Basic properties of a mean field laser equation
arXiv:2006.13001 · doi:10.1142/S123016121950015X
Abstract
We study the non-linear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the non-linear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schröndiger equation. To this end, we find a regular solution for the non-autonomous linear quantum master equation in Gorini-Kossakowski-Sudarshan-Lindblad form, and we prove the uniqueness of the solution to the non-autonomous linear adjoint quantum master equation in Gorini-Kossakowski-Sudarshan-Lindblad form. Moreover, we obtain rigorously the Maxwell-Bloch equations from the mean field laser equation.
arXiv admin note: substantial text overlap with arXiv:1803.00875
References in corpus (5)
- Non-Markovian dynamics in open quantum systems
- Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions
- Numerical solution of conservative finite-dimensional stochastic Schrodinger equations
- A sharp version of Ehrenfest's theorem for general self-adjoint operators
- Numerical solution of stochastic master equations using stochastic interacting wave functions