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Exactly solvable models for strongly interacting quantum systems

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The main objective of the research is to solve exactly, at zero temperature and also at finite temperatures, strongly interacting models of quantum excitations which have proved to be important in high Tc superconductivity, low-dimensional magnetism and quantum optics.

The research will be divided into three areas which are quantum spin models, exciton-phonon systems and quantum optics. Although these research areas may appear rather different from each other, there are in fact surprising similarities between their relevant models, and cross-fertilization may prove very useful.

In the field of quantum optics the Tavis-Cummings model shall be generalised such that a nonideal cavity (Kerr nonlinearity) and a dynamic Stark shift can be included in the model. Other generalisations will be looked for to include two-photon transitions and intensity dependent coupling. Problems like sqeezing properties and collapse and revival properties of the atomic inversion will be considered. Similarly, new results can be derived through q-deformed models for the Maxwell-Bloch system with different boundary conditions. It is intended to construct a lattice version of the Maxwell-Bloch system for which a Hamiltonian formulation can be found by the quantum inverse method. Soliton solutions for this new q-deformed lattice model will also be worked out.

For quantum spin models connections between q-deformed lattice models and quantum spin models will be further pursued. It seems probable that quantum spin models provide a natural realisation of q-deformed models. This would open up new perspectives in the analysis of spin models which have received much recent interest, mainly because of important magnetic fluctuations which appear in compounds with a high transition temperature to a superconducting phase. It is evident that new results for the critical behaviour of quantum spin models are expected.

For Exciton-phonon systems the interaction of electronic excitations with lattice modes is an important problem with a long history in condensed matter physics. Recently similar mechanisms have also been proposed for long molecules which contain hydrogen bonded chains such as helical proteins. Especially in long molecules where one-dimensional treatment is applicable, the strength of the mode-mode coupling plays a crucial role. In the case of strong coupling the expression of the operators in terms of their q-deformed counterparts may provide new ways of solving the coupled Hamiltonian system. Preliminary results indicate that there is e.g. an integrable q-deformed model which can be reduced in one limit to the well known Davydov model. This new model will be analysed and it is hoped to solve its zero and finite temperature properties, and possibly its correlation functions.

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University of Jyväskylä
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Nisulank 78
90351 Jyväskylä
Finnland

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Letzte Aktualisierung: 19 September 1996

Mein Booklet

Permalink: https://cordis.europa.eu/project/id/INTAS-94-1194/de

European Union, 2024