Integrable nonlinear evolution of the qubit

The nonlinear generalization of the von Neumann equation is studied. The global version of this equation preserves convexity of the space of states. The particular case of the evolution of pure states refers to the nonlinear Schrödinger equation discovered by Gisin. The concrete realization of the n...

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Bibliographic Details
Published in:Annals of physics 2019-12, Vol.411, p.167955, Article 167955
Main Authors: Kowalski, K., Rembieliński, J.
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DENSITY MATRIX
DIFFERENTIAL EQUATIONS
MIXED STATE
MIXED STATES
Nonlinear evolution
NONLINEAR PROBLEMS
PURE STATES
QUANTUM MECHANICS
Qubit
QUBITS
STABILITY
von Neumann equation
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Summary:The nonlinear generalization of the von Neumann equation is studied. The global version of this equation preserves convexity of the space of states. The particular case of the evolution of pure states refers to the nonlinear Schrödinger equation discovered by Gisin. The concrete realization of the nonlinear von Neumann equation is investigated in detail for the density matrix representing the qubit states. Such equation reduces to the integrable classical Riccati system of nonlinear ordinary differential equations. An interesting property of the nonlinear dynamics described by this system is the global asymptotical stability of stationary solutions related to evolution from mixed states to pure states. •We study the nonlinear generalization of the von Neumann equation.•We discuss the nonlinear von Neumann equation for the qubit states.•We analyze solutions to the Riccati system corresponding to evolution of a qubit.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2019.167955