The double-well splitting of the low energy levels for the Schrödinger operator of discrete φ4-models on tori

DOI10.1063/1.531174zbMath0820.60097OpenAlexW2057575151MaRDI QIDQ4836803

Vassili N. Kolokol'tsov, S. Yu. Dobrokhotov

Publication date: 31 August 1995

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531174

zbMATH Keywords

Schrödinger operatorasymptotics of the splitting of the first two eigenvalues

Mathematics Subject Classification ID

Other physical applications of random processes (60K40) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44)

Related Items (7)

Local Exponential Estimates for h-Pseudo-Differential Operators with Operator-Valued Symbols ⋮ Semiclassical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. ⋮ PHASE TRANSITION IN THE SEMICLASSICAL REGIME ⋮ Tunneling for spatially cut-off \(P(\phi)_2\)-Hamiltonians ⋮ Sharp tunneling estimates for a double-well model in infinite dimension ⋮ Semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. II: \(P(\phi)_2\)-model on a finite volume ⋮ Local exponential estimates for \(h\)-pseudodifferential operators and tunneling for Schrödinger, Dirac, and square root Klein-Gordon operators

Cites Work

• Semiclassical analysis of low lying eigenvalues. II: Tunneling
• Tunnelling between tori in phase space
• Double wells
• Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation \(hu_ t=h^ 2\Delta u/2-V(x)u\)
• Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential
• Multiple wells in the semi-classical limit I

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