Journal of the Indian Institute of Science最新文献

Probability distributions play a central role in quantum mechanics, and even more so in quantum optics with its rich diversity of theoretically conceivable and experimentally accessible quantum states of light. Quantifiers that compare two different states or density matrices in terms of ‘distances’ between the respective probability distributions include the Kullback–Leibler divergence (D_text{KL}), the Bhattacharyya distance (D_text{B}), and the p-Wasserstein distance ( W_{p}). We present a novel application of these notions to a variety of photon states, focusing particularly on the (p=1) Wasserstein distance ( W_{1}) as it is a proper distance measure in the space of probability distributions.

Physicist and Nobel Laureate Richard P. Feynman once remarked, "We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by “explaining” how it works. We will just tell you how it works. In telling you how it works, we will have told you about the basic peculiarities of all quantum mechanics"¹. The phenomenon of interference is ubiquitous in the quantum world and indeed holds within itself the explanation for many counterintuitive quantum phenomena. In this review, we choose to focus on a few ramifications and manifestations of quantum interference that have deep implications for the foundations of quantum mechanics. These include single-photon or second-order interference, two-photon or fourth-order interference and higher-order interference.

Quantum mechanics is a paradigm-shift in our understanding of dynamics of particles in this universe. It took shape rapidly over the first couple decades of the twentieth century, following a sequence of more gradual developments starting in the mid-nineteenth century. In this article we describe the developments in physics, relevant to the formulation of quantum physics, since the mid-nineteenth century until around 1935, spanning the entire period of evolution of quantum mechanical ideas. We lay special emphasis on those aspects of the scientific and logical history of this period which we believe were the most significant milestones, but are currently not part of the modern pedagogy of the subject. After reading this article, we hope that a beginner-student, someone with even a cursory idea of classical mechanics in the Hamiltonian formalism, will be able to understand how quantum mechanical ideas originated—ideas like the wave function, operators, the quantum jumps, quantum state-collapse under measurement etc.

Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It requires a formalism allowing creation and destruction of particles. This gets proper treatment only in a framework called quantum field theory. This article is a semi-historic account of the intriguing new features which emerge as a part of quantum field theory. Such a discussion is impossible without a basic presentation of the formalism itself. Hence some mathematics is included in finer print. The article is directed mostly to those familiar with essential classical mechanics and basic quantum mechanics, though I strive to provide a flavour of the subject to the keenly interested nonphysics reader.

Water scarcity poses a critical challenge globally, with its implications extending across socioeconomic, environmental, economic and public health domains. This study highlights the transformative role of treated wastewater reuse in achieving the United Nations’ sustainable development goals (SDGs), particularly in resource-limited contexts like India. Globally, the reuse of treated wastewater has been increasingly recognized as a vital strategy for achieving sustainable water security. In India, only 37% of urban wastewater undergoes treatment, with an even smaller portion (1–3%) reused, highlighting significant gaps in the nation’s water security. However, successful initiatives such as Karnataka’s Koramangala-Challaghatta valley project, Chennai project, Surat model, and Nagpur model demonstrate that treated wastewater can effectively replenish groundwater, enhance agricultural productivity, serve industrial purposes, and reduce the health burden. Through a systematic review, this study explores the multifaceted contributions of wastewater reuse, positioning it not only as a cornerstone for achieving SDG-6 (clean water and sanitation) but also as a catalytic force driving progress across all other SDGs through natural resource conservation, increased agricultural production, employment generation, technological innovation, income enhancement, and greenhouse gas reduction. By serving as a pivotal pillar of sustainable development, wastewater reuse promotes a synergistic integration among social well-being, environmental conservation, and economic resilience. It recommends that decision-makers prioritize continuous water quality monitoring, adopt cost-effective technological innovations, implement decentralized wastewater treatment systems and encouraging collaboration among stakeholders. By implementing this integrative approach, nations can make significant strides toward achieving global sustainable development goals.

A number of research institutes sought to address this disconnect in the post-independence development path and the IISc responded with its own research programmes dedicated to the needs of rural India in 1974 with the setting up of the Centre for Application of Science and Technology to Rural Areas (ASTRA, now renamed Centre for Sustainable Technologies (CST). What commenced as a discourse on alternative developmental models with a thrust on appropriate technologies centred around renewable energy and local resources gradually crystallised by the late 1980s into ideas of sustainable development. As its canvas of concerns grew, the ASTRA-CST had to reorient its vision incorporating the larger ‘sustainable development goals (SDG) as we understand today. The paper attempts to fathom how certain fields of research and development (R&D) became mainstreamed at this Centre and led to various technology development efforts. The first phase of activity of ASTRA-CST has not been adequately discussed in literature and this paper attempts to extend and to address that shortcoming. At this time, villages of rural India could best be described as reasonably closed ecosystems with moderate interactions achieving a low-level equilibrium. However, there was very little data about the various material flows, natural and man-made resource cycles, especially that relevant to land productivity, food consumption and its production pattern, water resource and security, health, rural industry, resource transformations and underlying skills, processes and efficiencies, residue management and re-use, environmental impacts, etc. and evolving such a knowledge-base was the key output of the first phase. The second phase involving various ‘homegrown’ technological and socio-technical interventions including stages of participatory technology development efforts resulted in large scale ‘dissemination’. A third phase addressed larger sustainable technologies solutions transgressing boundaries of the rural and urban that had marked the earlier phases. It is heartening to note that in some areas such as biomethanation, water-wastewater reuse, eco-friendly houses, biomass based alternative fuel platforms, rural industrial skilling, participatory technology development, etc. have gradually become policies at the national and global level and ASTRA-CST’s contribution is yeoman.

Quantum chaos is the study of footprints of classical chaos in the quantum world. The quantum signatures of chaos can be understood by studying quantum systems whose classical counterpart is chaotic. However, the concepts of integrability, non-integrability and chaos extend to systems without a classical analogue. Here, we first review the classical route from order into chaos. Since nature is fundamentally quantum, we discuss how chaos manifests in the quantum domain. We briefly describe semi-classical methods, and discuss the consequences of chaos in quantum information processing. We review the quantum version of Lyapunov exponents, as quantified by the out-of-time ordered correlators (OTOC), Kolmogorov–Sinai (KS) entropy and sensitivity to errors. We then review the study of signatures of quantum chaos using quantum tomography. Classically, if we know the dynamics exactly, as we maintain a constant coarse-grained tracking of the trajectory, we gain exponentially fine-grained information about the initial condition. In the quantum setting, as we track the measurement record with fixed signal-to-noise, we gain increasing information about the initial condition. In the process, we have given a new quantification of operator spreading in Krylov subspaces with quantum state reconstruction. The study of these signatures is not only of theoretical interest but also of practical importance.