scholarly journals A Semi-classical Trace Formula for Schrödinger Operators in the Case of a Critical Energy Level

1997 ◽  
Vol 146 (2) ◽  
pp. 299-351 ◽  
Author(s):  
David Khuat-Duy
Keyword(s):  
Energy Level ◽  
Trace Formula ◽  
Schrödinger Operators ◽  
Critical Energy ◽  
Schrodinger Operators

scholarly journals A Trace Formula for Multidimensional Schrödinger Operators

1996 ◽  
Vol 141 (2) ◽  
pp. 449-465 ◽  
Author(s):  
F Gesztesy ◽  
H Holden ◽  
B Simon ◽  
Z Zhao
Keyword(s):  
Trace Formula ◽  
Schrödinger Operators ◽  
Schrodinger Operators

scholarly journals Resonance free domain for a system of Schrödinger operators with energy-level crossings

2020 ◽  
pp. 2150007
Author(s):  
Kenta Higuchi
Keyword(s):  
Energy Level ◽  
Differential Operators ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Level Crossings ◽  
Diagonal Part ◽  
Free Domain ◽  
Small Interactions ◽  
Directed Cycles

We consider a [Formula: see text] system of 1D semiclassical differential operators with two Schrödinger operators in the diagonal part and small interactions of order [Formula: see text] in the off-diagonal part, where [Formula: see text] is a semiclassical parameter and [Formula: see text] is a constant larger than [Formula: see text]. We study the absence of resonance near a non-trapping energy for both Schrödinger operators in the presence of crossings of their potentials. The width of resonances is estimated from below by [Formula: see text] and the coefficient [Formula: see text] is given in terms of the directed cycles of the generalized bicharacteristics induced by two Hamiltonians.

The Trace Formula for Schrödinger Operators from Infinite Dimensional Oscillatory Integrals

1996 ◽  
Vol 182 (1) ◽  
pp. 21-65 ◽  
Author(s):  
Sergio Albeverio ◽  
Anne Boutet De Monvel-Berthier ◽  
Zdzislaw Brzeźniak
Keyword(s):  
Trace Formula ◽  
Schrödinger Operators ◽  
Oscillatory Integrals ◽  
Schrodinger Operators ◽  
Infinite Dimensional
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