arXiv subjects

Kazushi Yoshitomi

Publications and source records attributed to Kazushi Yoshitomi.

3 recordsLinked to original sources

arXiv2002

Persistent currents for 2D Schrödinger operator with a strong $δ$-interaction on a loop

We investigate the two-dimensional magnetic Schrödinger operator $H_{B,β}=(-i\nabla-A)^2 -βδ(\cdot-Γ)$, where $Γ$ is a smooth loop and the vector potential $A$ corresponds to a homogeneous magnetic field $B$ perpendicular to the plane. The asymptotics of negative eigenvalues of $H_{B,β}$ for $β\to\infty$ is found. It shows, in particular, that for large enough positive $β$ the system exhibits persistent currents.

math-ph↗

arXiv2001

Band gap of the Schroedinger operator with a strong delta-interaction on a periodic curve

In this paper we study the operator $H_β=-Δ-βδ(\cdot-Γ)$ in $L^{2}(\mathbb{R}^{2})$, where $Γ$ is a smooth periodic curve in $\mathbb{R}^{2}$. We obtain the asymptotic form of the band spectrum of $H_β$ as $β$ tends to infinity. Furthermore, we prove the existence of the band gap of $σ(H_β)$ for sufficiently large $β>0$. Finally, we also derive the spectral behaviour for $β\to\infty$ in the case when $Γ$ is non-periodic and asymptotically straight.

math-ph↗

arXiv2001

Asymptotics of eigenvalues of the Schroedinger operator with a strong delta-interaction on a loop

In this paper we investigate the operator $H_β=-Δ-βδ(\cdot-Γ)$ in $L^{2}({\Bbb R}^{2})$, where $β>0$ and $Γ$ is a closed $C^{4}$ Jordan curve in ${\Bbb R}^{2}$. We obtain the asymptotic form of each eigenvalue of $H_β$ as $β$ tends to infinity. We also get the asymptotic form of the number of negative eigenvalues of $H_β$ in the strong coupling asymptotic regime.

math-ph↗