https://dspace.imsc.res.in/xmlui/handle/123456789/488 2026-06-04T11:00:37Z https://dspace.imsc.res.in/xmlui/handle/123456789/334 Exclusion Statistics: From Pauli to Haldane[MatSciRep: 120] Murthy, M.V.N.; Shankar, R. Quantum statistics provides a way of understanding the statistical mechanics of particles whose dynamical evolution is inherently governed by quantum mechanics. The statistics of all observed particles are covered by the two well known realisations of quantum statistics, namely, the Bose-Einstein (BE) statistics and the Fermi-Dirac (FD) statistics. Particles that obey these statistics are called bosons and fermions respectively. While this is true for all elementary particles which can have arbitrarily large momenta and exist in asymptotically free states, in recent years there has been much interest in the physics of “quasi-particles” obeying fractional statistics. Such quasi-particles may correspond to an elementary excitations that can only exist in the interior of a many body interacting system. The discussions in this report include many aspects of Fractional Exclusion Statistics (FES). The central ideal of Fractional Exclusion Statistics(FES), that it provides a frame-work to describe in a rather simple way a certain class of strongly interacting systems is developed further. There may be many important contributions which may not be covered in these pages. What is included is partly based on Authors' understanding of what is important in this field and partly due to their own work forming the basis of this presentation. Obviously it is almost impossible to cover all the of work in Fractional Exclusion Statistics(FES) that has followed Haldane’s seminal work. If some work of importance in the field is left out it is partly due to our ignorance or lack of understanding. 2013-01-28T11:06:38Z https://dspace.imsc.res.in/xmlui/handle/123456789/332 Matrix models Random surfaces and 2D gravity: November 19 - 23, 1990 [MatSciRep: 113] Haridass, N. D. This report containing proceedings of the "Mini Workshop on Matrix Models, Random Surfaces and 2-D Gravity" held during November 1990. This was first in the series of Workshops held at our Institute. The organizing committee consisted of G. Date, T.R. Govindarajan, N.D. Hari Dass (Convenor) and R.Ramachandran. This conference had a total of 42 participants with 23 from outside Madras. The workshop was held for five days. The workshop consisted of Review talks on the central theme as well as a few seminars during which original contributions were presented. Typically afternoons were used for detailed discussions on the talks held during mornings. 2012-10-30T08:25:19Z https://dspace.imsc.res.in/xmlui/handle/123456789/325 Schrodinger Operators: Workshop Proceedings, 4-14 December, 1995[MatSciRep: 118] Krishna, M., Ed. In its seven decades of existence, Quantum Mechanics still has many results which are believed not rigorously established, though routinely used in practice by Physicists. The question of unitarity of the S matrix is one such fundamental question, established rigorously only in the last decade, for N particle scattering interacting via a class of pair potentials. The question on transport (or the lack of it) of charge carriers in condensed matter systems, structure of potentials having a given energy spectrum, questions on existence and the number of resonance for a given potential are some other examples of questions in need of a rigorous mathematical framework, not to mention broader questions like existence of Crystals , rigorous foundations for QCD etc.,. This workshop on "Schrodinger Operators" was aimed to gather a few experts working on such rigorous questions relating to the Schrodinger equation/ Operator to introduce the subject to some of the students and teachers in India. This report will serve as not only a record of the activity that took place at IMSc, but also serve to enthuse future students to enter this difficult and challenging area of research. 2012-07-25T11:31:21Z https://dspace.imsc.res.in/xmlui/handle/123456789/321 Classical and quantum aspects of gravitation and cosmology: Proceedings of IAGRG -XVIII February 15-17 1996 dedicated to S. Chandrasekhar[MatSciRep: 117] Date, G; Bala R. Iyer, Eds., Prof. Naresh Dadhich suggested the idea that the XVIII conference of the IAGRG may be hosted by the Institute of Mathematical Sciences. There was a perception that while classical general relativity, gravitation, astrophysics, cosmology are active areas in their own right and as such have been discussed at the IAGRG meetings in the past, it is perhaps time now to expand the scope of these meetings to include the quantum gravity and particle physics aspects as well. Traditionally the general relativity community and the particle physics community have followed some what non overlapping developments. It would be mutually beneficial and healthier if both communities can interact more closely and share their experiences and perceptions. It is here that IMSc had a significant opportunity to play a role. Some of the members concurred with this perception and it is decided to host the XVIII Conference of the IAGRG at IMSc. Just around the time of deciding the announcement of this conference, Prof. S. Chandrasekhar passed away. In view of the phenomenal contributions of Chandra to General Relativity and Gravitation, it was but natural to dedicate this meeting to his memory. IMSc owes a special debt to Chandra as he played a crucial role in the foundation and the early stages of development of this Institute. Indeed the birth of the Institute of Mathematical Sciences was marked by the inaugural lecture by Prof. Chandrasekhar on January 3, 1962 in the lecture halls of Presidency College. This IMSc report reflects the envisaged expanded scope of the IAGRG meeting. Hopefully these proceedings will make the frontline developments accessible to a larger body of researchers in the country particularly to those from the universities and colleges. 2012-07-11T11:56:21Z