Long-time asymptotics for a classical particle interacting with a scalar wave field

Komech, Alexander; Spohn, Herbert; Kunze, Markus

doi:10.1080/03605309708821264

Cited by 63 publications

(97 citation statements)

References 15 publications

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“…The "left" reservoir consists of the particles with labels in (−∞, −N ] and the right reservoir consists of the particles with labels in [N, +∞). The system a A series of results has been obtained for systems coupled to a single reservoir, such as nonrelativistic atoms coupled to the quantized electromagnetic field at temperature zero 3,4,5 , finite level atoms coupled to a boson field at positive temperature 43,44,19 , classical particles coupled to a scalar field at temperature zero 49,50 or at positive temperature 45 . b For quantum spin systems axioms are formulated in [78] which establish the existence of a stationary state and its mixing property for finite systems coupled to several reservoirs at different temperatures luc10: submitted to World Scientific on February 5, 2008consists of the particles in the middle.…”

Section: Hamiltonian Reservoirsmentioning

confidence: 99%

Fourier's Law: A Challenge to Theorists

Bonetto

Lebowitz

Rey-Bellet

2000

Mathematical Physics 2000

350

515

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We present a selective overview of the current state of our knowledge (more precisely of our ignorance) regarding the derivation of Fourier's Law, J(r) = −κ∇T (r); J the heat flux, T the temperature and κ, the heat conductivity. This law is empirically well tested for both fluids and crystals, when the temperature varies slowly on the microscopic scale, with κ an intrinsic property which depends only on the system's equilibrium parameters, such as the local temperature and density. There is however at present no rigorous mathematical derivation of Fourier's law and ipso facto of Kubo's formula for κ, involving integrals over equilibrium time correlations, for any system (or model) with a deterministic, e.g. Hamiltonian, microscopic evolution.

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Section: Hamiltonian Reservoirsmentioning

confidence: 99%

Fourier's Law: A Challenge to Theorists

Bonetto

Lebowitz

Rey-Bellet

2000

Mathematical Physics 2000

350

515

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“…but now with 77) and with U given in (A.75). Notice that the structure of f m does not figure in this spinless LED, which is therefore identical to the spinless version of Nodvik's LED, due to Spohn [43], in which f m is a point mass distribution from the outset.…”

Section: A2 Point Mass and Point Charge Limits Of Massive Ledmentioning

confidence: 97%

“…In particular, we mention the recent rigorous treatments in [72][73][74][75][76] with m b = 0 is used instead of the Newtonian (A.85) (see also [77,78] for work on a simpler scalar field-particle theory). In this case, of course also the Newtonian kinetic energy in (A.90) is to be replaced by its Einsteinian counterpart (A.101)…”

Section: A3 Semi-relativistic Ledmentioning

confidence: 99%

Mass and Spin Renormalization in Lorentz Electrodynamics

Appel¹,

Kiessling²

2001

Annals of Physics

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A new, relativistically covariant, massive Lorentz Electrodynamics (LED) is presented in which the bare particle has a finite positive bare rest mass and moment of inertia. The particle's electromagnetic self-interaction renormalizes its mass and spin. Most crucially, the renormalized particle is a soliton: after any scattering process its rest mass and spin magnitude are dynamically restored to their pre-scattering values. This guarantees that ``an electron remains an electron,'' poetically speaking. A renormalization flow study of the limit of vanishing bare rest mass is conducted for this model. This limit yields a purely electromagnetic classical field theory with ultra-violet cutoff at about the electron's Compton wavelength! The renormalized limit model matches the empirical electron data as orderly as one can hope for at the level of Lorentz theory. In particular, no superluminal equatorial gyration speeds occur.Comment: LaTeX, 70 pages, 2 eps figures, submitted; a small computational blunder in Eq. (10.25)ff of earlier version has been correcte

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“…In this case, the attractor S consists of the zero solution only, and the asymptotics mean well-known local energy decay. (ii) The global attraction (1) with |E ± = 0 was established first in [7,10,8,9] for a number of nonlinear wave problems. There the attractor S is the set of all static stationary states.…”

Section: Introductionmentioning

confidence: 99%

On the global attraction to solitary waves for the Klein–Gordon equation coupled to a nonlinear oscillator

Komech

2006

Comptes Rendus. Mathématique

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The long-time asymptotics are analyzed for all finite energy solutions to a model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a point. Our main result is that each finite energy solution converges as t → ±∞ to the set of 'nonlinear eigenfunctions' ψ(x) e −iωt . To cite this article: A.I. Komech, A.A. Komech, C. R. Acad. Sci. Paris, Ser. I 343 (2006). Résumé Attraction globale vers des ondes solitaires pour l'équation de Klein-Gordon couplé à un oscillateur non linéaire. On s'intéresse aux solutions d'énergie finie d'une équation non linéaire de Klein-Gordon U(1)-invariante monodimensionnelle, avec une non linéarité ponctuelle, et on analyse leur comportement asymptotique aux temps longs. Le principal résultat que nous avons obtenu est que toute solution d'énergie finie converge pour t → ±∞ vers un ensemble de « fonctions propres non linéaires » ψ(x) e −iωt . Pour citer cet article : A.I. Komech, A.A. Komech, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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Long-time asymptotics for a classical particle interacting with a scalar wave field

Cited by 63 publications

References 15 publications

Fourier's Law: A Challenge to Theorists

Fourier's Law: A Challenge to Theorists

Mass and Spin Renormalization in Lorentz Electrodynamics

On the global attraction to solitary waves for the Klein–Gordon equation coupled to a nonlinear oscillator

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