Scale invariant distribution functions in quantum systems with few degrees of freedom

Scale invariance usually occurs in extended systems where correlation functions decay algebraically in space and/or time. Here we introduce a new type of scale invariance, occurring in the distribution functions of physical observables. At equilibrium these functions decay over a typical scale set by the temperature, but they can become scale invariant in a sudden quantum quench. We exemplify this effect through the analysis of linear and non-linear quantum oscillators. We find that their distribution functions generically diverge logarithmically close to the stable points of the classical dynamics. Our study opens the possibility to address integrability and its breaking in distribution functions, with immediate applications to matter-wave interferometers.Comment: 8+10 pages. Scipost Submissio

Influence of Coformer Stoichiometric Ratio on Pharmaceutical Cocrystal Dissolution: Three Cocrystals of Carbamazepine/4-Aminobenzoic Acid

Cocrystallization is a technique to optimize solid forms that shows great potential to improve the solubility of active pharmaceutical ingredients (APIs). In some systems, an API can form cocrystals in multiple stoichiometries with the same coformer. However, it remains unclear how coformer stoichiometry influences solubility. This paper investigates the pharmaceutical:coformer pair carbamazepine (CBZ)/<i>p</i>-aminobenzoic acid (PABA); both CBZ/PABA 1:1 and 2:1 cocrystals are known, and a novel 4:1 CBZ/PABA cocrystal is reported here. The 4:1 cocrystal is structurally characterized, and phase stability data suggest that it is a thermodynamically unstable form. Dissolution experiments show that there is no correlation between the cocrystal stoichiometry and dissolution rate in this system. On the other hand, with the relatively weak intermolecular interactions, metastable forms can be beneficial to dissolution rate, which suggests that more effort should be devoted to cocrystal production with kinetic growth methods

The 2-dimensional array pattern by using contour lines after the adaptive processing of the original MUSIC algorithm.

<p>The 2-dimensional array pattern by using contour lines after the adaptive processing of the original MUSIC algorithm.</p

The pattern in azimuth view of the array patterns of the original PI and the proposed PI with a wide- band jammer.

<p>The pattern in azimuth view of the array patterns of the original PI and the proposed PI with a wide- band jammer.</p

A anti-jamming method for satellite navigation system based on multi-objective optimization technique

<div><p>In this paper, an anti-jamming method, which turns the single objective optimization problem into a multi-objective optimization problem by utilizing 2-norm, is proposed. The proposed jamming suppression method can reduce the wide nulls and wrong nulls problems, which are generated by the common adaptive nulling methods. Therefore a better signal-noise-ratio (SNR) can be achieved, especially when the jammers are close to satellite signals. It can also improve the robustness of the algorithm. The effectiveness of the proposed method is evaluated by simulation and practical outdoor experiments with the GPS L1 band C/A signals. The experimental results show that with the dedicated method, the nulls targeting at the corresponding jammers become narrower and the wrong nulls can be eliminated.</p></div

The 2-dimensional array pattern by using contour lines after the adaptive processing of the proposed 2-norm matrix constrained MUSIC algorithm.

<p>The 2-dimensional array pattern by using contour lines after the adaptive processing of the proposed 2-norm matrix constrained MUSIC algorithm.</p

The experimental results of single satellite comparison.

<p>The experimental results of single satellite comparison.</p

The experimental results of multiple satellites comparison.

<p>The experimental results of multiple satellites comparison.</p

Simulation procedure of the experiments.

<p>Simulation procedure of the experiments.</p

The experiment setup.

<p>The experiment setup.</p