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arXiv · 1804.11293

Spectral theory of Liouvillians for dissipative phase transitions

Fabrizio Minganti·Alberto Biella·Nicola Bartolo·Cristiano Ciuti
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Abstract

A state of an open quantum system is described by a density matrix, whose dynamics is governed by a Liouvillian superoperator. Within a general framework, we explore fundamental properties of both first-order dissipative phase transitions and second-order dissipative phase transitions associated with a symmetry breaking. In the critical region, we determine the general form of the steady-state density matrix and of the Liouvillian eigenmatrix whose eigenvalue defines the Liouvillian spectral gap. We illustrate our exact results by studying some paradigmatic quantum optical models exhibiting critical behavior.

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Fabrizio Minganti, Alberto Biella, Nicola Bartolo, Cristiano Ciuti. 2018-04-30. Spectral theory of Liouvillians for dissipative phase transitions. https://doi.org/10.1103/physreva.98.042118

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