Publications
42 results found
Graefe E, Korsch HJ, Niederle AE, 2010, Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer, Phys. Rev. A, Vol: 82
We investigate the many-particle and mean-field correspondence for anon-Hermitian N-particle Bose-Hubbard dimer where a complex onsite energydescribes an effective decay from one of the modes. Recently a generalizedmean-field approximation for this non-Hermitian many-particle system yieldingan alternative complex nonlinear Schr\"odinger equation was introduced. Here wegive details of this mean-field approximation and show that the resultingdynamics can be expressed in a generalized canonical form that includes ametric gradient flow. The interplay of nonlinearity and non-Hermiticityintroduces a qualitatively new behavior to the mean-field dynamics: Thepresence of the non-Hermiticity promotes the self-trapping transition, whiledamping the self-trapping oscillations, and the nonlinearity introduces astrong sensitivity to the initial conditions in the decay of the normalization.Here we present a complete characterization of the mean-field dynamics and thefixed point structure. We also investigate the full many-particle dynamics,which shows a rich variety of breakdown and revival as well as tunnelingphenomena on top of the mean-field structure.
Brody DC, Graefe EM, 2010, Coherent states and rational surfaces, J PHYS A-MATH THEOR, Vol: 43
The state spaces of generalised coherent states associated with special unitary groups are shown to form rational curves and surfaces in the space of pure states. These curves and surfaces are generated by the various Veronese embeddings of the underlying state space into higher dimensional state spaces. This construction is applied to the parameterisation of generalised coherent states, which is useful for practical calculations, and provides an elementary combinatorial approach to the geometry of the coherent state space. The results are extended to Hilbert spaces with indefinite inner products, leading to the introduction of a new kind of generalised coherent states.
Kolovsky AR, Korsch HJ, Graefe E-M, 2009, Bloch oscillations of Bose-Einstein condensates: Quantum counterpart of dynamical instability, PHYSICAL REVIEW A, Vol: 80, ISSN: 1050-2947
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- Citations: 46
Graefe EM, Korsch HJ, Niederle AE, 2008, Mean-Field Dynamics of a Non-Hermitian Bose-Hubbard Dimer, PHYSICAL REVIEW LETTERS, Vol: 101, ISSN: 0031-9007
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- Citations: 173
Graefe EM, Guenther U, Korsch HJ, et al., 2008, A non-Hermitian PT symmetric Bose-Hubbard model:: eigenvalue rings from unfolding higher-order exceptional points, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 41, ISSN: 1751-8113
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- Citations: 177
Korsch HJ, Graefe EM, Jodl H-J, 2008, The kicked rotor: Computer-based studies of chaotic dynamics, AMERICAN JOURNAL OF PHYSICS, Vol: 76, Pages: 498-503, ISSN: 0002-9505
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- Citations: 1
Strzys MP, Graefe EM, Korsch HJ, 2008, Kicked Bose-Hubbard systems and kicked tops - destruction and stimulation of tunneling, NEW JOURNAL OF PHYSICS, Vol: 10, ISSN: 1367-2630
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- Citations: 33
Graefe EM, Korsch HJ, 2007, Semiclassical quantization of an <i>N</i>-particle Bose-Hubbard model, PHYSICAL REVIEW A, Vol: 76, ISSN: 1050-2947
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- Citations: 46
Witthaut D, Graefe EM, Wimberger S, et al., 2007, Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and crossing of resonances, PHYSICAL REVIEW A, Vol: 75, ISSN: 1050-2947
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- Citations: 28
Graefe EM, Korsch HJ, 2006, Crossing scenario for a nonlinear non-Hermitian two-level system, CZECHOSLOVAK JOURNAL OF PHYSICS, Vol: 56, Pages: 1007-1020, ISSN: 0011-4626
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- Citations: 29
Witthaut D, Graefe EM, Korsch HJ, 2006, Towards a generalized Landau-Zener formula for an interacting Bose-Einstein condensate in a two-level system, PHYSICAL REVIEW A, Vol: 73, ISSN: 1050-2947
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- Citations: 77
Graefe EM, Korsch HJ, Witthaut D, 2006, Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models, and stimulated Raman adiabatic passage, PHYSICAL REVIEW A, Vol: 73, ISSN: 2469-9926
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- Citations: 130
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