87 citations · 877 across the 97 of their papers we have counts for
18 papers · 1 filter
Spectral series of the Schrödinger operator with delta-potential on a three-dimensional spherically symmetric manifold
Tudor S. Ratiu, Asilya Suleymanova, Andrei Shafarevich
The spectral series of the Schrödinger operator with a delta-potential on a three-dimensional compact spherically symmetric manifold in the semiclassical limit as are descr…
Noether theorems and quantum anomalies
John Gough, Tudor S. Ratiu, Oleg G. Smolyanov
In this communication, we show that both infinite-dimensional versions of Noether's theorems, and the explanation of quantum anomalies can be obtained using similar formulas for th…
Momentum Maps and Stochastic Clebsch Action Principles
A. B. Cruzeiro, D. D. Holm, T. S. Ratiu
We derive stochastic differential equations whose solutions follow the flow of a stochastic nonlinear Lie algebra operation on a configuration manifold. For this purpose, we develo…
Quantum Anomalies and Logarithmic Derivatives
J. E. Gough, T. S. Ratiu, O. G. Smolyanov
This papers deals with connections between quantum anomalies and transformations of Feynman pseudo-measures. Mathematical objects related to the notion of the volume element in an…
Stochastic variational principles for dissipative equations with advected quantities
Xin Chen, Ana Bela Cruzeiro, Tudor S. Ratiu
This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group. Such variational principles yie…
Wigner Measures and Quantum Control
J. E. Gough, T. S. Ratiu, O. G. Smolyanov
We study several examples from quantum control theory in the framework of Wigner functions and measures for infinite dimensional open quantum systems. An axiomatic definition of co…
Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties
Mahouton Norbert Hounkonnou, Partha Guha, Tudor Ratiu
Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 --245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication r…
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…
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…
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,…
Integrable G-Strands on semisimple Lie groups
François Gay-Balmaz, Darryl D. Holm, Tudor S. Ratiu
The present paper derives systems of partial differential equations that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. It also deter…
Gradient flows in the normal and Kähler metrics and triple bracket generated metriplectic systems
Anthony M. Bloch, Philip J. Morrison, Tudor S. Ratiu
The dynamics of gradient and Hamiltonian flows with particular application to flows on adjoint orbits of a Lie group and the extension of this setting to flows on a loop group are…
Geometry of non-holonomic diffusion
Simon Hochgerner, Tudor S. Ratiu
We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are…
The Geometric Structure of Complex Fluids
François Gay-Balmaz, Tudor S. Ratiu
This paper develops the theory of affine Euler-Poincaré and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills an…
Affine Lie-Poisson Reduction, Yang-Mills magnetohydrodynamics, and superfluids
François Gay-Balmaz, Tudor S. Ratiu
This paper develops the theory of affine Lie-Poisson reduction and applies this process to Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids. As a consequence of…
Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids
François Gay-Balmaz, Tudor S. Ratiu
The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are determined. Using a Kaluza-Klein point of view, the equations of motion are obtained by Lagrangian an…
A Class of Integrable Geodesic Flows on the Symplectic Group and the Symmetric Matrices
Anthony M. Bloch, Arieh Iserles, Jerrold E. Marsden +1
This paper shows that the left-invariant geodesic flow on the symplectic group relative to the Frobenius metric is an integrable system that is not contained in the Mishchenko-Fome…