87 citations · 877 across the 97 of their papers we have counts for
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Noether's Theorem for Dissipative Quantum Dynamical Semigroups
John E. Gough, Tudor S. Ratiu, O. G. Smolyanov
Noether's Theorem on constants of the motion of dynamical systems has recently been extended to classical dissipative systems (Markovian semi-groups) by Baez and Fong. We show how…
The tropical momentum map: a classification of toric log symplectic manifolds
Marco Gualtieri, Songhao Li, Alvaro Pelayo +1
We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We…
Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions
François Gay-Balmaz, Darryl D. Holm, Tudor S. Ratiu
Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for Lagrangian and Hamiltonian…
A new Lagrangian dynamic reduction in field theory
François Gay-Balmaz, Tudor S. Ratiu
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a…
Lagrangian reductions and integrable systems in condensed matter
François Gay-Balmaz, Michael Monastyrsky, Tudor S. Ratiu
We consider a general approach for the process of Lagrangian and Hamiltonian reduction by symmetries in chiral gauge models. This approach is used to show the complete integrabilit…
Feynman, Wigner, and Hamiltonian Structures Describing the Dynamics of Open Quantum Systems
J. E. Gough, T. S. Ratiu, O. G. Smolyanov
This paper discusses several methods for describing the dynamics of open quantum systems, where the environment of the open system is infinite-dimensional. These are purifications,…