2024/08/21 by Léonce Dupays, Dupays, Léonce
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical Physics (physics.class-ph) #Computer science #FOS: Physical sciences #Master equation #Mathematical Physics (math-ph) #Mathematics #Ornstein–Uhlenbeck process #Physics #Process (computing) #Quantum #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph) #Quantum mechanics #Spectral Theory in Mathematical Physics #Statistical physics #Statistics #Stochastic process
paper · pdf · doi:10.48550/arxiv.2408.11893
openalex publication_date 2024/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Third quantization is used in open quantum systems to construct a superoperator basis in which quadratic Lindbladians can be turned into a normal form. From it follows the spectral properties of the Lindbladian, including eigenvalues and eigenvectors. However, the connection between third quantization and the semiclassical representations usually employed to obtain the dynamics of open quantum systems remains opaque. We introduce an alternative basis for third quantization that bridges this gap between third quantization and the Q representation by projecting the master equation onto a superoperator coherent-state basis. The equation of motion reduces to a multidimensional complex Ornstein-Uhlenbeck process.