Equations of superconductivity for transition metals in the Wannier representation

Vujičić, G. M.; Kuzemskii, A. L.; Плакида, Н. М.

doi:10.1007/bf01014801

Cited by 7 publications

(18 citation statements)

References 16 publications

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“…We derive the equations for superconductivity in the site representation by means of the irreducible Green's function method 33-35 in Section 2, using ideas developed previously in connection with the derivation of Eliashberg-type equations for pure transition metals in the Wannier representation. 35 Various attempts at configurational averaging are discussed in Section 3, where the formula for Tc is also obtained. Section 4 contains a discussion and conclusions.…”

Section: Introductionmentioning

confidence: 99%

The theory of strong coupling superconductivity in disordered transition metal alloys

Wysokiński

Kuzemsky

1983

J Low Temp Phys

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Section: Introductionmentioning

confidence: 99%

The theory of strong coupling superconductivity in disordered transition metal alloys

Wysokiński

Kuzemsky

1983

J Low Temp Phys

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“…One should note that the BCS-Bogoliubov superconductivity theory [1,3,5,10,15] is formulated in terms of a trial (approximating) Hamiltonian H mod , which is a quadratic form with respect to the second-quantized creation and annihilation operators, including the terms responsible for anomalous (or non-diagonal) averages. For the single-band Hubbard model the BCS-Bogoliubov functional of generalized mean fields can be written in the following form [92,93,94,95]…”

Section: The Mean Field Conceptmentioning

confidence: 99%

Variational principle of Bogoliubov and generalized mean fields in many-particle interacting systems

Kuzemsky

2015

Int. J. Mod. Phys. B

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The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex statistical systems. The analysis is centered around the variational principle of Bogoliubov for free energy in the context of its applications to various problems of statistical mechanics. The review presents a terse discussion of selected works carried out over the past few decades on the theory of many-particle interacting systems in terms of the variational inequalities. It is the purpose of this paper to discuss some of the general principles which form the mathematical background to this approach and to establish a connection of the variational technique with other methods, such as the method of the mean (or self-consistent) field in the many-body problem. The method is illustrated by applying it to various systems of many-particle interacting systems, such as Ising, Heisenberg and Hubbard models, superconducting (SC) and superfluid systems, etc. This work proposes a new, general and pedagogical presentation, intended both for those who are interested in basic aspects and for those who are interested in concrete applications. particle interacting systems; the variational principle of Bogoliubov; Bogoliubov inequality; generalized mean fields; model Hamiltonians of many-particle interacting systems. PACS numbers: 05.30-d, 05.30.Fk, 05.30.Jp, 05.70.-a, 05.70.Fh, 02.90.+p 1530010-1 Int. J. Mod. Phys. B 2015.29. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/24/15. For personal use only. 1530010-2 Int. J. Mod. Phys. B 2015.29. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/24/15. For personal use only. 1530010-5 Int. J. Mod. Phys. B 2015.29. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/24/15. For personal use only. 1530010-8 Int. J. Mod. Phys. B 2015.29. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/24/15. For personal use only. 1530010-9 Int. J. Mod. Phys. B 2015.29. Downloaded from www.worldscientific.com by RUTGERS UNIVERSITY on 08/24/15. For personal use only.

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Section: Effective and Generalized Mean Fieldsmentioning

confidence: 99%

“…It is important to emphasize that the BCS-Bogolyubov theory of superconductivity [12,41,42] was formulated on the basis of a trial Hamiltonian which consists of a quadratic form of creation and annihilation operators, including "anomalous" (off-diagonal) averages [13]. The strong-coupling BCS-Bogolyubov theory of superconductivity was formulated for the Hubbard model in the localized Wannier representation in [57,60,61]. Therefore, instead of the algebra of the operator of a normal state a iσ , a motivated an intensification of research in superconductivity, not only because applications are promising, but because they also represent a new state of matter that breaks certain fundamental symmetries.…”

Section: -15mentioning

confidence: 99%

See 1 more Smart Citation

Quasiaverages, symmetry breaking and irreducible Green functions method

Kuzemsky¹

2010

Condens. Matter Phys.

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The development and applications of the method of quasiaverages to quantum statistical physics and to quantum solid state theory and, in particular, to quantum theory of magnetism, were considered. It was shown that the role of symmetry (and the breaking of symmetries) in combination with the degeneracy of the system was reanalyzed and essentially clarified within the framework of the method of quasiaverages. The problem of finding the ferromagnetic, antiferromagnetic and superconducting "symmetry broken" solutions of the correlated lattice fermion models was discussed within the irreducible Green functions method. A unified scheme for the construction of generalized mean fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the equations of motion and Dyson equation was generalized in order to include the "source fields". This approach complements previous studies of microscopic theory of antiferromagnetism and clarifies the concepts of Neel sublattices for localized and itinerant antiferromagnetism and "spin-aligning fields" of correlated lattice fermions. 05.30.Fk,

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Equations of superconductivity for transition metals in the Wannier representation

Cited by 7 publications

References 16 publications

The theory of strong coupling superconductivity in disordered transition metal alloys

The theory of strong coupling superconductivity in disordered transition metal alloys

Variational principle of Bogoliubov and generalized mean fields in many-particle interacting systems

Quasiaverages, symmetry breaking and irreducible Green functions method

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