed balance, leads to enhanced fluctuations in the population amplitudes.Comment: 21 pages, 8 figure

Dynamics of collapsing and exploding Bose-Einstein condensed vortex state

Using the time-dependent mean-field Gross-Pitaevskii equation we study the dynamics of small repulsive Bose-Einstein condensed vortex states of ^{85}Rb atoms in a cylindrical trap with low angular momentum hbar L per atom (L <= 6), when the atomic interaction is suddenly turned attractive by manipulating the external magnetic field near a Feshbach resonance. Consequently, the condensate collapses and ejects atoms via explosion and a remnant condensate with a smaller number of atoms emerges that survives for a long time. Detail of this collapse and explosion is compared critically with a similar experiment performed with zero angular momentum (L=0). Suggestion for future experiment with vortex state is made.Comment: 8 REVTEX4 pages, 8 EPS figures, final version accepted in Phys. Rev. A after minor change

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

We present a numerical study of the coupled time-dependent Gross-Pitaevskii equation, which describes the Bose-Einstein condensate of several types of trapped bosons at ultralow temperature with both attractive and repulsive interatomic interactions. The same approach is used to study both stationary and time-evolution problems. We consider up to four types of atoms in the study of stationary problems. We consider the time-evolution problems where the frequencies of the traps or the atomic scattering lengths are suddenly changed in a stable preformed condensate. We also study the effect of periodically varying these frequencies or scattering lengths on a preformed condensate. These changes introduce oscillations in the condensate which are studied in detail. Good convergence is obtained in all cases studied.Comment: 9 pages, 10 figures, accepted in Physical Review

Resonance in Bose-Einstein condensate oscillation from a periodic variation in scattering length

Using the explicit numerical solution of the axially-symmetric Gross-Pitaevskii equation we study the oscillation of the Bose-Einstein condensate induced by a periodic variation in the atomic scattering length $a$. When the frequency of oscillation of $a$ is an even multiple of the radial or axial trap frequency, respectively, the radial or axial oscillation of the condensate exhibits resonance with novel feature. In this nonlinear problem without damping, at resonance in the steady state the amplitude of oscillation passes through maximum and minimum. Such growth and decay cycle of the amplitude may keep on repeating. Similar behavior is also observed in a rotating Bose-Einstein condensate.Comment: 14 REVTEX4 pages, 18 PS figures, final version Accepted in Journal of Physics