Debye screening

Federbush, Paul; Brydges, David C.

doi:10.1007/bf01197700

Cited by 158 publications

(171 citation statements)

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“…Theorem II.1 is a combination of results from (Brydges 1978, Brydges & Federbush 1980, Imbrie 1983b, Brydges & Kennedy 1987. It is shown in (Imbrie 1983a) that there is Debye screening in Jellium and in systems with irrational charges.…”

Section: B Theorems On Debye Screeningmentioning

confidence: 99%

“…The results below are valid in a thermodynamic limit in which there are boundary conditions on the Coulomb potential. Details may be found on page 199 of (Brydges & Federbush 1980); the boundary conditions are a little artificial but their essence is that the walls of the container are grounded, so that all electrostatic potentials vanish at the boundary ∂Λ.…”

Section: B Theorems On Debye Screeningmentioning

confidence: 99%

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Brydges

Martin

1999

Journal of Statistical Physics

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142

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Results on the correlations of low density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system -Debye-Hückel screening -is compared and contrasted with the quantum case where strong arguments are presented for the absence of exponential screening. Results and techniques for detailed calculations that determine the asymptotic decay of correlations for quantum systems are discussed. Theorems on the existence of molecules in the Saha regime are reviewed. Finally, new combinatoric formulas for the coefficients of Mayer expansions are presented and their role in proofs of results on Debye-Hückel screening is discussed.Typeset using REVT E X III-3 C. The scaling limit of the lattice dipole gas III-5 IV. Semi-classical Coulomb gas IV-1 A. The Feynman-Kac representation IV-1 B. The gas of charged filaments IV-3 C. Quantum fluctuations destroy exponential screening IV-7 D. Origin of the van der Waals forces IV-9 E. Semi-classical analysis of Coulombic correlations IV-11 F. Breakdown of exponential screening in the Quantum Sine-Gordon representation IV-15 V. The emergence of thermodynamics and of various physical laws from the more fundamental levels of atomic theory and statistical mechanics were high points in our education in physics. But by the time we reached textbook treatments of the complex world of the Coulomb interaction, for example, formation of atoms and molecules and equilibria between them, we learned to demand less from theory and to be more content with reasoning by analogy consistent with thermodynamics. We know experimentally that atoms and molecules form, that they can behave like mixtures of ideal gases, so phenomenologically they have chemical potentials and we no longer insist that this emerge in some limit from N-body quantum Coulomb systems. We also know that Coulomb systems can have screening and dielectric phases. But when screening is expected to occur, it is quite a common practice to rather bluntly replace the Coulomb potential by a screened potential inherited from meanfield theories without inquiring too deeply into the legitimacy of this change. Likewise, there does not exist a first principle theory of the dielectric constant that does not presuppose the existence of atoms and molecules. At best, assuming that atoms form, one uses several laws, such as the Clausius-Mosotti formula, whose microscopic foundations have to be elucidated. In all these cases, this is a sensible attitude since most of non-relativistic physics is reputed to be hidden within the N-particle Coulomb Hamiltonian. There are however basic facts that can be cleanly formulated as limiting theories and shown to persist near the limit as well.This review is devoted to these types of results on Coulomb systems at low density. At low density the most famous properties of Coulomb systems are related to screening. The classical Debye-Hückel theory and its quantum analogue the random phase approximation have...

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Section: B Theorems On Debye Screeningmentioning

confidence: 99%

Section: B Theorems On Debye Screeningmentioning

confidence: 99%

Untitled

Brydges

Martin

1999

Journal of Statistical Physics

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142

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“…Then it was applied in [20,22] for the proof of the Debye screening in dilute charged particle systems. This type of cluster expansions includes derivatives acting on the Gibbs factor exp[−V Λ ].…”

Section: Remark 23mentioning

confidence: 99%

Gibbs state uniqueness for an anharmonic quantum crystal with a non-polynomial double-well potential

Rebenko¹,

Zagrebnov²

2006

J. Stat. Mech.

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We construct the Gibbs state for ν-dimensional quantum crystal with site displacements from IR d , d ≥ 1, and with a one-site non-polynomial double-well potential, which has harmonic asymptotic growth at infinity. We prove the uniqueness of the corresponding Euclidean Gibbs measure (EGM) in the lightmass regime for the crystal particles. The corresponding state is constructed via a cluster expansion technique for an arbitrary temperature T ≥ 0. We show that for all T ≥ 0 the Gibbs state (correlation functions) is analytic with respect to external field conjugated to displacements provided that the mass of particles m is less than a certain value m * > 0. The high temperature regime is also discussed.Keywords : quantum crystal model, Gibbs state, Euclidean Gibbs measures, quantum fluctuations, light-mass regime, cluster expansions. Mathematics Subject Classification : 60H30, 82B31 IntroductionIt is generally excepted that for investigation of different physical phenomena in quantum crystals one can consider an infinite system of interacting anharmonic oscillators, which are situated in the sites of ν-dimensional lattice Z Z ν . The heuristic Hamiltonian of such a system (in the case of 2-body interaction) has the following form:where m is the mass of particles, the operator ∆ j corresponds the kinetic energy of the system and, in fact, is d-dimensional Laplace operator in the one-particle Hilbert space, where dq is the Lebesgue measure onν is displacement of a particle from its position in the site j ∈ Z Z ν . For general case d ≤ ν ≥ 1. But the most of results, which where obtained earlier are for d = 1. The particles are confined near their sites by potential W (q j ). A harmonic one-site potential W harm (q j ) = 1 2 aq 2 j , a > 0 together with a harmonic two-particle interaction Q(·, ·) define a well-known harmonic crystal model (1.1). To produce a model describing a (ferroelectric) structural phase transition one usually takes for W (·) a doublewell anharmonic potential, keeping Q(·, ·) harmonic (see e.g. [1,19,24]). For example,or semibounded from below polynomials of higher degree with more than two equal minima. Here q 2 ≡ q · q is the scalar square of displacement vector q ∈ IR d . The proof of existence of phase transition in such kind of systems for harmonic interaction Q(q i , q j ) were obtained in [12,15,26,34,40,47,53] for the case2) whereQ = (Q ij ) i,j∈Z Z ν is a matrix of non-negative harmonic-force constants. The term h · q j = d α=1 h α q α j break the symmetry in the direction of the 1 external field h. The non-uniqueness of Gibbs states for h = 0 is proved when the mass of the particles m is sufficiently large and the temperature T is sufficiently low, or β = (kT ) −1 is sufficiently large. From the other side, another interesting phenomenon, the suppression of the long-range order by strong quantum fluctuations in such systems was experimentally observed (see, e.g. [55]) and was discussing long time ago from the physical point of view, see [51], or the books [1,19]. A rigorous stu...

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“…In the setting of a quantum mechanical Coulomb gas the idea goes back to Debeye (Debeye screening) [37]. The point is that under certain circumstances the potential for large distances is not of Coulomb but rather of Yukawa type; the quantum mechanical system becomes self-screening.…”

Section: The Schwinger-higgs Screening Mechanism and The Standard Modelmentioning

confidence: 99%

“…The existence of two different proposals from just knowing the S-matrix demonstrates this. 37 In his own words [84]: Two-dimensional spacetime, despite all its peculiarities has proved many times to be a fruitfull theoretical laboratory where one can test a number of ideas in soluable models and many times draw inspirations for more realistic models.…”

Section: The Unfinished Business Of Gauge Theorymentioning

confidence: 99%

Jorge A. Swieca’s contributions to quantum field theory in the 60s and 70s and their relevance in present research

Schroer¹

2010

EPJ H

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Debye screening

Cited by 158 publications

References 15 publications

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Gibbs state uniqueness for an anharmonic quantum crystal with a non-polynomial double-well potential

Jorge A. Swieca’s contributions to quantum field theory in the 60s and 70s and their relevance in present research

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