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On dissipation operators of Quantum Optics

A. I. Komech, E. A. Kopylova

Abstract

We consider dissipation operators used in Quantum Optics for the description of quantum spontaneous emission in the context of damped driven Jaynes-Cummings equations. The equations describe quantised one-mode Maxwell field coupled to a two-level molecule. Our main result is the symmetry and nonpositivity of basic dissipation operator of Quantum Optics.

On dissipation operators of Quantum Optics

Abstract

We consider dissipation operators used in Quantum Optics for the description of quantum spontaneous emission in the context of damped driven Jaynes-Cummings equations. The equations describe quantised one-mode Maxwell field coupled to a two-level molecule. Our main result is the symmetry and nonpositivity of basic dissipation operator of Quantum Optics.

Paper Structure

This paper contains 5 sections, 3 theorems, 16 equations.

Table of Contents

  1. Jaynes--Cummings equation
  2. Dissipation operators and main results
  3. Nonpositivity and symmetry
  4. Injectivity
  5. Acknowledgements

Key Result

Theorem 2.3

i) Both dissipation operators $D$ and $\De$ are defined on the domain ${\cal D}\subset{\rm HS}$ and nonpositive: ii) The operator $D:{\cal D}\to{\cal D}$ is symmetric: while $\De$ is not symmetric. iii) Both operators $D,\De:{\cal D}\to{\cal D}$ are injective.

Theorems & Definitions (8)

  • Definition 2.1
  • Definition 2.2
  • Theorem 2.3
  • Corollary 2.4
  • Lemma 3.1
  • proof
  • Remark 3.2
  • Remark 4.1