Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Stark localization of interacting particles

Wojciech De Roeck, Amirali Hannani, Alessio Lerose, Nathan Vandenbosch

Abstract

We consider N interacting quantum particles on a one-dimensional lattice, and subjected to an external linear potential. For N = 1, the corresponding Hamiltonian is explicitly diagonalizable, with superexponentially localized eigenstates. This is called Stark localization. We prove that superexponential spectral localization persists for arbitrary N and every interaction strength.

Stark localization of interacting particles

Abstract

We consider N interacting quantum particles on a one-dimensional lattice, and subjected to an external linear potential. For N = 1, the corresponding Hamiltonian is explicitly diagonalizable, with superexponentially localized eigenstates. This is called Stark localization. We prove that superexponential spectral localization persists for arbitrary N and every interaction strength.
Paper Structure (9 sections, 15 theorems, 93 equations, 1 figure)

This paper contains 9 sections, 15 theorems, 93 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Result
  3. Fermions and bosons
  4. Notation and preliminaries
  5. Conventions
  6. Basic properties of Bessel functions
  7. $H^{(N)}$ has pure point spectrum
  8. Decay in the $a = \sum m_i$ direction
  9. Decay in all $|m_i|$ direction

Key Result

Theorem 2.1

If $h\neq 0$, the operator $H^{(N)}$ has pure point spectrum.

Figures (1)

  • Figure :

Theorems & Definitions (33)

  • Theorem 2.1: Spectral Localization
  • Corollary 2.2
  • Theorem 2.3: Superexponential localization
  • Lemma 3.1
  • proof
  • Remark 3.2
  • Lemma 4.1
  • proof
  • Lemma 4.2
  • proof
  • ...and 23 more