By Victor Albert (Caltech)
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. An important property of Lindbladians is their behavior in the limit of infinite time, and in this talk I will discuss a formula for the map corresponding to infinite-time Lindbladian evolution. This formula allows us to determine to what extent decay affects a system's linear or adiabatic response. It also allows us to determine geometrical structures (holonomy, curvature, and metric) associated with adiabatically deformed steady-state subspaces.
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