Elements of naturality in dynamical simulation frameworks for Hamiltonian, thermostatic, and Lindbladian flows on classical and quantum state-spaces

Details Elements of naturality in dynamical simulation frameworks for Hamiltonian, thermostatic, and Lindbladian flows on classical and quantum state-spaces Elements of naturality in dynamical simulation frameworks for Hamiltonian, thermostatic, and Lindbladian flows on classical and quantum state-spaces

2010-07-12

arxiv.org/abs/1007.1958v1

Physics

Quantum Physics

Prepared for the 3rd nano-MRI Research Conference: Exploring the Frontiers of Magnetic Resonance Imaging, 12-16 July 2010, Dom

Scientific paper

The practical focus of this work is the dynamical simulation of polarization transport processes in quantum spin microscopy and spectroscopy. The simulation framework is built-up progressively, beginning with state-spaces (configuration manifolds) that are geometrically natural, introducing coordinates that are algebraically natural; and finally specifying dynamical potentials that are physically natural; in each respect explicit criteria are given for "naturality." The resulting framework encompasses Hamiltonian flow (both classical and quantum), quantum Lindbladian processes, and classical thermostatic processes. Constructive validation and verification criteria are given for metric and symplectic flows on classical, quantum, and hybrid state-spaces, with particular emphasis to tensor network state-spaces. Both classical and quantum examples are presented, including dynamic nuclear polarization (DNP). A broad span of applications and challenges is discussed, ranging from the design and simulation of quantum spin microscopes to the design and simulation of quantum oracles.

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