Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical physics

1985/04/01 by Masuo Suzuki · 404 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Algebra over a field #Basis (linear algebra) #Decomposition #Exponential function #Geometry #Lie algebra #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum mechanics #Quantum optics and atomic interactions #Relaxation (psychology) #Statistical physics #Theoretical and Computational Physics

paper · doi:10.1063/1.526596

published in Journal of Mathematical Physics 26(4), 601-612 (American Institute of Physics)

openalex publication_date 1985/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07

Abstract

Decomposition formulas of general exponential operators in a Banach algebra and in a Lie algebra are presented that yield a basis of Monte Carlo simulation of quantum systems. They are applied to study the relaxation and fluctuation from the initially unstable point and to confirm algebraically the scaling theory of transient phenomena. A global approximation method of transient phenomena is also formulated on the basis of decomposition formulas. It is applied to the laser model as a simple example.

Citations

• On the product of semi-groups of operators
• Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems

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