• S Chaturvedi

      Articles written in Pramana – Journal of Physics

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

      S Chaturvedi E Ercolessi G Marmo G Morandi N Mukunda R Simon

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      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

      S Chaturvedi E Ercolessi G Marmo G Morandi N Mukunda R Simon

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      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.

    • Hamilton’s theory of turns revisited

      N Mukunda S Chaturvedi R Simon

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      We present a new approach to Hamilton’s theory of turns for the groups $SO(3)$ and $SU(2)$ which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.

    • Multiscale simulations of damage of perfect crystal Cu at high strain rates

      S Rawat M Warrier S Chaturvedi V R Ikkurthi

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      We use the molecular dynamics code, large-scale atomic/molecular massively parallel simulator (LAMMPS), to simulate high strain rate triaxial deformation of crystal copper to understand void nucleation and growth (NAG) within the framework of an experimentally fitted macroscopic NAG model for polycrystals (also known as DFRACT model). It is seen that void NAG at the atomistic scales for crystal copper (Cu) has the same qualitative behaviour as the DFRACT model, albeit with a different set of parameters. The effect of material temperature on the nucleation and growth of voids is studied. As the temperature increases, there is a steady decrease in the void NAG thresholds and close to the melting point of Cu, a double-dip in the pressure–time profile is observed. Analysis of this double-dip shows disappearance of the long-range order due to the creation of stacking faults and the system no longer has a face centred cubic (fcc) structure. Molecular dynamics simulation of shock in crystal Cu at strain rates high enough to cause spallation of crystal Cu are then carried out to validate the void NAG parameters. We show that the pre-history of the material affects the void nucleation threshold of the material. We also simulate high-strain-rate triaxial deformation of crystal Cu with defects and obtain void NAG parameters. The parameters are then used in a macroscale hydrodynamic simulation to obtain spallation threshold of realistic crystal Cu. It is seen that our results match experimental results within the limit of 20% error.

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