Ground state for point particles interacting through a massless scalar Bose field

Hirokawa, Masao; Hiroshima, Fumio; Spohn, Herbert

doi:10.1016/s0001-8708(04)00098-2

Cited by 6 publications

(6 citation statements)

References 21 publications

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“…The particles in this system are not necessarily regularly distributed. At last, quantum anharmonic oscillators are used as parts of the models describing interaction of vibrating quantum particles with a radiation (photon) field [40,68] or strong electron-electron correlations caused by the interaction of electrons with vibrating ions responsible for such phenomena as superconductivity, charge density waves, etc, see [32,33]. Thus, infinite systems of interacting quantum anharmonic oscillators are quite important models and their rigorous description is still a challenging mathematical task.…”

Section: Introductionmentioning

confidence: 99%

Euclidean Gibbs Measures of Interacting Quantum Anharmonic Oscillators

Kozitsky

Pasurek

2007

J Stat Phys

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A rigorous description of the equilibrium thermodynamic properties of an infinite system of interacting ν-dimensional quantum anharmonic oscillators is given. The oscillators are indexed by the elements of a countable set L ⊂ R d , possibly irregular; the anharmonic potentials vary from site to site. The description is based on the representation of the Gibbs states in terms of path measures -the so called Euclidean Gibbs measures. It is proven that: (a) the set of such measures G t is non-void and compact; (b) every µ ∈ G t obeys an exponential integrability estimate, the same for the whole set G t ; (c) every µ ∈ G t has a Lebowitz-Presutti type support; (d) G t is a singleton at high temperatures. In the case of attractive interaction and ν = 1 we prove that |G t | > 1 at low temperatures. The uniqueness of Gibbs measures due to quantum effects and at a nonzero external field are also proven in this case. Thereby, a qualitative theory of phase transitions and quantum effects, which interprets most important experimental data known for the corresponding physical objects, is developed. The mathematical result of the paper is a complete description of the set G t , which refines and extends the results known for models of this type.

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Section: Introductionmentioning

confidence: 99%

Euclidean Gibbs Measures of Interacting Quantum Anharmonic Oscillators

Kozitsky

Pasurek

2007

J Stat Phys

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“…Another relevant physical object of this kind is a system of apex oxygen ions in YBaCuO-type high-temperature superconductors, see [27,57,74,75]. Quantum anharmonic oscillators are also used in models describing interaction of vibrating quantum particles with a radiation (photon) field, see [32,33,58], or strong electronelectron correlations caused by the interaction of electrons with vibrating ions, see [25,26], responsible for such phenomena as superconductivity, charge density waves etc. Finally, we mention systems of light atoms, like Li, doped into ionic crystals, like KCl.…”

Section: Introduction and Setupmentioning

confidence: 99%

Phase Transitions and Quantum Stabilization in Quantum Anharmonic Crystals

2008

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A unified theory of phase transitions and quantum effects in quantum anharmonic crystals is presented. In its framework, the relationship between these two phenomena is analyzed. The theory is based on the representation of the model Gibbs states in terms of path measures (Euclidean Gibbs measures). It covers the case of crystals without translation invariance, as well as the case of asymmetric anharmonic potentials. The results obtained are compared with those known in the literature.

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“…However, Arai [1] takes a non-Fock representation and then shows the existence of a ground state of H under (1.8). Finally Hirokawa et al [24] proved the existence of a ground state of H under (1.8) and without any ultraviolet cutoffs.…”

Section: The Nelson Modelmentioning

confidence: 99%