Gakushuin University

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19932026

most citedNearly-flat bands with nontrivial topology

954 citations

Showing 2018 · math-phShow all

5 papers · 2 filters

math-ph2018★ 61 cited

Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry

Yoshiko Ogata, Hal Tasaki

We prove that a quantum spin chain with half-odd-integral spin cannot have a unique ground state with a gap, provided that the interaction is short ranged, translation invariant, a…

math-ph2018

SL(3,C) structure of one-dimensional Schrödinger equation

Toru Miyazawa

We present a new formalism for describing solutions of the one-dimensional stationary Schrödinger equation in terms of the Lie group SL(3,C) and its Lie algebra. In this formalism,…

math-ph2018

Instability of resonances under Stark perturbations

Arne Jensen, Kenji Yajima

Let $H^{ε} = - \frac{d ^{2}}{d x ^{2}} + ε x + V$ , $ε \geq 0$ , on $L^{2} (R)$ . Let $V = \sum_{k = 1}^{N} c_{k} ∣ ψ_{k} ⟩ ⟨ ψ_{k} ∣$ be a rank $N$ operator, where the…

math-ph2018★ 4 cited

Remarks on scattering matrices for Schrödinger operators with critically long-range perturbations

Shu Nakamura

We consider scattering matrix for Schrödinger-type operators on $R^{d}$ with perturbation $V (x) = O (⟨ x ⟩^{- 1})$ as $∣ x ∣ \to \infty$ . We show that the scattering matr…

math-ph2018★ 2 cited

Long-range Scattering Matrix for Schrödinger-type Operators

Shu Nakamura

We show that the scattering matrix for a class of Schrödinger-type operators with long-range perturbations is a Fourier integral operator with the phase function which is the gener…