Unitary Integration with Operator Splitting for Weakly Dissipative Systems

Abstract

Unitary integration is a numerical method that preserves the structure of the quantum Liouville equation by evolving the density via unitary transformations. Unitary integrators preserve the kinematic invariants C(sub j) = trp(sup j), j = 1,..., n to all orders in the time step. Here we extend unitary integration to weakly dissipative systems. We apply the technique of operator splitting, using a unitary integrator for the Hamiltonian evolution and a conventional integrator for the dissipative piece. In this way, we guarantee that all dissipation and decoherence (variation of the C(sub j)) is due to the new non-Hamiltonian terms and not to any numerical artifacts. We illustrate the method with examples.

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Document Details

Document Type
Technical Report
Publication Date
Jun 20, 2001
Accession Number
ADA395111

Entities

People

  • B. A. Shadwick
  • W. F. Buell

Organizations

  • The Aerospace Corporation

Tags

Communities of Interest

  • Advanced Electronics
  • Materials and Manufacturing Processes
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Algorithms
  • Buildings And Structures
  • Corporations
  • Differential Equations
  • Dissipation
  • Equations
  • Error Analysis
  • Errors
  • Guarantees
  • Integrators
  • Liouville Equation
  • Personal Information Managers
  • Physical Properties
  • Quantum Computing
  • Splitting

Fields of Study

  • Mathematics
  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Linear Algebra

Technology Areas

  • Quantum Computing