Quantum statistical master equation

Ravinder Rupchand Puri

A.G. Hall

A classical statistical probability amplitude is introduced whose square modulus is the distribution function. This enables the analogy between classical statistical mechanics and quantum mechanics to be completed. The analogy is developed until quantum statistical derivations can be used in classical statistical mechanics. Two master equations are found: the classical equivalent of the Pauli Master Equation, and a generally valid master equation. Well-known classical equations are deduced from these in a special representation. Interference terms are found and discussed.

Mikayla Z. Fahrenbruch, Anthony W. Schlimgen, Kade Head-Marsden

Microscopic master equations have gained traction for the dissipative treatment of molecular spin and solid-state systems for quantum technologies. Single particle approximations are often invoked to treat these systems, which can lead to unphysical evolution when combined with master equation approaches. We present a mathematical constraint on the system-environment parameters to ensure that microscopically-derived Markovian master equations preserve fermionic, $N$-representable statistics when applied to reduced systems. We demonstrate these constraints for the recently derived unified master equation and universal Lindblad equation, along with the Redfield master equation for cases when positivity issues are not present. For operators that break the constraint, we explore the addition of Pauli factors to recover $N$-representability. This work promotes feasible applications of novel microscopic master equations for realistic chemical systems.

Xiang Li, Yu Su, Zi‐Hao Chen +4 more

Dissipaton theory had been proposed as an exact, nonperturbative approach to deal with open quantum system dynamics, where the influence of the Gaussian environment is characterized by statistical quasi-particles, named dissipatons. In this work, we revisit the dissipaton equation of motion theory and establish an equivalent dissipaton-embedded quantum master equation (DQME) that gives rise to dissipatons as generalized Brownian particles. As explained in this work, the DQME supplies a direct approach to investigate the statistical characteristics of dissipatons and, thus, the physically supporting hybrid bath modes. Numerical demonstrations are carried out on the electron transfer model, exhibiting the transient statistical properties of the solvation coordinate.

Shigeji Fujita, Kei Ito, Salvador Godoy