On the Liouville–von Neumann Equation for Unbounded Hamiltonians

Lonigro D, Hahn A, Burgarth D (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Open Systems & Information Dynamics World Scientific Publishing / Springer Verlag (Germany)

Book Volume: 31

Issue: 04

DOI: 10.1142/S1230161224500185

Abstract

The evolution of mixed states of a closed quantum system is described by a group of evolution superoperators whose infinitesimal generator (the quantum Liouville superoperator, or Liouvillian) determines the mixed-state counterpart of the Schrödinger equation: the Liouville–von Neumann equation. When the state space of the system is infinite-dimensional, the Liouville superoperator is unbounded whenever the corresponding Hamiltonian is. In this paper, we provide a rigorous, pedagogically-oriented, and self-contained introduction to the quantum Liouville formalism in the presence of unbounded operators. We present and discuss a characterization of the domain of the Liouville superoperator originally due to M. Courbage; starting from that, we develop some simpler characterizations of the domain of the Liouvillian and its square. We also provide, with explicit proofs, some domains of essential selfadjointness (cores) of the Liouvillian.

Authors with CRIS profile

Davide Lonigro Professur für Theoretische Physik Daniel Burgarth Professur für Theoretische Physik

Involved external institutions

Macquarie University AU Australia (AU)

How to cite

APA:

Lonigro, D., Hahn, A., & Burgarth, D. (2024). On the Liouville–von Neumann Equation for Unbounded Hamiltonians. Open Systems & Information Dynamics, 31. https://doi.org/10.1142/S1230161224500185

MLA:

Lonigro, Davide, Alexander Hahn, and Daniel Burgarth. "On the Liouville–von Neumann Equation for Unbounded Hamiltonians." Open Systems & Information Dynamics 31 (2024).

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