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Alternative Algebraic Structures from Bi-Hamiltonian Quantum Systems
G. Marmo, G. Scolarici, A. Simoni +1
We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We a…
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.…
Classical and Quantum Systems: Alternative Hamiltonian Descriptions
G. Marmo, G. Scolarici, A. Simoni +1
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible He…
Alternative structures and bi-Hamiltonian systems on a Hilbert space
G. Marmo, G. Scolarici, A. Simoni +1
We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional compl…
The Quantum-Classical Transition: The Fate of the Complex Structure
G Marmo, G Scolarici, A Simoni +1
According to Dirac, fundamental laws of Classical Mechanics should be recovered by means of an "appropriate limit" of Quantum Mechanics. In the same spirit it is reasonable to enqu…