5 papers · 2 filters
Variational Dissipative Mechanics on Lie Algebroids
Alexandre Anahory Simoes, Leonardo Colombo
We formulate a Herglotz-type variational principle on a Lie algebroid and derive the corresponding Euler--Lagrange--Herglotz equations for a Lagrangian depending on an additional s…
Lindblad Quantum Dynamics as Euler-Poincaré Reduction on Adjoint-Coupled Semidirect Products
Leonardo Colombo
We present a geometric and variational derivation of the Gorini--Kossakowski--Sudarshan--Lindblad equation from Euler--Poincar'e reduction on an adjoint--coupled semidirect product…
A Presymplectic and Symmetry Reduced Formulation of the Maxwell Vlasov System
Leonardo Colombo
We develop a unified geometric formulation of the Maxwell-Vlasov system using the infinite-dimensional Skinner-Rusk (SR) formalism. In this framework, particles and fields are trea…
Reduction of hybrid Hamiltonian systems with non-equivariant momentum maps
Leonardo Colombo, María Emma Eyrea Irazú, María Eugenia García +2
We develop a reduction scheme à la Marsden-Weinstein-Meyer for hybrid Hamiltonian systems. Our method does not require the momentum map to be equivariant, neither to be preserved b…
Homogeneous bi-Hamiltonian structures and integrable contact systems
Leonardo Colombo, Manuel de León, María Emma Eyrea Irazú +1
Bi-Hamiltonian structures can be utilised to compute a maximal set of functions in involution for certain integrable systems, given by the eigenvalues of the recursion operator rel…