arXiv subjects

J. C. Bronski

Publications and source records attributed to J. C. Bronski.

4 recordsLinked to original sources

arXiv2002

Dynamics of a trapped 2D Bose-Einstein condensate with periodically and randomly varying atomic scattering length

In this work we consider the oscillations and associated resonance of a 2D Bose-Einstein condensate under periodic and random modulations of the atomic scattering length. For random oscillations of the trap potential and of the atomic scattering length we are able to calculate the mean growth rate for the width of the condensate. The results obtained from the reduced ODE's for oscillations of the width of condensate are compared with the numerical simulations of the full 2D Gross-Pitaevskii equation with modulated in time coefficients.

cond-mat.soft↗

arXiv2000

Stability of Attractive Bose-Einstein Condensates in a Periodic Potential

Using a standing light wave trap, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is modeled by the cubic nonlinear Schrödinger equation with attractive nonlinearity and an elliptic function potential of which a standing light wave is a special case. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schrödinger equation nor in the integrable nonlinear Schrödinger equation. Their stability is examined using analytic and numerical methods. Trivial-phase solutions are experimentally stable provided they have nodes and their density is localized in the troughs of the potential. Stable time-periodic solutions are also examined.

cond-mat↗

arXiv2000

Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential

The cubic nonlinear Schrödinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schrödinger equation nor in the integrable nonlinear Schrödinger equation. Their stability is examined using analytic and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schrödinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas-Fermi limit.

cond-mat↗

arXiv1999

Rigorous estimates of the tails of the probability distribution function for the random linear shear model

In previous work Majda and McLaughlin computed explicit expressions for the $2N$th moments of a passive scalar advected by a linear shear flow in the form of an integral over ${\bf R}^N$. In this paper we first compute the asymptotics of these moments for large moment number. We are able to use this information about the large N behavior of the moments, along with some basic facts about entire functions of finite order, to compute the asymptotics of the tails of the probability distribution function. We find that the probability distribution has Gaussian tails when the energy is concentrated in the largest scales. As the initial energy is moved to smaller and smaller scales we find that the tails of the distribution grow longer, and the distribution moves smoothly from Gaussian through exponential and ``stretched exponential''. We also show that the derivatives of the scalar are increasingly intermittent, in agreement with experimental observations, and relate the exponents of the scalar derivative to the exponents of the scalar.

physics.flu-dyn↗