652 research outputs found
Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate
We study the exact solution for a two-mode model describing coherent coupling
between atomic and molecular Bose-Einstein condensates (BEC), in the context of
the Bethe ansatz. By combining an asymptotic and numerical analysis, we
identify the scaling behaviour of the model and determine the zero temperature
expectation value for the coherence and average atomic occupation. The
threshold coupling for production of the molecular BEC is identified as the
point at which the energy gap is minimum. Our numerical results indicate a
parity effect for the energy gap between ground and first excited state
depending on whether the total atomic number is odd or even. The numerical
calculations for the quantum dynamics reveals a smooth transition from the
atomic to the molecular BEC.Comment: 5 pages, 4 figure
Аналіз лінійних ситем в області трансформант кратного перетворення EIWAL
The algorithm for solution of differential equations of liner systems in basis of EIWAL transformation is suggestedПредложен алгоритм решения дифференциальных уравнений линейных систем в базисе преобразования EIWALЗапропоновано алгоритм розв‘язання диференційних рівнянь рівноваги лінійних систем в базисі кратного ортогонального перетворення EIWA
An algebraic approach to the Tavis-Cummings problem
An algebraic method is introduced for an analytical solution of the
eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on
polynomially deformed su(2), i.e. su_n(2), algebras. In this method the
eigenvalue problem is solved in terms of a specific perturbation theory,
developed here up to third order. Generalization to the N-atom case of the Rabi
frequency and dressed states is also provided. A remarkable enhancement of
spontaneous emission of N atoms in a resonator is found to result from
collective effects.Comment: 13 pages, 7 figure
Exact solutions for a family of spin-boson systems
We obtain the exact solutions for a family of spin-boson systems. This is
achieved through application of the representation theory for polynomial
deformations of the Lie algebra. We demonstrate that the family of
Hamiltonians includes, as special cases, known physical models which are the
two-site Bose-Hubbard model, the Lipkin-Meshkov-Glick model, the molecular
asymmetric rigid rotor, the Tavis-Cummings model, and a two-mode generalisation
of the Tavis-Cummings model.Comment: LaTex 15 pages. To appear in Nonlinearit
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