Quesne, Christiane, Tkachuk, Volodymyr M. (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Regniers, Gilles, Van der Jeugt, Joris (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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González León, M.A., Mateos Guilarte, J., de la Torre Mayado, M. (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Benjamin Schlein (2011)
Journées Équations aux dérivées partielles
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In these notes, we review some recent mathematical results concerning the derivation of effective evolution equations from many body quantum mechanics. In particular, we discuss the emergence of the Hartree equation in the so-called mean field regime (for example, for systems of gravitating bosons), and we show that the Gross-Pitaevskii equation approximates the dynamics of initially trapped Bose-Einstein condensates. We explain how effective evolution equations can be derived, on the...
Glinka, Lukasz-Andrzej (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Duviryak, Askold (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Kalnins, Ernest G., Kress, Jonathan M., Miller, Willard jun. (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Joachim Seifert (1997)
Banach Center Publications
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Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for two physically relevant cases are found and expressed as Stieltjes Wigert polynomials. ...
Cagnache, Eric, Wallet, Jean-Christophe (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Cariñena, José F., Rañada, Manuel F., Santander, Mariano (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Najarbashi, Ghader, Maleki, Yusef (2011)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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