Open quantum system model of the one-dimensional Burgers equation with tunable shear viscosity

Journal Article · Sun Oct 15 00:00:00 EDT 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.74.042322· OSTI ID:20857840

Yepez, Jeffrey ^[1]

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1. Air Force Research Laboratory, 29 Randolph Road, Hanscom Field, Massachusetts 01731 (United States)

Presented is an analysis of an open quantum model of the time-dependent evolution of a flow field governed by the nonlinear Burgers equation in one spatial dimension. The quantum model is a system of qubits where there exists a minimum time interval in the time-dependent dynamics. Each temporally discrete unitary quantum-mechanical evolution is followed by state reduction of the quantum state. The mesoscopic behavior of this quantum model is described by a quantum Boltzmann equation with a naturally emergent entropy function and H theorem and the model obeys the detailed balance principle. The macroscopic-scale effective field theory for the quantum model is derived using a perturbative Chapman-Enskog expansion applied to the linearized quantum Boltzmann equation. The entropy function is consistent with the quantum-mechanical collision process and a Fermi-Dirac single-particle distribution function for the occupation probabilities of the qubit's energy eigenstates. Comparisons are presented between analytical predictions and numerical predictions and the agreement is excellent, indicating that the nonlinear Burgers equation with a tunable shear viscosity is the operative macroscopic scale effective field theory.

• OSTI ID: 20857840
• Journal Information: Physical Review. A, Vol. 74, Issue 4; Other Information: DOI: 10.1103/PhysRevA.74.042322; (c) 2006 U. S. Government; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BOLTZMANN EQUATION
COLLISIONS
COMPARATIVE EVALUATIONS
DETAILED BALANCE PRINCIPLE
DISTRIBUTION FUNCTIONS
EIGENSTATES
ENTROPY
H THEOREM
HYDRODYNAMICS
NAVIER-STOKES EQUATIONS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PROBABILITY
QUANTUM COMPUTERS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUBITS
SHEAR
SHOCK WAVES
TIME DEPENDENCE
VISCOSITY