Multiple tunnelings in d-dimensions : a quantum particle in a hierarchical potential

 Access to full text

 Full (PDF)

1. [1] G. Jona-Lasinio, F. Martinelli, E. Scoppola, Quantum Particle in a hierarchical potential with tunneling over arbitrarily large scales. Preprint Université Paris VI. PAR LPTHE 84/09. March 1984. To appear in J. Phys. A : Math. and Gen. Zbl1188.81106MR763617
2. [2] G. Jona-Lasinio, F. Martinelli, E. Scoppola, New Approach to the Semiclassical Limit of Quantum Mechanics. I. Multiple tunneling in one dimension. Comm. Math. Phys., t. 80, 1981, p. 223-254. G. Jona-Lasinio, F. Martinelli, E. Scoppola, The Semiclassical Limit of Quantum Mechanics: a qualitative theory via Stochastic Mechanics. Phys. Rep., t. 77, n° 3, 1981, p. 313-327. A different approach to the same kind of problems has been developed recently by B. Helffer and J. Sjöstrand, Multiple Wells in the Semiclassical Limit. I. To appear in CPDE. Puits Multiples en Limite Semiclassique. II. Preprint 1984. See also: S. Graffi, V. Grecchi, G. Jona-Lasinio, Tunneling Instability via Perturbation Theory, to appear in J. Phys. A. Zbl0483.60094MR623159
3. [3] G. Jona-Lasinio, F. Martinelli, E. Scoppola, paper in preparation. 
4. [4] D.B. Pearson, Singular Continuous Measures in Scattering Theory, Comm. Math. Phys., t. 60, 1978, p. 13-36. Zbl0451.47013MR484145
5. [5] J. Fröhlich, T. Spencer, Absence of diffusion in the Anderson tight binding model for large disorder or low energy. Comm. Math. Phys., t. 88, 1983, p. 151-184. J. Fröhlich, T. Spencer, A rigorous approach to Anderson localization, Phys. Reports, t. 108, n° 1-4, 1984, p. 9. Zbl0519.60066MR696803
6. [6] H. Kunz, B. Souillard, Sur le spectre des opérateurs aux différences finies aléatoires. Comm. Math. Phys., t. 78, 1980, p. 201-246. Zbl0449.60048MR597748
7. [7] H. Holden, F. Martinelli, On absence of Diffusion near the Bottom of the Spectrum for a random Schrödinger Operator on L2 (Rν). Comm. Math. Phys., t. 93, 1984, p. 197-217. Zbl0546.60063MR742193
8. [8] B. Simon, Schrödinger Semigroups. Bull. Amer. Math. Soc., t. 7, 1983, p. 447. Zbl0524.35002MR670130
9. [9] M. Reed, B. Simon, Methods of Modern Mathematical Physics, IV. Academic Press, 1975-1978. Zbl0401.47001MR751959
10. [10] B. Simon, Functional integration and Quantum Physics. Academic Press, New York, 1979. Zbl0434.28013MR544188
11. [11] F. Wegner, Bounds on the density of states in disordered systems. Z. Physik, t. B44, 1981, p. 9-15. MR639135
12. [12] Ju.M. Berezanskii, Expansion in eigenfunctions of selfadjoint operators. Translations of Mathematical Monographs, t. 17, A. M. S., 1968. Zbl0157.16601MR222718

1. Fabio Martinelli, The wave equation in random domains : localization of the normal modes in the small frequency region
2. T. F. Pankratova, Semi-classical eigenstates at the bottom of a multidimensional well