Mutual information and electron correlation in momentum space

Differential Shannon Entropies and Mutual Information in a Curve Crossing System: Adiabatic and Diabatic Decompositions

The differential Shannon entropy provides a measure for the localization of a wave function. We regard the vibrational wave packet motion in a curve crossing system and calculate time-dependent entropies. Using a numerical example, we analyze how localization inside diabatic and adiabatic states can be accessed and discuss the differences between these two representations. In order to do so, we extend the usual entropy definition and introduce novel state-selective entropies. These quantities contain information on the form of the nuclear density components on the one hand and on the state population on the other, and it is shown how the contribution of the population can be removed. Having the state-selective entropies at hand, two additional functions derived from these, namely, the conditional entropy and the mutual information, are determined and compared. We find that these quantities relate closely to correlation effects rooted in different electronic properties of the system.

Characteristic features of the Shannon information entropy of dipolar Bose-Einstein condensates

Calculation of the Shannon information entropy (S) and its connection with the order-disorder transition and with inter-particle interaction provide a challenging research area in the field of quantum information. Experimental progress with cold trapped atoms has corroborated this interest. In the present work, S is calculated for the Bose-Einstein condensate (BEC) with dominant dipolar interaction for different dipole strengths, trap aspect ratios, and number of particles (N). Trapped dipolar bosons in an anisotropic trap provide an example of a system where the effective interaction is strongly determined by the trap geometry. The main conclusion of the present calculation is that the anisotropic trap reduces the number of degrees of freedom, resulting in more ordered configurations. Landsberg's order parameter exhibits quick saturation with the increase in scattering length in both prolate and oblate traps. We also define the threshold scattering length which makes the system completely disordered. Unlike non-dipolar BEC in a spherical trap, we do not find a universal linear relation between S and lnN, and we, therefore, introduce a general quintic polynomial fit rather well working for a wide range of particle numbers.

The role of interparticle interaction and environmental coupling in a two-particle open quantum system

The effects of bath coupling on an interacting two-particle quantum system are studied using tools from information theory. Shannon entropies of the one (reduced) and two-particle distribution functions in position, momentum and separable phase-space are examined. Results show that the presence of the bath leads to a delocalization of the distribution functions in position space, and a localization in momentum space. This can be interpreted as a loss of information in position space and a gain of information in momentum space. The entropy sum of the system, in the presence of a bath, is shown to be dependent on the strength of the interparticle potential and also on the strength of the coupling to the bath. The statistical correlation between the particles, and its dependence on the bath and interparticle potential, is examined using mutual information. A stronger repulsive potential between particles, in the presence of the bath, yields a smaller correlation between the particles positions, and a larger one between their momenta.

Reducing false alarms in syndromic surveillance

Algorithms for identifying public health threats or disease outbreaks are vulnerable to false alarms arising from sudden shifts in health-care utilization or data participation. This paper describes a method of reducing false alerts in automated public health surveillance algorithms, and in particular, automated syndromic surveillance algorithms, that rely on health-care utilization data. The technique is based on monitoring syndromic counts with reference to a suitable background, or reference, series of counts. The suitability of the background time series in decreasing the false-alarm rate will be shown to be related mathematically to the so-called mutual information that exists between the random variables representing the syndromic and background time series of counts. The method can be understood as a noise cancellation filter technique in which one noisy (reference) channel is used to cancel the background noise of the monitored (measured) channel. The issues discussed here may also be relevant to the appropriate use of rates in epidemiology and biostatistics.

Information entropies for eigendensities of homogeneous potentials

For homogeneous potentials, the sum S(T), of position and momentum Shannon information entropies Sr and Sp is shown to be independent of the coupling strength scaling. The other commonly used uncertainty like products also follow similar behavior. The ramifications of this scaling property in the cases of hydrogenlike, harmonic oscillator, Morse, and Poeschl-Teller potentials are discussed with the example of S(T).