We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our paper [8]) that for some special choices of the reparametrisation parameter ǫ, one can obtain space-space noncommuting structures which are Lie-algebraic in for...

Several recent works have shown that the onedimensional fully asymmetric exclusion model, which describes a ystem of panicles hopping in a preferred direction with hard core interactions, can be solved exactb in the case of open boundaries. Here we present a new approach based on representing the weights of each mnfiguration in the steady state as a product of noncommuting matrices. Wth this ap...

Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, terms Linear Matrix Inequalities and Bilinear Inequalities.

We describe the action of symplectic group on homogeneous space squeezed states (quantum blobs) and extend this to semigroup. then metaplectic representation (or oscillator) semigroup study properties such an extension using Bargmann-Fock space. The shape geometry squeezing is analyzed noncommuting elements from are proposed be used in simultaneous monitoring quantum variables — which should le...