The Polaron Revisited

Møller, Jacob Schach

doi:10.1142/s0129055x0600267x

Cited by 49 publications

(77 citation statements)

References 29 publications

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“…To summarize, by combining (18), (19), (20) and the facts Δ κ (P ) ≥ 1 − P 2 /4 and 2E p,κ − E κ (P ) ≥ E bin,κ − P 2 /4 which follow from Proposition 4.1 (i), we have the following. …”

Section: T Miyao and H Spohn Ann Henri Poincarémentioning

confidence: 76%

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The Bipolaron in the Strong Coupling Limit

Miyao

Spohn

2007

Ann. Henri Poincaré

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The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Fröhlich approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons. Otherwise the electrons form a bound pair. We prove the validity of the Pekar-Tomasevich energy functional in the strong coupling limit, yielding estimates on the coupling parameters for which the binding energy is strictly positive. Under the condition of a strictly positive binding energy we prove the existence of a ground state at fixed total momentum P , provided P is not too large.

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Section: T Miyao and H Spohn Ann Henri Poincarémentioning

confidence: 76%

“…We refer to [27] for a survey and to [12] for a listing of theoretical investigations. Spectral properties of the Fröhlich polaron are investigated in [20,29].…”

Section: Introductionmentioning

confidence: 99%

The Bipolaron in the Strong Coupling Limit

Miyao

Spohn

2007

Ann. Henri Poincaré

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“…Consequently there is a huge literature, both experimental and theoretical, devoted to its study. See, e.g., [1,13,29,34,35] and references therein. Our concern here is with the binding or non-binding of several polarons: whether the ordinary Coulomb repulsion among the electrons can, if strong enough, prevent the binding that would otherwise be created by the electric field of the polar crystal.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stability and absence of binding for multi-polaron systems

et al. 2011

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We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N ≥ 2 polarons. Fröhlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling √ α, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U < 2α, stability of matter does hold for U > 2α, that is, the ground state energy per particle has a finite limit as N → ∞. (ii) There is no binding of any kind if U exceeds a critical value that depends on α but not on N. The same results are shown to hold for the Pekar-Tomasevich model.

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“…8. The existence of the ground state at p = 0 for σ = 0 (see also [19]), and renormalization of the electron mass is an important ingredient for the phenomenon of enhanced binding [7,11,12]. A Schrödinger operator with a non-confining potential can exhibit a bound state when the interaction of the electron with the quantized electromagnetic field is included.…”

Section: Remark 27mentioning

confidence: 99%

The renormalized electron mass in non-relativistic quantum electrodynamics

Bach

Chen

Fröhlich

et al. 2007

Journal of Functional Analysis

167

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This work addresses the problem of infrared mass renormalization for a non-relativistic electron minimally coupled to the quantized electromagnetic field (the standard, translationally invariant system of an electron in non-relativistic QED). We assume that the interaction of the electron with the quantized electromagnetic field is subject to an ultraviolet regularization and an infrared regularization parametrized by σ > 0. For the value p = 0 of the conserved total momentum of electron and photon field, bounds on the renormalized mass are established which are uniform in σ → 0, and the existence of a ground state is proved. For |p| > 0 sufficiently small, bounds on the renormalized mass are derived for any fixed σ > 0.A key ingredient of our proofs is the operator-theoretic renormalization group based on the isospectral smooth Feshbach map. It provides an explicit, finite algorithm for determining the renormalized electron mass at p = 0 to any given precision.

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The Polaron Revisited

Cited by 49 publications

References 29 publications

The Bipolaron in the Strong Coupling Limit

The Bipolaron in the Strong Coupling Limit

Stability and absence of binding for multi-polaron systems

The renormalized electron mass in non-relativistic quantum electrodynamics

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