Zobrazeno 1 - 9
of 9
pro vyhledávání: '"Michal Jex"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 11 (2023)
One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, that is, below the essential spectrum, is well understood, the situation of zero energy bound states at the edge of the
Externí odkaz:
https://doaj.org/article/da70401246244436b897972352567597
We provide upper and lower bounds on the lowest free energy of a classical system at given one-particle density $\rho(x)$. We study both the canonical and grand-canonical cases, assuming the particles interact with a pair potential which decays fast
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ccffcf3f8b6ce39b8f4da61a042ab8d3
Publikováno v:
Journal of Mathematical Analysis and Applications
Journal of Mathematical Analysis and Applications, 2021, 500 (2), pp.article n° 125124. ⟨10.1016/j.jmaa.2021.125124⟩
Journal of Mathematical Analysis and Applications, Elsevier, 2021, 500 (2), pp.article n° 125124. ⟨10.1016/j.jmaa.2021.125124⟩
Journal of Mathematical Analysis and Applications, 2021, 500 (2), pp.article n° 125124. ⟨10.1016/j.jmaa.2021.125124⟩
Journal of Mathematical Analysis and Applications, Elsevier, 2021, 500 (2), pp.article n° 125124. ⟨10.1016/j.jmaa.2021.125124⟩
We obtain a trace Hardy inequality for the Euclidean space with a bounded cut Σ ⊂ R d , d ≥ 2 . In this novel geometric setting, the Hardy-type inequality non-typically holds also for d = 2 . The respective Hardy weight is given in terms of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a41a163eb6a6770123e3ad136a231e2c
https://hal.science/hal-03178339
https://hal.science/hal-03178339
Publikováno v:
Journal of the European Mathematical Society, 23 (8), 2583-2600
We provide new estimates on the best constant of the Lieb-Thirring inequality for the sum of the negative eigenvalues of Schr\"odinger operators, which significantly improve the so far existing bounds.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2823b28f26a8bf367c06c849f70ff3be
https://publikationen.bibliothek.kit.edu/1000135256/149445771
https://publikationen.bibliothek.kit.edu/1000135256/149445771
Autor:
Pavel Exner, Michal Jex
Publikováno v:
Physics Letters A. 378:2091-2095
We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive δ ′ interaction supported by a smooth surface in R 3 , either infinite and asymptotically planar, or compact and closed. Its second term is found to be determ
Autor:
Michal Jex
We consider a generalized Schrodinger operator in $L^2(\mathbb R^2)$ describing an attractive $\delta'$ interaction in a strong coupling limit. $\delta'$ interaction is characterized by a coupling parameter $\beta$ and it is supported by a $C^4$-smoo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2bf10b21b4792661910b7708b4d92117
https://doi.org/10.1142/9250
https://doi.org/10.1142/9250
Autor:
Michal Jex, Pavel Exner
We consider a generalized Schr\"odinger operator in $L^2(\R^2)$ with an attractive strongly singular interaction of $\delta'$ type characterized by the coupling parameter $\beta>0$ and supported by a $C^4$-smooth closed curve $\Gamma$ of length $L$ w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8df52ce3dbcbe3acc7726e51ecfc570f
http://arxiv.org/abs/1304.7696
http://arxiv.org/abs/1304.7696
On absence of bound states for weakly attractiveδ′-interactions supported on non-closed curves in ℝ2
Autor:
Michal Jex, Vladimir Lotoreichik
Publikováno v:
Journal of Mathematical Physics. 57:022101
Let Λ ⊂ ℝ2 be a non-closed piecewise-C1 curve, which is either bounded with two free endpoints or unbounded with one free endpoint. Let u±|Λ ∈ L2(Λ) be the traces of a function u in the Sobolev space H1(ℝ2∖Λ) onto two faces of Λ. We p
Autor:
Pavel Exner, Michal Jex
We study relations between the ground-state energy of a quantum graph Hamiltonian with attractive $\delta$ coupling at the vertices and the graph geometry. We derive a necessary and sufficient condition under which the energy increases with the incre
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::86f1b21434c570c833ee83b8bf4a6429
http://arxiv.org/abs/1110.1800
http://arxiv.org/abs/1110.1800