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Gerisch, T.; Rieckers, Alfred

doi:10.1023/a:1023089930061

Cited by 7 publications

(15 citation statements)

References 30 publications

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“…Notice that the results of Section 2.1 together with results of [13,32,37,[43][44][45][46] give the full picture of behavior of model (1) for U ≤ 0, W = 0, and J z , J xy = 0 within VA approach. Cases of U > 0 as well as J z , J xy = 0 are left to future works.…”

Section: Summary and Final Commentsmentioning

confidence: 81%

Superconductivity, Charge Orderings, Magnetism, and Their Phase Separations in the Ground State of Lattice Models of Superconductor with Very Short Coherence Length

Kapcia

2014

J Supercond Nov Magn

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We present the ground state results for lattice models of superconductor (SC) with extremely short coherence length, which also involve the interplay with charge (CO) and (anti-)ferromagnetic orderings. Our preliminary results at zero temperature (derived by means of the variational approach which treats the on-site interaction term exactly and the intersite interactions within the mean field approximation, exact in d → +∞), yields that the SC phase can coexist with the CO or magnetic (M) phases in states with electron phase separation (PS:SC/CO and PS:SC/M, respectively).

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Section: Summary and Final Commentsmentioning

confidence: 81%

Superconductivity, Charge Orderings, Magnetism, and Their Phase Separations in the Ground State of Lattice Models of Superconductor with Very Short Coherence Length

Kapcia

2014

J Supercond Nov Magn

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“…We have described in [9] a singular perturbation theory in order to construct the inhomogeneous, reduced limiting dynamics in an extended C*-algebra, which beside the electron observables contains also classical observables. The latter are indexed by means of states on the one-cell algebra B.…”

Section: Model Assumptions Limiting Dynamics and Kms-statesmentioning

confidence: 99%

“…In this modified notation we may use the results of [9] to reveal an interesting connection between the stable spectral values and subgroups resp. subsemigroups of R. Observe that the quasi-particle energy of the homogeneous model is E 0 (β) = η 2 + ∆ 0 (β) 2 .…”

Section: (Note the Contradistinction Between Operator And State Occupmentioning

confidence: 99%

“…In previous publications [9,10] we have elaborated an alternative method, by which we extend the normclosed quasilocal CAR-algebra (based on the Canonical Anticommutation Relations for the conducting electrons near the Fermi surface) to a C*-algebra with a non-trivial center. By this we are able to describe the Heisenberg dynamics in the thermodynamic limit in form of a C*-dynamical system, that means a representation independent form of the dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…(Mathematically a C*-dynamical system is a one-parameter group of transformations, which act on the observables in a linear, multiplicative and * -preserving way and which depend on the time parameter in a strongly continuous manner [11]). The merits of this formulation, the mathematical technicalities of which are given in [9] and [10], are a unified theoretical frame for the various situations resp. reservoir couplings, a superconductor may encounter.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spectral Properties Of Weakly Inhomogeneous Bcs-Models In Different Representations

Benner

Rieckers

2005

Zeitschrift Für Naturforschung A

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For a class of Bardeen-Cooper-Schrieffer (BCS)-models, with complex, weakly momentum dependent interaction coefficients, the representation dependent effective Hamiltonians and their spectra are reconsidered in order to obtain a consistent physical picture by means of operator algebraic methods. The starting point is the limiting dynamics, the existence of which had been proved in a previous work, in terms of a C*-dynamical system acting in a classically extended, electronic Canonical Anticommutation Relations (CAR)-algebra. The C*-algebraic KMS-theory, including the low temperature limit, specifies the order parameters. These appear as classical observables, which commute with all other observables, constituting elements of the center of the algebra. The algebraic spectral theory, in the sense of Arveson, is first applied to the dynamics in general pure energy state representations. The spectra of the finite temperature representations are analyzed, identifying the gap as the lowest of those energy values, which are stable under local perturbations. Further insights are obtained by decomposing the thermal dynamical systems into the pure energy state Heisenberg dynamics, after having first extended them to more comprehensive W*-dynamical systems. The decomposing orthogonal measure is transferred to the infinite product space of quasi-particle occupation numbers and its support is characterized in terms of 0-1-laws leading to an asymptotic ratio of quasi-particles and holes, which depends on the temperature. This ratio is connected with an algebraic invariant of the representation dependent observable algebra. Energy renormalization aspects and pair occupation probabilities are discussed. The latter reveal, beside other things, the difference between macroscopic term occupation and coherent macroscopic term occupation for a condensate.

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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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Untitled

Cited by 7 publications

References 30 publications

Superconductivity, Charge Orderings, Magnetism, and Their Phase Separations in the Ground State of Lattice Models of Superconductor with Very Short Coherence Length

Superconductivity, Charge Orderings, Magnetism, and Their Phase Separations in the Ground State of Lattice Models of Superconductor with Very Short Coherence Length

Spectral Properties Of Weakly Inhomogeneous Bcs-Models In Different Representations

Algebraic Quantum Theory of the Josephson Microwave Radiator

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