An Optimal Control Problem for the Wigner Equation

Control/observation systems governed by partial differential equations (93C20) Statistical mechanics of semiconductors (82D37) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Existence theories for optimal control problems involving partial differential equations (49J20) PDEs in connection with control and optimization (35Q93) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53) Quantum control (81Q93)

Cites Work

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A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes
On Wigner measures
On the connection between the Wigner and the Bohm quantum formalism
A numerical investigation of Brockett's ensemble optimal control problems
A theoretical investigation of Brockett's ensemble optimal control problems
Applications of the Wigner distribution function in signal processing
Quantum corrected Liouville model: Mathematical analysis
Wigner model for quantum transport in graphene
Computational Optimization of Systems Governed by Partial Differential Equations
On the equivalence of the Schrödinger and the quantum Liouville equations
A Spectral Method for the Numerical Simulation of Quantum Tunneling Phenomena
On the Quantum Correction For Thermodynamic Equilibrium
Formulation and Numerical Solution of Quantum Control Problems
An Operator Splitting Method for the Wigner–Poisson Problem
Effective classical Liouville-like evolution equation for the quantum phase-space dynamics
Adding Decoherence to the Wigner Equation
Optimal Control of the Keilson-Storer Master Equation in a Monte Carlo Framework
Second-order analysis of Fokker–Planck ensemble optimal control problems
Charge Transport in Low Dimensional Semiconductor Structures
Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport
Wigner-function formulation for quantum transport in semiconductors: Theory and Monte Carlo approach

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