Journal of the Indian Institute of Science最新文献

We review old and new results concerning the (DS) functor and associated varieties for Lie superalgebras. These notions were introduced in the unpublished manuscript (Duflo and Serganova in On associated variety for Lie super-algebras, 2005) by Michel Duflo and the third author. This paper includes the results and proofs of the original manuscript, as well as a survey of more recent results.

The design of realistic quantum technologies relies intricately on the understanding of open quantum systems. Such open systems are often studied as an input–output theory, where time is often not explicitly parameterized. Such maps have a rich structure that has been elucidated by several authors over the years. In contrast to this, the master equation approach is a dynamical description where the infinitesimal evolution of the quantum system is studied. These two descriptions are related to each other when the underlying maps are parametrized in time or equivalently when the system dynamics is integrated for finite time. In this overview, we will briefly discuss some established results in this field alongside commenting on some recent results relating to deriving the transient and steady state dynamics of open quantum systems. We discuss structure of CP maps, review canonical forms of (mathcal {A}) and (mathcal {B}) maps and highlight their relationship to Lindblad equations. We review properties of Liouville superoperators and highlight some stable numerical methods to find steady states. We conclude the overview with a summary of results relating Zeno dynamics and the open systems approach to driven system engineering.

Modeling of any phenomenon requires the knowledge of the subject and the mathematical skill that is required to express the phenomenon in the form of mathematical relationship(s). In the process of model building, the researcher(s) experience several failures and learnings before getting the final model. While large number of final models are developed and published, learnings of model development are seldom documented. Hence, there is a need to bring such articles which could present the learning of model development. Under this premise, the author which has experience of developing stochastic models of human reproduction aims, in this article, to narrate those learnings which he had encountered in the development of large number of models. Since detailed descriptions of those models are already available in publications, the article would skips detail derivations of those models but to provide learnings of the development of the models.

Superconducting qubits are currently the leading platform for quantum computing and quantum information processing in general. Over the last decade, there have been rapid developments in the performance of small-scale quantum processors based on superconducting qubits, showing promise for a practical quantum processor in the coming years. These developments have taken place in terms of control and measurement techniques, connectivity, qubit architecture, and coherence performance. It has been led by novel design strategies, improvements in materials and fabrication processes, as well as advances in peripheral control electronics. In this article, we present a review of the various superconducting qubit devices, their coupling schemes, performance, and developments on the materials front.

Ultracold atoms and ions provide novel test-beds for quantum sensing and metrology. Technological advancement towards the construction of ultrastable and narrow linewidth lasers, optical frequency combs, and microwave electronics made it possible to realize atom interferometers with state of the art sensitivity and the most accurate clocks in the world based on long-lived quantum states of atoms and ions. Such systems have been utilized in applications starting from geodesy and navigation to the measurement and redefinition of fundamental constants. The field awaits a more enriched future in addition to the proposed applications of such systems in improving the Global Positioning System, secured communications, and exploring mineral and underground water resources. Here, we briefly report on the initiatives and current status of India in this research field in view of the global progress.

Contemporary social scientists have cast serious doubts over traditional statistical testing procedures and questioned the reproducibility of the findings. The Bayesian approach provides sound statistical tools to draw inferences about unknown parameters and potential outcomes in a methodical way. This paper reviews D. B. Rubin’s work from the orthodox Bayesian viewpoint and discusses how his brilliant ideas and suggestions should be applied when social scientists deal with real data. The discussion focuses on making inferences about causal relationships and handling missing data. It is argued that social scientists who are confident about both the Bayesian coherent system and the necessitated effective software for numerical solutions can build relevant statistical models and derive relevant information from the Bayesian analysis of real data. This paper specifically explains how to deal with the data, using examples from situations that social scientists should often encounter.

Polynomials in an infinite sequence of variables can be evaluated as class functions of symmetric groups on (n) letters across all (n). When they represent characters of families of representations, they are called character polynomials. This article is an introduction to the theory of character polynomials and their Frobenius characteristics. As an application, some generating functions describing the restriction of a polynomial representation of (GL_n) to (S_n) are obtained.