Quantum space-time Poincar\'e inequality for Lindblad dynamics

Understand

We investigate the mixing properties of primitive Markovian Lindblad dynamics (i.e., quantum Markov semigroups), where the detailed balance is disrupted by a coherent drift term.

• It is known that the sharp $L^2$-exponential convergence rate of Lindblad dynamics is determined by the spectral gap of the generator.
• We show that incorporating a Hamiltonian component into a detailed balanced Lindbladian can generically enhance its spectral gap, thereby accelerating the mixing.
• In addition, we analyze the asymptotic behavior of the spectral gap for Lindblad dynamics with a large coherent contribution.