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Instantons, double wells and large deviations. (English) Zbl 0529.35059

MSC:
35P15 Estimates of eigenvalues in context of PDEs
81V70 Many-body theory; quantum Hall effect
60J65 Brownian motion
35J10 Schrödinger operator, Schrödinger equation
35B40 Asymptotic behavior of solutions to PDEs
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[1] S. Agmon, On exponential decay of solutions of second order elliptic equations in unbounded domains, Proc. A. Pleijel Conf. · Zbl 0503.35001
[2] Shmuel Agmon, Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of \?-body Schrödinger operators, Mathematical Notes, vol. 29, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1982. · Zbl 0503.35001
[3] R. Carmona and B. Simon, Pointwise bounds on eigenfunctions and wave packets in \?-body quantum systems. V. Lower bounds and path integrals, Comm. Math. Phys. 80 (1981), no. 1, 59 – 98. Elliott H. Lieb and Barry Simon, Pointwise bounds on eigenfunctions and wave packets in \?-body quantum systems. VI. Asymptotics in the two-cluster region, Adv. in Appl. Math. 1 (1980), no. 3, 324 – 343. · Zbl 0482.35065
[4] S. Coleman, The uses of instantons, Proc. Internat. School of Physics, Erice, 1977.
[5] S. Combes, P. Duclos and R. Seiler, Krein’s formula and one dimensional multiple-well, J. Functional Analysis (to appear). · Zbl 0562.47002
[6] E. Gildener and A. Patrascioiu, Pseudoparticle contributions to the energy spectrum of a one dimensional system, Phys. Rev. D16 (1977), 425-443.
[7] Evans M. Harrell, On the rate of asymptotic eigenvalue degeneracy, Comm. Math. Phys. 60 (1978), no. 1, 73 – 95. · Zbl 0395.34023
[8] Evans M. Harrell, Double wells, Comm. Math. Phys. 75 (1980), no. 3, 239 – 261. · Zbl 0445.35036
[9] Martin Pincus, Gaussian processes and Hammerstein integral equations, Trans. Amer. Math. Soc. 134 (1968), 193 – 214. · Zbl 0175.12502
[10] M. Schilder, Some asymptotic formulas for Wiener integrals, Trans. Amer. Math. Soc. 125 (1966), 63 – 85. · Zbl 0156.37602
[11] Barry Simon, Functional integration and quantum physics, Pure and Applied Mathematics, vol. 86, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. · Zbl 0434.28013
[12] B. Simon, Semiclassical analysis of low lying eigenvalues. I. Non-degenerate minima: Asymptotic expansions, Ann. Inst. H. Poincaré (to appear). · Zbl 0537.35023
[13] B. Simon, Semiclassical analysis of low lying eigenvalues.II. Tunneling (in preparation).
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