Second-quantized Landau-Zener theory for dynamical instabilities

Journal Article · Thu May 01 00:00:00 EDT 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.67.051601· OSTI ID:20636335

Anglin, J R ^[1]

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1. Center for Ultracold Atoms, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (United States)

State engineering in nonlinear quantum dynamics sometimes may demand driving the system through a sequence of dynamically unstable intermediate states. This very general scenario is especially relevant to the dilute Bose-Einstein condensates, for which ambitious control schemes have been based on the powerful Gross-Pitaevskii mean-field theory. Since this theory breaks down on logarithmically short time scales in the presence of dynamical instabilities, an interval of instabilities introduces quantum corrections, which may possibly derail a control scheme. To provide a widely applicable theory for such quantum corrections, this paper solves a general problem of time-dependent quantum-mechanical dynamical instability, by modeling it as a second-quantized analog of a Landau-Zener avoided crossing: a 'twisted crossing'.

• OSTI ID: 20636335
• Journal Information: Physical Review. A, Vol. 67, Issue 5; Other Information: DOI: 10.1103/PhysRevA.67.051601; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BOSE-EINSTEIN CONDENSATION
COMPUTERIZED SIMULATION
CONTROL
CORRECTIONS
EIGENFUNCTIONS
EIGENVALUES
INSTABILITY
INTERMEDIATE STATE
MEAN-FIELD THEORY
NONLINEAR PROBLEMS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
STABILITY
TIME DEPENDENCE