Lindbladians with multiple steady states: theory and applications

Abstract

Markovian master equations, often called Liouvillians or Lindbladians, are used to describe decay and decoherence of a quantum system induced by that system's environment. While a natural environment is detrimental to fragile quantum properties, an engineered environment can drive the system toward exotic phases of matter or toward subspaces protected from noise. These cases often require the Lindbladian to have more than one steady state, and such Lindbladians are dissipative analogues of Hamiltonians with multiple ground states. This thesis studies Lindbladian extensions of topics commonplace in degenerate Hamiltonian systems, providing examples and historical context along the way.

134 pages. (1) intro; (2) conserved quantities [arXiv:1310.1523], infinite-time limit [arXiv:1512.08079], symmetries, and extensions; (3) few/many-body examples; (4-6) perturbation theory, geometric phases, and quantum geometry, respectively [arXiv:1512.08079]; (7) extended study of a cat code [arXiv:1312.2017, arXiv:1503.00194]; (8) multimode cat codes [arXiv:1801.05897]

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Cited by in corpus (5)

• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
• Stationary State Degeneracy of Open Quantum Systems with Non-Abelian Symmetries
• Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states
• A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint