In classical mechanics, spontaneous symmetry breaking of the Hamiltonian can embroil the dynamics of some regular systems into chaos. The classical and quantum pictures are not entirely different in these broken symmetric regions. There exists a correspondence between them, but for a brief time window. However, our numerical observations show that quantum mechanics can emulate the opposite role and forge exponential fluctuations in classically non-chaotic systems within an early-time window by introducing a symmetry-breaking term to the Hamiltonian. In this work, we have taken four one-dimensional quantum mechanical models: two Inverted Harmonic Oscillators(IHOs), a triple Well and IHO with a plateau. Then we spontaneously break the already existing symmetry in their Hamiltonian with varying perturbation strength to bring anomaly into the system. Then, we use numerical diagnostic tools such as OTOC, Loschmidt echo and spectral form factor(SFF) to detect the anomalies that may sweep into the system with the introduction of the asymmetry. Our primary focus is on the behaviour of OTOC as it reduces to the Lyapunov exponent in the classical limit, and we observe exponential growth, as expected. However, these exponential growths of OTOC are not widespread over the entire potential well but are limited only to the eigenstates in the neighbourhood of the broken symmetry. These results suggest that the exponential growth of OTOC, backed by Loschmidt echo and SFF, is due to asymmetry. In other words, OTOC detects the effect of symmetry-breaking, which is often synonymous with the butterfly effect.
The present research deals with the quantification of health hazard in a fluorosis prone area from east‐coast of India. The average health hazard quotients are 2.09, 2.42, 1.79, and 1.69 for infants, children, male, and female adults, respectively. These values are more than the tolerance limit (1) in 92% groundwater samples and 96% of the study area. The children are more vulnerable to fluorosis than infants and adults. Ca2+/ Na+ versus HCO3−/Na+ and Ca2+/Na+ versus Mg2+/Na+ plots suggest silicate weathering as the prime factor while linear relationship of TDS versus NO3− + (Cl−/HCO3−) supports the anthropogenic input of F− to the aquifer system. The study suggests that the F− ions are chiefly derived from fluorite, apatite, biotite, and hornblende present in the granitic basement under alkaline environment. The secondary sources are domestic and industrial sewage as well as return flow from irrigation with ingredients of phosphate fertilizers. The adverse effects of fluorosis can be minimized by mass awareness programmes, alternative source of potable drinking water, defluoridation techniques, dilution of high F− concentration in groundwater, and minimizing the use of phosphate fertilizers.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.