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http://hdl.handle.net/2289/22
2017-07-08T12:06:28ZNegative partial density of states in mesoscopic systems
http://hdl.handle.net/2289/6673
Title: Negative partial density of states in mesoscopic systems
Authors: Satpathi, Urbashi; Deo, Singha P.
Abstract: Since the experimental observation of quantum mechanical scattering phase shift in mesoscopic systems, several aspects of it have not yet been understood. The experimental observations have also accentuated many theoretical problems related to Friedel sum rule and negativity of partial density of states. We address these problems using the concepts of Argand diagram and Burgers circuit. We can prove the possibility of negative partial density of states in mesoscopic systems. Such a conclusive and general evidence cannot be given in one, two or three dimensions. We can show a general connection between phase drops and exactness of semi classical Friedel sum rule. We also show Argand diagram for a scattering matrix element can be of few classes based on their topology and all observations can be classified accordingly.
Description: Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)2016-12-01T00:00:00ZExact distributions of cover times for N independent random walkers in one dimension
http://hdl.handle.net/2289/6666
Title: Exact distributions of cover times for N independent random walkers in one dimension
Authors: Majumdar, Satya N.; Sabhapandit, Sanjib; Schehr, Gregory
Abstract: We study the probability density function (PDF) of the cover time tc of a finite interval of size L by N independent one-dimensional Brownian motions, each with diffusion constant D. The cover time tc is the minimum time needed such that each point of the entire interval is visited by at least one of the N walkers. We derive exact results for the full PDF of tc for arbitrary N≥1 for both reflecting and periodic boundary conditions. The PDFs depend explicitly on N and on the boundary conditions. In the limit of large N, we show that tc approaches its average value of ⟨tc⟩≈L2/(16DlnN) with fluctuations vanishing as 1/(lnN)2. We also compute the centered and scaled limiting distributions for large N for both boundary conditions and show that they are given by nontrivial N independent scaling functions.
Description: Open Access2016-12-01T00:00:00ZFluctuation theorem for entropy production of a partial system in the weak-coupling limit
http://hdl.handle.net/2289/6664
Title: Fluctuation theorem for entropy production of a partial system in the weak-coupling limit
Authors: Gupta, Deepak; Sabhapandit, Sanjib
Abstract: Small systems in contact with a heat bath evolve by stochastic dynamics. Here we show that, when one such small system is weakly coupled to another one, it is possible to infer the presence of such weak coupling by observing the violation of the steady-state fluctuation theorem for the partial entropy production of the observed system. We give a general mechanism due to which the violation of the fluctuation theorem can be significant, even for weak coupling. We analytically demonstrate on a realistic model system that this mechanism can be realized by applying an external random force to the system. In other words, we find a new fluctuation theorem for the entropy production of a partial system, in the limit of weak coupling.
Description: Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)2016-09-01T00:00:00ZA Random walk in relativity and cosmology: essays in honour of P.C. Vaidaya and A.K. Raychaudhuri
http://hdl.handle.net/2289/6624
Title: A Random walk in relativity and cosmology: essays in honour of P.C. Vaidaya and A.K. Raychaudhuri
Authors: Dadhich, N; Krishna Rao, J; Narlikar, J.V; Vishveshwara, C.V
Abstract: This volume is a collection of essays written in honour of Professor P.C. Vaidya and Professor A.K. Raychaudhuri. These two distinguished scientists are well-known for their important contributions to general relativity and cosmology, and are widely respected as inspiring teachers. Topics in general relativity fall broadly into two types namely the study of gravitational effects around local objects and the investigation of the global structure of spacetime. The Vaidya metric is an example of the former while the Raychaudhuri equation belongs to the latter category. Appropriately, the articles in this volume highlight problems of both kinds and are written by experts in the respective fields. These essays span a wide spectrum of diverse areas from abstract concepts to observational techniques within the framework of relativity, cosmology and astrophysics. Some of them represent original results of recent research, while others are broad-based state of the art reviews. The variety of subjects discussed here includes the detection of gravitational radiation, structure of spacetimes, the nature of singularities, positivity of gravitational energy, relativistic astrophysics in relation to gravitational collapse, neutron stars and black holes and fundamental conceptual problems in general relativity and cosmology. General relativity and associated fields constitute today a rapidly expanding area of research. A Random Walk in Relativity and Cosmology, by presenting new ideas and offering a glimpse of the excitement of ongoing exploration, should be both useful and stimulating to any interested reader.
Description: Table of Contents1985-01-01T00:00:00Z