Phase Transition and Padé Approximants for Fröhlich Polarons

Selyugin, O. V.; Smondyrev, M. A.

doi:10.1002/pssb.2221550114

Cited by 31 publications

(26 citation statements)

References 14 publications

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“…Among the most important shortcomings of Padé approximants, we may mention the following: the necessity of having many perturbative terms, the appearance of unphysical poles, the ability of dealing only with the so-called compatible variables, the possibility of describing only those functions that have at infinity a power-law behaviour with rational powers, and the impossibility to correctly treat nonmonotonic crossover. These difficulties are well known and repeatedly discussed in literature [10][11][12][13][14][15][16][17][18]. In addition, we remind that Padé approximation is rather a numerical method.…”

Section: Introductionmentioning

confidence: 90%

“…[51][52][53]. The motion in the space of approximations, near a quasifixed point, is described by the evolution integral (15), which can be written as…”

Section: General Approachmentioning

confidence: 99%

“…The Fröhlich optical polaron problem [3] is an interesting physical example of a crossover about which there existed a controversy lasting for around 30 years. Some researchers, analysing the polaron ground-state energy e(α) as a function of the electron-phonon coupling parameter α, found an indication to a phase transition from a state of freely moving weak-coupling polaron to a localized state of a strong-coupling polaron (see discussion in [15]). One of the first such indications has been suggested by Gross [59].…”

Section: Fröhlich Polaronmentioning

confidence: 99%

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Unified approach to crossover phenomena

Gluzman

Yukalov

1998

Phys. Rev. E

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A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions. The method can be employed for such difficult problems for which only a few terms of asymptotic expansions are available, and no other techniques are applicable. As an illustration, analytical solutions for several important physical problems are presented. 02.30.Lt, 11.10.Hi

show abstract

Section: Introductionmentioning

confidence: 90%

“…[51][52][53]. The motion in the space of approximations, near a quasifixed point, is described by the evolution integral (15), which can be written as…”

Section: General Approachmentioning

confidence: 99%

Section: Fröhlich Polaronmentioning

confidence: 99%

See 1 more Smart Citation

Unified approach to crossover phenomena

Gluzman

Yukalov

1998

Phys. Rev. E

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“…A solution in the weak coupling limit was given by Froehlich [11], and that in the strong coupling one was found by Pekar [1], [12]. By now rather an exact solution has been obtained for the energy of the polaron ground state in the weak coupling limit [13], [14] :…”

mentioning

confidence: 92%

Pekar's ansatz and the strong coupling problem in polaron theory

Лахно¹

2015

Phys.-Usp.

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A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz. A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on the basis of Pekar ansatz which was considered as an asymptotically exact solution in the strong coupling limit. In the case of bipolarons the theory yields the best values of the coupling energy and critical parameters of their stability. Numerous physical consequences of the existence of translation-invariant polarons and bipolarons are discussed.

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“…The polaron effects of electron-interface-optical-phonon interaction result in some changes to the electron self-energy and the effective mass which are very different from those in 3D system, and have been investigated extensively. In the past years, many works on the properties of interface polaron were studied using the perturbation-theory method [3][4][5], the Lee-Low-Pines(LLP) variational method [6][7][8] and the Feynman path integral approach [9][10][11]. Hai [5], for example, investigated the polaron energy and effective mass in a quantum well by applying the perturbation-theory method, Li and Gu [7] investigated intermediate-coupling polaron in a polar-crystal slab by using LLP variational method.…”

Section: Introductionmentioning

confidence: 99%

Electron self-energy and effective mass in a single heterostructure

Xiu-kun¹,

Wu²,

Li³

2003

Chinese Phys.

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In this paper, we investigate the electron self-energy and effective mass in a single heterostructure using Green-function method. Numerical calculations of the electron self-energy and effective mass for GaAs/AlAs heterostructure are performed. The results show that the self energy (effective mass) of electron, which incorporate the energy of electron coupling to interface-optical phonons and half three-dimension LO phonons, monotonically increase(decrease) from that of interface polaron to that of 3D bulk polaron with the increase of the distance between the position of the electron and interface.

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Phase Transition and Padé Approximants for Fröhlich Polarons

Cited by 31 publications

References 14 publications

Unified approach to crossover phenomena

Unified approach to crossover phenomena

Pekar's ansatz and the strong coupling problem in polaron theory

Electron self-energy and effective mass in a single heterostructure

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