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


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
Full Text: DOI


[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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.