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pro vyhledávání: '"Tušek, Matěj"'
In this paper we introduce and study a family of self-adjoint realizations of the Laplacian in $L^2(\mathbb{R}^2)$ with a new type of transmission conditions along a closed bi-Lipschitz curve $\Sigma$. These conditions incorporate jumps in the Dirich
Externí odkaz:
http://arxiv.org/abs/2410.10448
In this paper we study the self-adjointness and spectral properties of two-dimensional Dirac operators with electrostatic, Lorentz scalar, and anomalous magnetic $\delta$-shell interactions with constant weights that are supported on a smooth unbound
Externí odkaz:
http://arxiv.org/abs/2312.00181
Autor:
Heriban, Lukáš, Tušek, Matěj
In this paper, new self-adjoint realizations of the Dirac operator in dimension two and three are introduced. It is shown that they may be associated with the formal expression $\mathcal{D}_0+|F\delta_\Sigma\rangle\langle G\delta_\Sigma|$, where $\ma
Externí odkaz:
http://arxiv.org/abs/2311.02638
In this paper the two-dimensional Dirac operator with a general hermitian $\delta$-shell interaction supported on a straight line is introduced as a self-adjoint operator and its spectral properties are investigated in detail. In particular, it is de
Externí odkaz:
http://arxiv.org/abs/2208.12761
Autor:
Heriban, Lukáš, Tušek, Matěj
The one-dimensional Dirac operator with a singular interaction term which is formally given by $A\otimes|\delta_0\rangle\langle\delta_0|$, where $A$ is an arbitrary $2\times 2$ matrix and $\delta_0$ stands for the Dirac distribution, is introduced as
Externí odkaz:
http://arxiv.org/abs/2205.05005
In this note the two dimensional Dirac operator $A_\eta$ with an electrostatic $\delta$-shell interaction of strength $\eta\in\mathbb R$ supported on a straight line is studied. We observe a spectral transition in the sense that for the critical inte
Externí odkaz:
http://arxiv.org/abs/2107.01156
In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four elementary intera
Externí odkaz:
http://arxiv.org/abs/2102.09988
Publikováno v:
J. Evol. Equ. 21 (2021) 1651-1675
We develop a Hilbert-space approach to the diffusion process of the Brownian motion in a bounded domain with random jumps from the boundary introduced by Ben-Ari and Pinsky in 2007. The generator of the process is introduced by a diffusion elliptic d
Externí odkaz:
http://arxiv.org/abs/2006.14392
Autor:
Tušek, Matěj
We show that the one-dimensional Dirac operator with quite general point interaction may be approximated in the norm resolvent sense by the Dirac operator with a scaled regular potential of the form $1/\varepsilon~h(x/\varepsilon)\otimes B$, where $B
Externí odkaz:
http://arxiv.org/abs/1904.01061
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