Comparison of weakly inhomogeneous BCS- and Hubbard models

Gerisch, T.; Rieckers, Alfred

doi:10.1016/s0378-4371(97)00256-2

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…One of the most popular examples is the BCS-model [55 -57]. Very similar in their pure phase state structure are homogenizations of the Hubbard model [58,59]. In the notation of Sect.…”

Section: Remarks On Model Discussionmentioning

confidence: 99%

Thermodynamic Formalism and Phase Transitions of Generalized Mean-Field Quantum Lattice Models

Gerisch

Rieckers²,

Volkert³

1998

Zeitschrift Für Naturforschung A

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The general structure of thermodynamic equilibrium states for a class of quantum mechanical (multi-lattice) systems is elaborated, combining quantum statistical and thermodynamical methods. The quantum statistical formulation is performed in terms of recent operator algebraic concepts emphasizing the role of the permutation symmetry due to homogeneous coarse graining and employing the internal symmetries. The variational principle of the free energy functional is derived, which determines together with the symmetries the general form of the limiting Gibbs states in terms of their central decomposition. The limiting minimal free energy density and its possible equilibrium states are analyzed on various levels of the description by means of convex analysis, where the Fenchel transforms of the free energies provide entropy like potentials. On the thermodynamic level a modified entropy surface is obtained, which specifies only in combination with its concave envelope the regions of pure and mixed phase states. The symmetry properties of a certain model allow to specify the (non-) differentiability of the minimal free energy density. A characterization and classification of phase transitions in terms of quantum statistical equilibrium states is proposed, and the connection to the Landau theory is established demonstrating that the latter implies a (continuous) deformation of the sets of equilibrium states along a canonically given curve.

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“…One of the most popular examples is the BCS-model [55 -57]. Very similar in their pure phase state structure are homogenizations of the Hubbard model [58,59]. In the notation of Sect.…”

Section: Remarks On Model Discussionmentioning

confidence: 99%

Thermodynamic Formalism and Phase Transitions of Generalized Mean-Field Quantum Lattice Models

Gerisch

Rieckers²,

Volkert³

1998

Zeitschrift Für Naturforschung A

Self Cite

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“…For this, the techniques from [10], [47], [48], [49], [50], [51], where the homogeneous mean-field theory is perturbed with certain classes of momentum dependent inhomogeneities, would apply.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Quantum Theory of the Josephson Microwave Radiator

Gerisch

Honegger

Rieckers

2003

Ann. Henri Poincaré

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A closed, entirely quantum mechanical Josephson oscillator model is considered, consisting of two superconductors in tunneling contact, which weakly interact with the photon field. For each superconductor we use, for notational simplicity, the BCS model in the strong coupling approximation and restrict ourselves to Anderson's quasi-spin formulation. The thermodynamic limit of the global (nonequilibrium) dynamics is formulated for a large variety of states. It arises a generalization of previously developed cocycle equations, connecting the collective behaviour of the two superconductors with the photon field dynamics. In the physically most interesting situations, where the two superconductors are in thermal equilibrium (below the critical temperature) at voltage difference V , we show, that for arbitrary initial states the outgoing multi-photon states are quantum optically all-order coherent and constitute an almost monochromatic radiation of frequency 2eV / . Furthermore, we deduce in detail, how the collective behaviour of the superconductors influences the collective (that are the optical) features of the emitted microwave photons.

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Gerisch

Rieckers

1998

Journal of Statistical Physics

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Comparison of weakly inhomogeneous BCS- and Hubbard models

Cited by 4 publications

References 22 publications

Thermodynamic Formalism and Phase Transitions of Generalized Mean-Field Quantum Lattice Models

Thermodynamic Formalism and Phase Transitions of Generalized Mean-Field Quantum Lattice Models

Algebraic Quantum Theory of the Josephson Microwave Radiator

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