Investigation of the polaron model by the method of functional integration

Kochetov, Evgueny; Kuleshov, S.P.; Smondyrev, M. A.

doi:10.1007/bf01037638

Cited by 9 publications

(4 citation statements)

References 1 publication

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“…Similar difficulties were found in a functional-integral treatment of the formal partition function, corresponding to Hamiltonian (1): In fact, if Q 6 ¼ 0 is true, oscillating integrands prevent a nontrivial estimate of the integral (see Refs. [33,34]). It was only recently that two of the present authors [20] found a lower bound for the complete dispersion.…”

Section: A Variational Upper Bound Onmentioning

confidence: 96%

On the LO‐polaron dispersion in D dimensions

Gerlach¹,

Kalina

Smondyrev³

2003

Physica Status Solidi (b)

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We discuss the (LO)polaron dispersion for arbitrary spatial dimension D. Firstly, we review the existing literature; recent numerical work is critically analyzed. Secondly, we derive novel upper bounds for the dispersion, which incorporate the correct behaviour of the dispersion up to third order of the coupling constant a. A totally analytical evaluation is performed in the case D ¼ 1. We compare the upper bounds with previously published lower bounds. Apart from a surrounding of zero dispersion, the relative deviation is on a few-percent scale.

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Section: A Variational Upper Bound Onmentioning

confidence: 96%

On the LO‐polaron dispersion in D dimensions

Gerlach¹,

Kalina

Smondyrev³

2003

Physica Status Solidi (b)

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“…A significantly new development began with the advent of functional-integral methods (see the pioneering work of Feynman, 1955); in combination with refined variational procedures, they proved to be an extremely powerful tool, if not the most powerful. We refer to Osaka (1959); Schultz (1959) and; Marshall and Mills (1970); Abe and Okamoto (1971); Okamoto and Abe (1972); Smondyrev (1975) and(1982); Sa-yakanit (1979); Adamowski, Gerlach, and Leschke (1980b); Saitoh (1980a); Saitoh and Arisawa (1980); Kochetov and Smondyrev (1981); Fedyanin and Rodriguez (1982); Kholodenko and Freed (1983); Castrigiano, Kokiantonis, and Stierstorfer (1984); Wu, Peeters, and Devreese (1985a) ;Fisher and Zwerger (1986); and Gerlach, Lowen, and Schliffke (1987).…”

Section: A-> Comentioning

confidence: 99%

Analytical properties of polaron systems or: Do polaronic phase transitions exist or not?

Gerlach

Löwen²

1991

Rev. Mod. Phys.

228

176

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For more than 40 years it was thought that polaron-and exciton-phonon systems exhibited unexpected localization properties. Particular attention was paid to the so-called phonon-induced self-trapping transition, which, it was believed, should manifest itself as a point of nonanalyticity in the ground-state energy as a function of the electron-phonon coupling parameter. It will be demonstrated for a large class of (generalized Frohlich) models that no such transition exists. The dimensionality of space has no qualitative influence; insofar, an application of the authors' results to problems in lower dimensions (e.g., polarons in quantum wells) is straightforward. The same holds true if homogeneous external fields are involved; for example, a discontinuous mass stripping for magnetopolarons can be excluded. On the other hand, a phase-transition-like behavior will be found, if a polaron or exciton is exposed to a short-range potential, allowing a so-called pinning transition. The authors emphasize, however, that even in this case the transition is only modified, and not induced, by phonons.

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“…The latter appeared to be of the exactly RPA-approximated form, owing to which we could neglect it. This approximation can be used whether the crystal temperature is high enough or the intensity parameter α ∈ R + is not too small, being α > 5, 8, when a transition of the polaron from a non-localized state to a self-localized state is realized [23,24].…”

Section: Resultsmentioning

confidence: 99%

The Bogolubov representation of the polaron model and its completely integrable RPA-approximation

Bogolubov¹,

Prykarpatsky²,

Ghazaryan³

2010

Condens. Matter Phys.

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The polaron model in ionic crystal is studied in the Bogolubov representation using a special RPA-approximation. A new exactly solvable approximated polaron model is derived and described in detail. Its free energy at finite temperature is calculated analytically. The polaron free energy in the constant magnetic field at finite temperature is also discussed. Based on the structure of the Bogolubov unitary transformed polaron Hamiltonian there is stated a very important new result: the full polaron model is exactly solvable.

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Investigation of the polaron model by the method of functional integration

Cited by 9 publications

References 1 publication

On the LO‐polaron dispersion in D dimensions

On the LO‐polaron dispersion in D dimensions

Analytical properties of polaron systems or: Do polaronic phase transitions exist or not?

The Bogolubov representation of the polaron model and its completely integrable RPA-approximation

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