Solution to quantum Liouville equation in phase space via a stochastic process

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1986

OSTI ID:6159230

Sarah, J

A numerical technique for the solution of the Quantum Liouville equation is discussed which is expected to be useful for mixed states describing highly excited many body systems. The equation is represented in phase-space, where the density operator becomes the Wigner function. The Liouville operator which determines its time evolution, separates into a classical and quantum term. When the Wigner function varies slowly in momentum, the quasi-classical approximation is valid in which one keeps only the first order quantum term in the Liouville equation. This method is numerically tested for an anharmonic quartic potential. The contours of the Wigner function at different time intervals are compared with the purely classical and exact results. It is seen that it provides a definite improvement over the purely classical approximation. Various averages are also compared and sources of error discussed.

• Research Organization: College of William and Mary, Williamsburg, VA (USA)
• OSTI ID: 6159230
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANHARMONIC OSCILLATORS
ELECTRONIC EQUIPMENT
ENERGY LEVELS
EQUIPMENT
EXCITED STATES
LIOUVILLE THEOREM
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
NUMERICAL SOLUTION
OSCILLATORS
PHASE SPACE
POTENTIALS
QUANTUM MECHANICS
QUANTUM OPERATORS
SPACE
STOCHASTIC PROCESSES
WIGNER COEFFICIENTS