• G Marmo

Articles written in Pramana – Journal of Physics

• Wigner distributions for finite dimensional quantum systems: An algebraic approach

We discuss questions pertaining to the definition of ‘momentum’, ‘momentum space’, ‘phase space’ and ‘Wigner distributions’; for finite dimensional quantum systems. For such systems, where traditional concepts of ‘momenta’ established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail

• Ray space `Riccati' evolution and geometric phases for 𝑁-level quantum systems

We present a simple derivation of the matrix Riccati equations governing the reduced dynamics as one descends from the group $\mathbb{U}(N)$ describing the Schrõdinger evolution of an 𝑁-level quantum system to the various coset spaces and Grassmanian manifolds associated with it. The special case pertaining to the geometric phase in 𝑁-level systems is described in detail. Further, we show how the matrix Riccati equation thus obtained can be reformulated as an equation describing Hamiltonian evolution in a classical phase space and establish correspondences between the two descriptions.

• # Pramana – Journal of Physics

Current Issue
Volume 93 | Issue 5
November 2019

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