arXiv subjects

R. K. Bullough

Publications and source records attributed to R. K. Bullough.

5 recordsLinked to original sources

arXiv2003

Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases

We calculate the dynamic single-particle and many-particle correlation functions at non-zero temperature in one-dimensional trapped repulsive Bose gases. The decay for increasing distance between the points of these correlation functions is governed by a scaling exponent that has a universal expression in terms of observed quantities. This expression is valid in the weak-interaction Gross-Pitaevskii as well as in the strong-interaction Girardeau-Tonks limit, but the observed quantities involved depend on the interaction strength. The confining trap introduces a weak center-of-mass dependence in the scaling exponent. We also conjecture results for the density-density correlation function.

cond-mat.stat-mech↗

arXiv1999

Finite-temperature correlations in the trapped Bose gas

Previous functional integral methods for translationally invariant systems have been extended to the case of a confining trap potential. Essentially all finite-temperature properties of the repulsive Bose gas in a paraboloidal trap can be determined this way. New analytical results reported here are for the finite-temperature two-point correlation functions below the critical temperatures in d=3,2 and 1 dimensions. Only for d=3 are correlations both long range and coherent - at long range consistent with the existence of a coherent state of the condensate in the trap. The two-dimensional condensate is marginally stable in the sense that correlations decay by a power law.

cond-mat.stat-mech↗

arXiv1999

Stroboscopic theory of atomic statistics in the micromaser

We study the statistics of the atoms emerging from the cavity of a micromaser in a dynamical, discrete-time `stroboscopic' description which takes into account the measurements made, in general, with imperfect efficiencies, on the states of the outcoming atoms. Inverted atoms enter stochastically, in general, with a binomial distribution in discrete time; but we also consider the continuous-time limit of this input statistics which is Poissonian. We envisage two alternative experimental procedures: one of these is to consider a fixed number N of atoms pumped into the cavity and subsequently leaving it to undergo state detection; the other is to consider input of the excited atoms and their subsequent detection and collection in a fixed time t. We consider, in particular, the steady state behaviors achieved in the two limits, N -> infinity and t -> infinity, as well as the approaches to these two limits. Although these limits are the same for the state of the cavity field, they are not the same, in general, for the observable outcoming atom statistics. We evaluate, in particular, Mandel's Q-parameters $Q_{e}$ $(Q_{g})$ for outcoming atoms detected in their excited states (ground states), for both N -> infinity and t -> infinity, as functions of $N_{ex} = RT_{c}$: R is the mean rate of entry for the incoming atoms and $T_c$ is the cavity damping time. The behavior of these atomic Q-parameters is compared with that parameter for the cavity field.

quant-ph↗

arXiv1997

Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras

Polynomial-in-time dependent symmetries are analysed for polynomial-in-time dependent evolution equations. Graded Lie algebras, especially Virasoro algebras, are used to construct nonlinear variable-coefficient evolution equations, both in 1+1 dimensions and in 2+1 dimensions, which possess higher-degree polynomial-in-time dependent symmetries. The theory also provides a kind of new realisation of graded Lie algebras. Some illustrative examples are given.

solv-int↗

arXiv1997

Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP equations

By starting from known graded Lie algebras, including Virasoro algebras, new kinds of time-dependent evolution equations are found possessing graded symmetry algebras. The modified KP equations are taken as an illustrative example: new modified KP equations with $m$ arbitrary time-dependent coefficients are obtained possessing symmetries involving $m$ arbitrary functions of time. A particular graded symmetry algebra for the modified KP equations is derived in this connection homomorphic to the Virasoro algebras.

solv-int↗