On resonances and bound states of Smilansky Hamiltonian

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F16%3A00466593" target="_blank" >RIV/61389005:_____/16:00466593 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.17586/2220-8054-2016-7-5-789-802" target="_blank" >http://dx.doi.org/10.17586/2220-8054-2016-7-5-789-802</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.17586/2220-8054-2016-7-5-789-802" target="_blank" >10.17586/2220-8054-2016-7-5-789-802</a>

Result language
angličtina
Original language name
On resonances and bound states of Smilansky Hamiltonian
Original language description
We consider the self-adjoint Smilansky Hamiltonian H epsilon in L-2(R-2) associated with the formal differential expression -partial derivative(2)(x) - 1/2 (partial derivative(2)(y) + y(2)) - root 2 epsilon y delta(x) in the sub-critical regime, epsilon is an element of (0, 1). We demonstrate the existence of resonances for H-epsilon on a countable subfamily of sheets of the underlying Riemann surface whose distance from the physical sheet is finite. On such sheets, we find resonance free regions and characterize resonances for small epsilon > 0. In addition, we refine the previously known results on the bound states of H " in the weak coupling regime (epsilon -> 0+). In the proofs we use Birman-Schwinger principle for H-epsilon, elements of spectral theory for Jacobi matrices, and the analytic implicit function theorem.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
<a href="/en/project/GA14-06818S" target="_blank" >GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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