We compute the deterministic approximation of products Sobolev functions large Wigner matrices $W$ and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem [Voiculescu 1991] from polynomials to general functions, as well tracial quantities individual matrix elements. Applying result $\exp(\mathrm{i} tW)$ for $t$, we obtain...

We examine the affine Wigner distribution from a quantization perspective with an emphasis on underlying group structure. One of our main results expresses scalogram as (affine) convolution distributions. strive to unite literature distributions and we provide connection Mellin transform in rigorous manner. Moreover, present ambiguity function show how this can be used illuminate properties dis...

Schwinger’s finite (D) dimensional periodic Hilbert Space representations are studied on the toroidal lattice with specific emphasis on the deformed oscillator subalgebras and the generalized representations of the Wigner function. These subalgebras are shown to be admissible endowed with the non-negative norm of Hilbert space vectors. Hence, they provide the desired canonical basis for the alg...

The Wigner equation was used for the calculation of carrier transport in mesoscopic devices. The carrier transport has a coherent part determined by the Wigner potential Vw and a dissipative part accounting for the interaction with phonons. Models have been developed which solve the equation by using quasi-particles evolving over pieces of classical Newton trajectories. In a backward evolution ...

The Wigner function was first derived by E.P. Wigner around 1931 as an exotic outcome of the wave mechanics which, being defined in the phase space, does not favor either coordinate or momentum variables. Pioneered by H.J. Groenewold and J.E.Moyal theWigner formulation of quantum mechanics evolved until the end of last century, to a fully autonomous, independent alternative to Hilbert space mec...

We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-the...