The fate of Landau levels under delta-interactions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00573208" target="_blank" >RIV/61389005:_____/22:00573208 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4171/JST/422" target="_blank" >https://doi.org/10.4171/JST/422</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/JST/422" target="_blank" >10.4171/JST/422</a>

Result language
angličtina
Original language name
The fate of Landau levels under delta-interactions
Original language description
We consider the self-adjoint Landau Hamiltonian H-0 in L-2(R-2) whose spectrum consists of infinitely degenerate eigenvalues Lambda(q), q is an element of Z(+), and the perturbed Landau Hamiltonian H-upsilon = H-0 + upsilon delta(Gamma), where Gamma subset of R-2 is a regular Jordan C-1,C-1-curve and upsilon is an element of L-p(Gamma, R), p > 1, has a constant sign. We investigate ker(H-upsilon - Lambda(q)), q is an element of Z(+), and show that genericallynn0 <= dim ker(H-upsilon - Lambda(q)) - dim ker(T-q(upsilon delta(Gamma))) < infinity,nnwhere T-q(upsilon delta(Gamma)) = p(q)(upsilon delta(Gamma))p(q), is an operator of Berezin-Toeplitz type, acting in p(q)L(2)(R-2), and p(q) is the orthogonal projection onto ker(H-0 - Lambda(q)). If upsilon not equal 0 and q = 0, then we prove that ker(T-0(upsilon delta(Gamma))) = {0}. If q >= 1 and Gamma = C-r is a circle of radius r, then we show that dim ker(T-q(delta(Cr))) <= q, and the set of r is an element of (0, infinity) for which dim ker(T-q(delta(Cr))) >= 1 is infinite and discrete.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA21-07129S" target="_blank" >GA21-07129S: New Effects from Time-Reversal Non-Invariance</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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