Download Instabilities and Nonequilibrium Structures VII & VIII by O. Bénichou, M. Moreau, G. Oshanin (auth.), Orazio Descalzi, PDF

By O. Bénichou, M. Moreau, G. Oshanin (auth.), Orazio Descalzi, Javier Martínez, Enrique Tirapegui (eds.)

The contents of this publication correspond to classes VII and VIII of the overseas Workshop on Instabilities and Nonequilibrium buildings which came about in Viña del Mar, Chile, in December 1997 and December 1999, respectively. half I is dedicated to self-contained classes. 3 classes are regarding new advancements in Bose-Einstein condensation: the 1st one via Robert Graham experiences the classical dynamics of excitations of Bose condensates in anisotropic traps, the second one through Marc Etienne Brachet refers back to the bifurcations coming up in beautiful Bose-Einstein condensates and superfluid helium and the 3rd direction through André Verbeure is a pedagogical advent to the topic with particular emphasis on first ideas and rigorous effects. half I is done by means of classes given by way of Michel Moreau: the 1st one on diffusion constrained reactions of debris with fluctuating task and the second one at the part boundary dynamics in a one dimensional nonequilibrium lattice fuel. half II contains a collection of invited seminars at either Workshops.

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Instabilities and Nonequilibrium Structures VII & VIII

The contents of this publication correspond to classes VII and VIII of the overseas Workshop on Instabilities and Nonequilibrium buildings which came about in Viña del Mar, Chile, in December 1997 and December 1999, respectively. half I is dedicated to self-contained classes. 3 classes are regarding new advancements in Bose-Einstein condensation: the 1st one via Robert Graham reviews the classical dynamics of excitations of Bose condensates in anisotropic traps, the second one by way of Marc Etienne Brachet refers back to the bifurcations bobbing up in beautiful Bose-Einstein condensates and superfluid helium and the 3rd path through André Verbeure is a pedagogical advent to the topic with targeted emphasis on first rules and rigorous effects.

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In a bulk case, when there is no external potential U(z) the lowest lying excitations are phonons with linear wave-number dependence. ,. i.. . 0 z , ' , ",! 4 P FIG. 2. 01 (solid) and 1O-6(dotted). (From [1]) Numerically we have found that tending with the energy to zero, keeping I-' fixed the range of the classical motion outside the condensate for trajectories starting inside is getting smaller and smaller and in the limit the motion is confined to the region inside of the Thomas-Fermi surface.

The NLSE reads a'I/J i 8F c 7ft = - V2d. 8ijJ = i V2f" ([1- V(x)]'I/J -1'l/J1 2'I/J + f" V 'I/J) + U· V'I/J. 2 2 (11) We will be interested in the solutions of 8F /8ijJ = 0, for a given value of U. According to equation (3), these solutions are extrema of E at constant momentum P. 2 Numerical method When the extremum of F is a local minimum, the stationary solution 'l/Js of (11) can be reached by a relaxation method. If the extremum is not a minimum, Newton's iterative method is used to solve for 'l/Js.

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