Stochastic Liouville, Langevin, Fokker–Planck, and Master Equation Approaches to Quantum Dissipative Systems

By Y. Tanimura. 2006

760 citations recorded by the source corpus.

Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9 (1954) 316 and 935, respectively. In this review, we give an overview and extension of the stochastic Liouville equation focusing on its theoretical background and applications to help further the development of their works. With the aid of path integral formalism, we derive the stochastic Liouville equation for density matrices of a system. We then cast the equation into the hierarchy of equations which can be solved analytically or computationally in a nonperturbative manner including the effect of a colored noise. We elucidate the applications of the stochastic theory from the unified theoretical basis to analyze the dynamics of a system as probed by experiments. We illustrate this as a review of several experimental examples including NMR, dielectric relaxation, Mossbauer spectroscopy, neutron scattering, and linear and nonlinear laser spectroscop...

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/db90c6c4396e09ad8539b9250a49f5cffc204fb3

How researchers see this paper

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In Artificial Intelligence

1. Birgit Hein
2. Ting Lu
3. Daniel Alonso
4. Tobias Kramer
5. Xiaona Fang
6. Mirta Rodr'iguez
7. Jin Wang
8. Shaul Mukamel

In Atomic and Molecular Physics, and Optics

1. Seogjoo J. Jang
2. Ting Lu
3. Xiaona Fang
4. Karsten Kruse
5. Benedetta Mennucci
6. F. Schlawin
7. K. Dorfman
8. Birgit Hein

In Statistical and Nonlinear Physics

1. Ting Lu
2. Xiaona Fang
3. Karsten Kruse
4. Birgit Hein
5. Daniel Alonso
6. Tobias Kramer
7. Mirta Rodr'iguez
8. Jin Wang

Citations in the corpus

• Dynamics of non-Markovian open quantum systems (2015, background): “The time differentiation of these operators leads to (Tanimura, 2006, 2015) dρn dt = −( i ~ HXs − nγ)ρn − i ~ SXρn+1 − i n ~ Θρn−1,(179) where ρ0 = ρs, Θ = (~λ/2)[cot(~βγ/2)SX − iSo], with Aoρ = Aρ+ ρA and AXρ = Aρ− ρA.”
• Nonlinear optical signals and spectroscopy with quantum light (2016, methodology): “The third approach for a wave function is equivalent to the stochastic Liouville equation for the density matrix (Tanimura, 2006), which is based on ladder diagram book keeping.”
• Delocalized excitons in natural light-harvesting complexes (2018, background): “Among various higher order methods developed for decades, the hierarchical equations of motion (HEOM) approach (Tanimura, 2006, 2015; Tanimura and Mukamel, 1993) has gained popularity recently and its results are considered as benchmark data by many re- searchers.”
• Nonequilibrium physics in biology (2019, background): “…between molecules such as photosynthesis have been explored intensively in experiments (Avinun-Kalish et al., 2005; Ho, 2002; Ohtani et al., 1988; Park et al., 2000; Reed et al., 1997; Wu et al., 2004) and studied theoretically (Esposito and Galperin, 2009; Harbola et al., 2006; Tanimura, 2006).”
• Modelling of oscillations in two-dimensional echo-spectra of the Fenna–Matthews–Olson complex (2011, methodology): “The hierarchical equations of motions (HEOM), first developed by Tanimura and Kubo [19] and subsequently refined in [20, 21, 22, 23], show oscillations in the dynamics of the exciton populations that persist even at temperature T = 300 K [24, 25].”