%0 Journal Article %1 WOS:000351908300009 %A Aguiar, V %A Guedes, I %C TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND %D 2015 %I IOP PUBLISHING LTD %J PHYSICA SCRIPTA %K Cramer-Rao Leipnik Shannon Stam's and damped entropies; harmonic inequalities; inequalities} information; oscillators; quantum {fisher %N 4 %R 10.1088/0031-8949/90/4/045207 %T Fisher information of quantum damped harmonic oscillators %V 90 %X We calculate the time-dependent Fisher information in position (F-x) and momentum (F-p) for the lowest lying state (n = 0) of two classes of quantum damped (Lane-Emden (LE) and Caldirola-Kanai (CK)) harmonic oscillators. The expressions of F-x and F-p are written in terms of rho, a c-number quantity satisfying a nonlinear differential equation. Analytical solutions of rho were obtained. For the LE and CK oscillators, we observe that F-x increases while F-p decreases with increasing time. The product FxFp increases and tends to a constant value in the limit t --> infinity for the LE oscillator, while it is time-independent for the CK oscillator. Moreover, for the CK oscillator the product FxFp decreases as the damping (gamma) increases. Relations among the Fisher information, Leipnik and Shannon entropies, and the Stam and Cramer-Rao inequalities are given. A discussion on the squeezing phenomenon in position for the oscillators is presented.

@article{WOS:000351908300009, abstract = {We calculate the time-dependent Fisher information in position (F-x) and momentum (F-p) for the lowest lying state (n = 0) of two classes of quantum damped (Lane-Emden (LE) and Caldirola-Kanai (CK)) harmonic oscillators. The expressions of F-x and F-p are written in terms of rho, a c-number quantity satisfying a nonlinear differential equation. Analytical solutions of rho were obtained. For the LE and CK oscillators, we observe that F-x increases while F-p decreases with increasing time. The product FxFp increases and tends to a constant value in the limit t --> infinity for the LE oscillator, while it is time-independent for the CK oscillator. Moreover, for the CK oscillator the product FxFp decreases as the damping (gamma) increases. Relations among the Fisher information, Leipnik and Shannon entropies, and the Stam and Cramer-Rao inequalities are given. A discussion on the squeezing phenomenon in position for the oscillators is presented.}, added-at = {2022-05-23T20:00:14.000+0200}, address = {TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND}, author = {Aguiar, V and Guedes, I}, biburl = {https://www.bibsonomy.org/bibtex/2093ac9e29862fad908e0d26b0db302ff/ppgfis_ufc_br}, doi = {10.1088/0031-8949/90/4/045207}, interhash = {6956aa1b4f7909d7c6366eced522971c}, intrahash = {093ac9e29862fad908e0d26b0db302ff}, issn = {0031-8949}, journal = {PHYSICA SCRIPTA}, keywords = {Cramer-Rao Leipnik Shannon Stam's and damped entropies; harmonic inequalities; inequalities} information; oscillators; quantum {fisher}, number = 4, publisher = {IOP PUBLISHING LTD}, pubstate = {published}, timestamp = {2022-05-23T20:00:14.000+0200}, title = {Fisher information of quantum damped harmonic oscillators}, tppubtype = {article}, volume = 90, year = 2015 }