A New Look at the Schouten-Nijenhuis, Fr\"olicher-Nijenhuis and Nijenhuis-Richardson Brackets for Symplectic Spaces

In this paper we re-express the Schouten-Nijenhuis, the Fr\"olicher-Nijenhuis and the Nijenhuis-Richardson brackets on a symplectic space using the extended Poisson brackets structure present in the path-integral formulation of classical mechanics.Comment: 27+1 pages, Latex, no figure

Nonlinear effects for Bose Einstein condensates in optical lattices

We present our experimental investigations on the subject of dynamical nonlinearity-induced instabilities and of nonlinear Landau-Zener tunneling between two energy bands in a Rubidium Bose-Einstein condensate in an accelerated periodic potential. These two effects may be considered two different regimes (for small and large acceleration) of the same physical system and studied with the same experimental protocol. Nonlinearity introduces an asymmetry in Landau-Zener tunneling; as a result, tunneling from the ground state to the excited state is enhanced whereas in the opposite direction it is suppressed. When the acceleration is lowered, the condensate exhibits an unstable behaviour due to nonlinearity. We also carried out a full numerical simulation of both regimes integrating the full Gross-Pitaevskii equation; for the Landau-Zener effect we also used a simple two-level model. In both cases we found good agreement with the experimental results.Comment: 9 pages, 7 figures. Submitted to Laser Physic

Instabilities of a Bose-Einstein condensate in a periodic potential: an experimental investigation

By accelerating a Bose-Einstein condensate in a controlled way across the edge of the Brillouin zone of a 1D optical lattice, we investigate the stability of the condensate in the vicinity of the zone edge. Through an analysis of the visibility of the interference pattern after a time-of-flight and the widths of the interference peaks, we characterize the onset of instability as the acceleration of the lattice is decreased. We briefly discuss the significance of our results with respect to recent theoretical work.Comment: 7 pages, 3 figures; submitted to Optics Express (Focus Issue on Cold Atomic Gases in Optical Lattices

Giant electrocaloric effect around Tc_c

We use molecular dynamics with a first-principles-based shell model potential to study the electrocaloric effect (ECE) in lithium niobate, LiNbO$_3$, and find a giant electrocaloric effect along a line passing through the ferroelectric transition. With applied electric field, a line of maximum ECE passes through the zero field ferroelectric transition, continuing along a Widom line at high temperatures with increasing field, and along the instability that leads to homogeneous ferroelectric switching below $T_c$ with an applied field antiparallel to the spontaneous polarization. This line is defined as the minimum in the inverse capacitance under applied electric field. We investigate the effects of pressure, temperature and applied electric field on the ECE. The behavior we observe in LiNbO$_3$ should generally apply to ferroelectrics; we therefore suggest that the operating temperature for refrigeration and energy scavenging applications should be above the ferroelectric transition region to obtain large electrocaloric response. We find a relationship among $T_c$, the Widom line and homogeneous switching that should be universal among ferroelectrics, relaxors, multiferroics, and the same behavior should be found under applied magnetic fields in ferromagnets.Comment: 5 page

Impact of information technology on the development of the company

Приведено аспекти інформаційних технологій, які можуть вплинути на розвиток підприємства.Приведены аспекты информационных технологий, которые могут повлиять на развитие предприятия.Shows aspects of information technology, which may affect the development of the enterprise

Comment on "On the importance of the free energy for elasticity under pressure"

Marcus et al. (Marcus P, Ma H and Qiu S L 2002 J. Phys.: Condens. Matter 14 L525) claim that thermodynamic properties of materials under pressure must be computed using the Gibbs free energy $G$, rather than the internal energy $E$. Marcus et al. state that ``The minima of $G$, but not of $E$, give the equilibrium structure; the second derivatives of $G$, but not of $E$, with respect to strains at the equilibrium structure give the equilibrium elastic constants.'' Both statements are incorrect.Comment: Commen

Chaotic properties of quantum many-body systems in the thermodynamic limit

By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction strength drives the system away from integrability. A correspondence with the dynamical chaoticity of an associated $c$-number system is then used to infer properties of the quantum system in the thermodynamic limit.Comment: 4 pages RevTeX, 4 postscript figures included with psfig; Completely restructured version with new results on mixing properties added

Asymmetric Landau-Zener tunneling in a periodic potential

Using a simple model for nonlinear Landau-Zener tunneling between two energy bands of a Bose-Einstein condensate in a periodic potential, we find that the tunneling rates for the two directions of tunneling are not the same. Tunneling from the ground state to the excited state is enhanced by the nonlinearity, whereas in the opposite direction it is suppressed. These findings are confirmed by numerical simulations of the condensate dynamics. Measuring the tunneling rates for a condensate of rubidium atoms in an optical lattice, we have found experimental evidence for this asymmetry.Comment: 5 pages, 3 figure