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Asymptotics for the polaron. (English) Zbl 0538.60081

The polaron problem, the calculation of the asymptotic behaviour of an expectation value with respect to three dimensional Brownian motion tied down at both ends, is solved. Also the conjecture of S. I. Pekar [Theory of polarons. Zh. Ekhsperim. Teor. Fiz. 19 (1949)] is proved. The authors use large deviation results given in earlier papers on the asymptotic evaluation of certain Markov process expectations for large time.
Reviewer: G.Gerlich

MSC:

60J65 Brownian motion
60F10 Large deviations
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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References:

[1] Statistical Mechanics, W. A. Benjamin, Reading, MA, 1972.
[2] Pekar, Zh. Eksperim. i Teor. Fiz. 19 (1949)
[3] Donsker, Comm. Pure Appl. Math. 28 pp 1– (1975)
[4] Comm. Pure Appl. Math. 28 pp 279– (1975)
[5] Comm. Pure Appl. Math. 29 pp 389– (1976)
[6] Donsker, IV, Comm. Pure Appl. Math. 36 pp 183– (1983)
[7] , and , Strong coupling limit of polaron energy, revisited, Physical Letter, Sept. 1980, pp. 249–251.
[8] Lieb, Studies in Applied Mathematics 57 pp 93– (1977) · Zbl 0369.35022
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