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

✍ Scribed by Surajit Sen

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 252 KB
• Volume: 360
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2005.06.047

✦ Synopsis

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.