Solving the Liouville equation for conservative systems: Continued fraction formalism and a simple application

Surajit Sen

doi:10.1016/j.physa.2005.06.047

Solving the Liouville equation for conservative systems: Continued fraction formalism and a simple application

Surajit Sen

Physics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

There are very few formalisms available to solve the Liouville equation for energy-conserved systems. The continued fraction formalism, introduced through the works of Zwanzig, Mori, Kubo, Lee, Grigolini and others is described here. A detailed discussion is presented on ways to apply the continued fraction formalism to solve for relaxation functions and for the dynamical variable itself for a simple and exactly solvable quantum spin system.

Original language	English
Pages (from-to)	304-324
Number of pages	21
Journal	Physica A: Statistical Mechanics and its Applications
Volume	360
Issue number	2
DOIs	https://doi.org/10.1016/j.physa.2005.06.047
State	Published - Feb 1 2006

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abstract = "There are very few formalisms available to solve the Liouville equation for energy-conserved systems. The continued fraction formalism, introduced through the works of Zwanzig, Mori, Kubo, Lee, Grigolini and others is described here. A detailed discussion is presented on ways to apply the continued fraction formalism to solve for relaxation functions and for the dynamical variable itself for a simple and exactly solvable quantum spin system.",

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AB - There are very few formalisms available to solve the Liouville equation for energy-conserved systems. The continued fraction formalism, introduced through the works of Zwanzig, Mori, Kubo, Lee, Grigolini and others is described here. A detailed discussion is presented on ways to apply the continued fraction formalism to solve for relaxation functions and for the dynamical variable itself for a simple and exactly solvable quantum spin system.

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Solving the Liouville equation for conservative systems: Continued fraction formalism and a simple application

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