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Many-body Stark resonances by the complex absorbing potential method

Kentaro Kameoka

Abstract

The resonances of many-body Stark Hamiltonians are characterized by the complex absorbing potential method. Namely, the resonances are shown to be the limit points of complex discrete eigenvalues of many-body Stark Hamiltonians with quadratic complex potential when the coefficient of the complex potential tends to zero.

Many-body Stark resonances by the complex absorbing potential method

Abstract

The resonances of many-body Stark Hamiltonians are characterized by the complex absorbing potential method. Namely, the resonances are shown to be the limit points of complex discrete eigenvalues of many-body Stark Hamiltonians with quadratic complex potential when the coefficient of the complex potential tends to zero.
Paper Structure (4 sections, 5 theorems, 33 equations)

This paper contains 4 sections, 5 theorems, 33 equations.

Table of Contents

  1. Introduction
  2. Complex distortion
  3. Complex absorbing potential method
  4. Proof of the main estimate

Key Result

Theorem 1

Under Assumption asm-1, in $\{z\in \mathbb{C}|\, \mathrm{Im}\, z>-\delta_0\}$ including multiplicities. More precisely, for any $z$ with $\mathrm{Im}\, z>-\delta_0$, there exists $\gamma_0>0$ such that for any $0<\gamma<\gamma_0$ there exists $\varepsilon_0>0$ such that for any $0<\varepsilon<\varepsilon_0$, the number of

Theorems & Definitions (14)

  • Theorem 1
  • Remark 1.1
  • Remark 2.1
  • Remark 2.2
  • Proposition 2.3
  • proof
  • Proposition 2.4
  • proof
  • Proposition 3.1
  • proof : Proof of Theorem \ref{['thm-1']}
  • ...and 4 more