Chapter

Collective Oscillations of a Quasi One Dimensional Bose Condensate Under Damping

07/2009; DOI:10.1007/978-90-481-3120-4_16 pp.189-196

ABSTRACT Affect of the damping on collective oscillations of a quasi one-dimensional trapped repulsive Bose gas has been studied. Based
on the phenomenological damping approach (Zh. Eksp. Teor. Fiz. 35:408, 1958a; Sov. Phys. JETP 35:282, 1958b) developed by
Pitaevskii variational equations for the parameters of the condensate wave function have been derived. Analytical expressions
for the condensate parameters in the steady-state have been obtained. Combined effect of the resonant periodical variation of the trap strength and the damping has been shown to change drastically asymptotical behavior of the driven norm oscillations. Bistability in nonlinear oscillations
of the condensate under periodic variations of the trap potential is predicted.

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    ABSTRACT: The spatial dynamics of pulses in Kerr media with parabolic index profile are examined. It is found that when diffraction and graded-index have opposite signs propagating pulses exhibit an oscillatory pattern, similar to a breathing behavior. Furthermore, if the pulse and the index profile are not aligned the pulse oscillates around the index origin with frequency that depends on the values of the diffraction and index of refraction. These oscillations are not observed when diffraction and graded-index share the same sign.
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Keywords

collective oscillations
 
condensate parameters
 
condensate wave function
 
driven norm oscillations
 
periodic variations
 
phenomenological damping approach
 
Phys
 
Pitaevskii variational equations
 
repulsive Bose gas
 
resonant periodical variation
 
Sov
 
steady-state
 
Teor