M. U. Karelin | Searcharxiv

arXiv2004

Karhunen-Loeve analysis of complex spatio-temporal dynamics of thin-films optical system

Application of Karhunen-Loeve decomposition (KLD, or singular value decomposition) is presented for analysis of the spatio-temporal dynamics of wide-aperture vertical cavity surface emitting laser (VCSEL), considered as a thin-layer system. KLD technique enables to extract a set of dominant components from complex dynamics of system under study and separate them from noise and inessential underlying dynamical behavior. Properties of KLD spectrum and structure of its main components are studied for different regimes of VCSEL. Along with the analysis of VCSEL, a brief survey of KLD method and its usage for theoretical and experimental description of nonlinear dynamical systems is presented.

physics.optics↗

arXiv2000

Structure of the density matrix providing the minimum of generalized uncertainty relation for mixed states

For configurational space of arbitrary dimension a strict form of the uncertainty principle has been obtained, which takes into account the dependence of inequality limit on the effective number of pure states present in given statistical mixture. It is shown that in a state with minimal uncertainty the density operators eigenfunctions coincide with the stationary wavefunctions of a multidimensional harmonic oscillator. The mixed state obtained has a permutational symmetry which is typical for a system of identical bosons.

quant-ph↗