Quantum state diffusion with a moving basis: computing quantum-optical spectra

Quantum state diffusion (QSD) as a tool to solve quantum-optical master equations by stochastic simulation can be made several orders of magnitude more efficient if states in Hilbert space are represented in a moving basis of excited coherent states. The large savings in computer memory and time are due to the localization property of the QSD equation. We show how the method can be used to compute spectra and give an application to second harmonic generation.Comment: 8 pages in RevTeX, 1 uuencoded postscript figure, submitted to Phys. Rev.

Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics

We re-examine the problem of the "Loschmidt echo", which measures the sensitivity to perturbation of quantum chaotic dynamics. The overlap squared $M(t)$ of two wave packets evolving under slightly different Hamiltonians is shown to have the double-exponential initial decay $\propto \exp(-{\rm constant}\times e^{2\lambda_0 t})$ in the main part of phase space. The coefficient $\lambda_0$ is the self-averaging Lyapunov exponent. The average decay $\bar{M}\propto e^{-\lambda_1 t}$ is single exponential with a different coefficient $\lambda_1$. The volume of phase space that contributes to $\bar{M}$ vanishes in the classical limit $\hbar\to 0$ for times less than the Ehrenfest time $\tau_E=\frac{1}{2}\lambda_0^{-1}|\ln \hbar|$. It is only after the Ehrenfest time that the average decay is representative for a typical initial condition.Comment: 4 pages, 4 figures, [2017: fixed broken postscript figures

Semiclassical properties and chaos degree for the quantum baker's map

We study the chaotic behaviour and the quantum-classical correspondence for the baker's map. Correspondence between quantum and classical expectation values is investigated and it is numerically shown that it is lost at the logarithmic timescale. The quantum chaos degree is computed and it is demonstrated that it describes the chaotic features of the model. The correspondence between classical and quantum chaos degrees is considered.Comment: 30 pages, 4 figures, accepted for publication in J. Math. Phy

Quantum chaos in open systems: a quantum state diffusion analysis

Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with the environment, and makes the quasiclassical limit of such systems both more realistic and simpler in many respects than the more familiar quasiclassical limit for closed systems. A linearized version of this theory leads to the correct classical dynamics in the macroscopic limit, even for nonlinear and chaotic systems. We apply the theory to the forced, damped Duffing oscillator, comparing the numerical results of the full and linearized equations, and argue that this can be used to make explicit calculations in the decoherent histories formalism of quantum mechanics.Comment: 18 pages standard LaTeX + 9 figures; extensively trimmed; to appear in J. Phys.

COVID-19 Pandemic Worsening Gender Inequalities for Women and Girls in Sub-Saharan Africa

Pandemics such as COVID-19 have often resulted in international, national and sub-regional crises, with considerable inequities across many societies. With the already existing structural and socio-economic inequalities in sub-Saharan Africa, the stay-at-home orders, lockdowns, and shutdowns across the sub-regional states could worsen and have a tremendous impact on vulnerable groups. Numerous studies across a variety of contexts have well-documented gender, and cultures on varied health outcomes. However, these have not been contextualized in sub-Saharan Africa in the light of the COVID-19 pandemic. This mini review discusses the ways by which COVID-19 has impacted the lives of girls and women across sub-Saharan Africa and the strategies that can help mitigate these challenges. The mini review specifically shares light on a wide array of dimensions where the inequities exist. These include the disproportionate areas affected by COVID-19; household inequities; educational inequalities; work/employment inequalities; disparities related to healthcare, sexual and reproductive health as well as housing inequities. Conclusively, the review accentuates the need for sub-Saharan African countries to adopt low-cost preventive measures such as discouraging mass gatherings (e.g., local community gatherings), and face masking with non-medical cloth like masks for the local populace as these are crucial in managing the spread of the virus among disproportionate women population. For localities with limited access to handwashing facilities, alternative strategies like alcohol-based hand rub solutions could be deployed. The complex interrelated disparities require a broad set of policy actions to lessen the current burden faced by many women in sub-Saharan Africa