92 citations · 154 across the 13 of their papers we have counts for
7 papers · 1 filter
Geometry of quantum systems: density states and entanglement
Janusz Grabowski, Marek Kuś, Giuseppe Marmo
Various problems concerning the geometry of the space $u^*(\cH)$ of Hermitian operators on a Hilbert space $\cH$ are addressed. In particular, we study the canonical Poisson and Ri…
Quantum Bi-Hamiltonian systems, alternative Hermitian structures and Bi-Unitary transformations
G. Marmo, G. Scolarici, A. Simoni +1
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space.…
Reduction and Unfolding for Quantum Systems: the Hydrogen Atom
A. D'Avanzo, G. Marmo, A. Valentino
In this paper we propose a ``quantum reduction procedure'' based on the reduction of algebras of differential operators on a manifold. We use these techniques to show, in a systema…
Reduction and unfolding: the Kepler problem
Antonella D'Avanzo, Giuseppe Marmo
In this paper we show, in a systematic way, how to relate the Kepler problem to the isotropic harmonic oscillator. Unlike previous approaches, our constructions are carried over in…
Dynamics of autonomous systems with external forces
Giuseppe Marmo, Wodzimierz M. Tulczyjew, Pawel Urbanski
We consider a geometric framework for analytical mechanics with external forces. Four versions of this framework are considered. A variational principle with boundary terms and ext…
Non-holonomic constrained systems as implicit differential equations
L. A. Ibort, M. de Leon, G. Marmo +1
Non-holonomic constraints, both in the Lagragian and Hamiltonian formalism, are discussed from the geometrical viewpoint of implicit differential equations. A precise statement of…