Conditions for order and chaos in the dynamics of a trapped Bose-Einstein condensate in coordinate and energy space

We investigate numerically conditions for order and chaos in the dynamics of an interacting Bose- Einstein condensate (BEC) confined by an external trap cut off by a hard-wall box potential. The BEC is stirred by a laser to induce excitations manifesting as irregular spatial and energy oscillations of the trapped cloud. Adding laser stirring to the external trap results in an effective time-varying trapping frequency in connection with the dynamically changing combined external+laser potential trap. The resulting dynamics are analyzed by plotting their trajectories in coordinate phase space and in energy space. The Lyapunov exponents are computed to confirm the existence of chaos in the latter space. Quantum effects and trap anharmonicity are demonstrated to generate chaos in energy space, thus confirming its presence and implicating either quantum effects or trap anharmonicity as its generator. The presence of chaos in energy space does not necessarily translate into chaos in coordinate space. In general, a dynamic trapping frequency is found to promote chaos in a trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved by increasing the characteristic scale of the external trap with respect to the condensate size.Comment: 19 pages, 14 page

A HAMILTON-JACOBI TREATMENT OF DISSIPATIVE SYSTEMS

Dissipative systems are investigated within the framework of the Hamilton-Jacobi equation. The principal function is determined using the method of separation of variables. The equation of motion can then be readily obtained. Three examples are given to illustrate our formalism: the damped harmonic oscillator, a system with a variable mass, and a charged particle in a magnetic field

CANONICAL QUANTIZATION OF DISSIPATIVE SYSTEMS

The canonical method is invoked to quantize dissipative systems using the WKB approximation. The wave function is constructed such that its phase factor is simply Hamilton’s principal function. The energy eigenvalue is found to be in exact agreement with the classical case. To demonstrate our approach, the three examples considered in our previous work (ESJ 9(30), 70-81, 2013) are quantized in detail: the damped harmonic oscillator, a system with a variable mass, and a charged particle in a magnetic field

Thermodynamic properties of an interacting hard-sphere Bose gas in a trap using the static fluctuation approximation

A hard-sphere (HS) Bose gas in a trap is investigated at finite temperatures in the weakly-interacting regime and its thermodynamic properties are evaluated using the static fluctuation approximation (SFA). The energies are calculated with a second-quantized many-body Hamiltonian and a harmonic oscillator wave function. The specific heat capacity, internal energy, pressure, entropy and the Bose-Einstein (BE) occupation number of the system are determined as functions of temperature and for various values of interaction strength and number of particles. It is found that the number of particles plays a more profound role in the determination of the thermodynamic properties of the system than the HS diameter characterizing the interaction, that the critical temperature drops with the increase of the repulsion between the bosons, and that the fluctuations in the energy are much smaller than the energy itself in the weakly-interacting regime.Comment: 34 pages, 24 Figures. To appear in the International Journal of Modern Physics

Thermodynamic Properties of Graphene Using the Static Fluctuation Approximation (SFA)

The thermodynamic properties of two-dimensional graphene nanosystems are investigated using the static fluctuation approximation (SFA). These properties are analyzed using both extensive and nonextensive statistical mechanics. It is found that these properties are less sensitive to the temperature when using nonextensive â in contrast to extensive â statistical mechanics. It is also noted that the mean internal energy and the specific heat behave as a power-law,T^Îą, at TThe accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author