OTOC, complexity and entropy in bi-partite systems

There is a remarkable interest in the study of Out-of-time ordered correlators (OTOCs) that goes from many body theory and high energy physics to quantum chaos. In this latter case there is a special focus on the comparison with the traditional measures of quantum complexity such as the spectral statistics, for example. The exponential growth has been verified for many paradigmatic maps and systems. But less is known for multi-partite cases. On the other hand the recently introduced Wigner separability entropy (WSE) and its classical counterpart (CSE) provide with a complexity measure that treats equally quantum and classical distributions in phase space. We have compared the behavior of these measures in a system consisting of two coupled and perturbed cat maps with different dynamics: double hyperbolic (HH), double elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and the WSE have essentially the same behavior, providing with a complete characterization in generic bi-partite systems and at the same time revealing them as very good measures of quantum complexity for phase space distributions. Moreover, we establish a relation between both quantities by means of a recently proven theorem linking the second Renyi entropy and OTOCs.Comment: 6 pages, 5 figure

Quantum and classical complexity in coupled maps

We study a generic and paradigmatic two-degrees-of-freedom system consisting of two coupled perturbed cat maps with different types of dynamics. The Wigner separability entropy (WSE)—equivalent to the operator space entanglement entropy—and the classical separability entropy (CSE) are used as measures of complexity. For the case where both degrees of freedom are hyperbolic, the maps are classically ergodic and the WSE and the CSE behave similarly, growing to higher values than in the doubly elliptic case. However, when one map is elliptic and the other hyperbolic, the WSE reaches the same asymptotic value than that of the doubly hyperbolic case but at a much slower rate. The CSE only follows the WSE for a few map steps, revealing that classical dynamical features are not enough to explain complexity growth.Fil: Bergamasco, Pablo D.. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Carlo, Gabriel Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Rivas, Alejandro Mariano Fidel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentin

Relevant OTOC operators: footprints of the classical dynamics

The out-of-time order correlator (OTOC) has recently become relevant in different areas where it has been linked to scrambling of quantum information and entanglement. It has also been proposed as a good indicator of quantum complexity. In this sense, the OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. Here we have studied the OTOC-RE correspondence on physically meaningful bases like the ones constructed with the Pauli, reflection, and translation operators. The evolution is given by a paradigmatic bi-partite system consisting of two perturbed and coupled Arnold cat maps with different dynamics. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy and hence to reveal the character of the dynamics, up to a time t 0 . In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time. When represented in phase space, each one of these sets reveals the classical dynamical footprints with different depth according to the chosen base.Comment: 8 pages, 10 figure

Quantum Lyapunov exponent in dissipative systems

The out-of-time order correlator (OTOC) has been widely studied in closed quantum systems. However, there are very few studies for open systems and they are mainly focused on isolating the effects of scrambling from those of decoherence. Adopting a different point of view, we study the interplay between these two processes. This proves crucial in order to explain the OTOC behavior when a phase space contracting dissipation is present, ubiquitous not only in real life quantum devices but in the dynamical systems area. The OTOC decay rate is closely related to the classical Lyapunov exponent -- with some differences -- and more sensitive in order to distinguish the chaotic from the regular behavior than other measures. On the other hand, it reveals as a generally simple function of the longest lived eigenvalues of the quantum evolution operator. We find no simple connection with the Ruelle-Pollicott resonances, but by adding Gaussian noise of $\hbar_{\text{eff}}$ size to the classical system we recover the OTOC decay rate, being this a consequence of the correspondence principle put forward in [Physical Review Letters 108 210605 (2012) and Physical Review E 99 042214 (2019)]Comment: 5 pages, 7 figure

Ten golden rules for optimal antibiotic use in hospital settings: the WARNING call to action

Antibiotics are recognized widely for their benefits when used appropriately. However, they are often used inappropriately despite the importance of responsible use within good clinical practice. Effective antibiotic treatment is an essential component of universal healthcare, and it is a global responsibility to ensure appropriate use. Currently, pharmaceutical companies have little incentive to develop new antibiotics due to scientific, regulatory, and financial barriers, further emphasizing the importance of appropriate antibiotic use. To address this issue, the Global Alliance for Infections in Surgery established an international multidisciplinary task force of 295 experts from 115 countries with different backgrounds. The task force developed a position statement called WARNING (Worldwide Antimicrobial Resistance National/International Network Group) aimed at raising awareness of antimicrobial resistance and improving antibiotic prescribing practices worldwide. The statement outlined is 10 axioms, or “golden rules,” for the appropriate use of antibiotics that all healthcare workers should consistently adhere in clinical practice

Ten golden rules for optimal antibiotic use in hospital settings : the WARNING call to action

Abstract: Antibiotics are recognized widely for their benefits when used appropriately. However, they are often used inappropriately despite the importance of responsible use within good clinical practice. Effective antibiotic treatment is an essential component of universal healthcare, and it is a global responsibility to ensure appropriate use. Currently, pharmaceutical companies have little incentive to develop new antibiotics due to scientific, regulatory, and financial barriers, further emphasizing the importance of appropriate antibiotic use. To address this issue, the Global Alliance for Infections in Surgery established an international multidisciplinary task force of 295 experts from 115 countries with different backgrounds. The task force developed a position statement called WARNING (Worldwide Antimicrobial Resistance National/International Network Group) aimed at raising awareness of antimicrobial resistance and improving antibiotic prescribing practices worldwide. The statement outlined is 10 axioms, or "golden rules," for the appropriate use of antibiotics that all healthcare workers should consistently adhere in clinical practice