Symmetry of Bipolaron Bound States for Small Coulomb Repulsion

Frank, Rupert L.; Lieb, Élliott H.; Seiringer, Robert

doi:10.1007/s00220-012-1604-y

Cited by 11 publications

(16 citation statements)

References 21 publications

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“…The Pekar-Tomasevich minimization problem has been studied in great detail. 1,2,[7][8][9]11,20,21,25 In particular, the analogous statements of our Theorems 2.1, 3.1 and 4.1 remain valid for this model.…”

Section: The Pekar-tomasevich Approximationsupporting

confidence: 71%

Ground State Properties of Multi-Polaron Systems

Frank¹,

Lieb²,

Seiringer³

et al. 2013

XVIIth International Congress on Mathematical Physics

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We summarize our recent results on the ground state energy of multi-polaron systems. In particular, we discuss stability and existence of the thermodynamic limit, and we discuss the absence of binding in the case of large Coulomb repulsion and the corresponding binding-unbinding transition. We also consider the Pekar-Tomasevich approximation to the ground state energy and we study radial symmetry of the ground state density.

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Section: The Pekar-tomasevich Approximationsupporting

confidence: 71%

Ground State Properties of Multi-Polaron Systems

Frank¹,

Lieb²,

Seiringer³

et al. 2013

XVIIth International Congress on Mathematical Physics

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“…Nowadays we already reaped a rich harvest from the Fröhlich Hamiltonian by both approaches. Nevertheless it is still an attractive subject [2,8,13,14,15,20,21,30,34,39,48].…”

Section: Introductionmentioning

confidence: 99%

Monotonicity of the Polaron Energy

Miyao

2014

Reports on Mathematical Physics

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In condensed matter physics, the polaron has been fascinating subject. It is described by the Hamiltonian of H. Fröhlich. In this paper, the Fröhlich Hamiltonian is investigated from a viewpoint of operator inequalities proposed in [36]. This point of view clarifies the monotonicity of polaron energy, i.e., denoting the lowest energy of the Fröhlich Hamiltonian with the ultraviolet cutoff Λ by E Λ , we prove E Λ > E Λ ′ for Λ < Λ ′ .

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“…This is related to the study of bi-polarons in statistical mechanics, see the work of ) and Frank-Lieb-Seiringer ( [12]). The model is written by the path measures…”

Section: Coulomb Interactionmentioning

confidence: 99%

“…These measures describe the motion of two electrons coupled to an ionic crystal, and unlike the case of a single polaron, the interaction in (1.9) carries both attractive (contributions coming from the first term) and repulsive (the Coulomb force appearing in the second term) effects. Again for strong coupling regime, the behavior of the partition function lim λ→0 lim t→∞ Z λ,u,t = E(u) is expressed by the Pekar-Thomasevich energy functional ( [27], [12]), and E(u) determines, depending on the value of u, if in the lowest energy states two electrons form a bound pair, or they split into two well-separated polarons. Again questions concerning the behavior of the actual path measures P ⊗ λ,u,t remain widely open.…”

Section: Coulomb Interactionmentioning

confidence: 99%

Gibbs Measures on Mutually Interacting Brownian Paths under Singularities

Mukherjee

2017

Comm Pure Appl Math

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Abstract. We are interested in the analysis of Gibbs measures defined on two independent Brownian paths in R d interacting through a mutual self-attraction. This is expressed by the Hamiltonianwith two probability measures µ and ν representing the occupation measures of two independent Brownian motions. We will be interested in class of potentials V which are singular, e.g., Dirac or Coulomb type interactions in R 3 , or the correlation function of the parabolic Anderson problem with white noise potential.The mutual interaction of the Brownian paths inspires a compactification of the quotient space of orbits of product measures, which is structurally different from the self-interacting case introduced in [26], owing to the lack of shift-invariant structure in the mutual interaction. We prove a strong large deviation principle for the product measures of two Brownian occupation measures in such a compactification, and derive asymptotic path behavior under Gibbs measures on Wiener paths arising from mutually attracting singular interactions. For the spatially smoothened parabolic Anderson model with white noise potential, our analysis allows a direct computation of the annealed Lyapunov exponents and a strict ordering of them implies the intermittency effect present in the smoothened model.

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Symmetry of Bipolaron Bound States for Small Coulomb Repulsion

Cited by 11 publications

References 21 publications

Ground State Properties of Multi-Polaron Systems

Ground State Properties of Multi-Polaron Systems

Monotonicity of the Polaron Energy

Gibbs Measures on Mutually Interacting Brownian Paths under Singularities

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