The fate of Landau levels under delta-interactions
Result 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.
Keywords
Berezin-Toeplitz operatorsLaguerre polynomialsLandau Hamiltonian
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
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
—
Czech description
—
Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Spectral Theory
ISSN
1664-039X
e-ISSN
1664-0403
Volume of the periodical
12
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
32
Pages from-to
1203-1234
UT code for WoS article
000976030000008
EID of the result in the Scopus database
2-s2.0-85160033460
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2022