https://libjncir.jncasr.ac.in/xmlui/handle/10572/20 Sat, 04 Apr 2026 05:27:48 GMT 2026-04-04T05:27:48Z https://libjncir.jncasr.ac.in/xmlui/handle/10572/2583 A Homomorphism Theorem and a Trotter Product Formula for Quantum Stochastic Flows with Unbounded Coefficients Das, Biswarup; Goswami, Debashish; Sinha, Kalyan B. We give a new method for proving the homomorphic property of a quantum stochastic flow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter product formula for quantum stochastic flows and obtain quantum stochastic dilations of a class of quantum dynamical semigroups generalizing results of Goswami et al. (Inst H Poincare Probab Stat 41:505-522, 2005). Restricted Access Wed, 01 Jan 2014 00:00:00 GMT https://libjncir.jncasr.ac.in/xmlui/handle/10572/2583 2014-01-01T00:00:00Z https://libjncir.jncasr.ac.in/xmlui/handle/10572/2584 STOPPING THE CCR FLOW AND ITS ISOMETRIC COCYCLES Belton, Alexander C. R.; Sinha, Kalyan B. It is shown how to use non-commutative stopping times in order to stop the CCR flow of arbitrary index and also its isometric cocycles, i.e. left operator Markovian cocycles on Boson Fock space. Stopping the CCR flow yields a homomorphism from the semigroup of stopping times, equipped with the convolution product, into the semigroup of unital endomorphisms of the von Neumann algebra of bounded operators on the ambient Fock space. The operators produced by stopping cocycles themselves satisfy a cocycle relation. Restricted Access Wed, 01 Jan 2014 00:00:00 GMT https://libjncir.jncasr.ac.in/xmlui/handle/10572/2584 2014-01-01T00:00:00Z https://libjncir.jncasr.ac.in/xmlui/handle/10572/2582 Site-disorder driven superconductor-insulator transition: a dynamical mean field study Kamar, Naushad Ahmad; Vidhyadhiraja, N. S. We investigate the effect of site disorder on the superconducting state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength (U), the superconducting order parameter decreases monotonically with increasing disorder (x), while the single-particle spectral gap decreases for small x, reaches a minimum and keeps increasing for larger x. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor-insulator transition. We investigate this transition in depth considering the effects of weak and strong disorder for a range of interaction strengths. In the clean case, the order parameter is known to increase monotonically with increasing interaction, saturating at a finite value asymptotically for U -> infinity. The presence of disorder results in destruction of superconductivity at large U, thus drastically modifying the clean case behaviour. A physical understanding of our findings is obtained by invoking particle-hole asymmetry and the probability distributions of the order parameter and spectral gap. Restricted Access Wed, 01 Jan 2014 00:00:00 GMT https://libjncir.jncasr.ac.in/xmlui/handle/10572/2582 2014-01-01T00:00:00Z https://libjncir.jncasr.ac.in/xmlui/handle/10572/2581 Preformed excitons, orbital selectivity, and charge density wave order in 1T-TiSe2 Koley, S.; Laad, M. S.; Vidhyadhiraja, N. S.; Taraphder, A. Traditional routes to charge density wave (CDW) in transition-metal dichalcogenides, relying on Fermi surface nesting or Jahn-Teller instabilities, have recently been brought into question. While this calls for exploration of alternative views, a paucity of theoretical guidance sustains lively controversy on the origin of, and interplay between, CDW and superconductive orders in transition-metal dichalcogenides. Here, we explore a preformed excitonic liquid route, heavily supplemented by modern correlated electronic-structure calculations, to an excitonic CDW order in 1T-TiSe2. We show that orbital-selective dynamical localization arising from preformed excitonic liquid correlations is somewhat reminiscent of states proposed for d and f band quantum criticality at the border of magnetism. Excellent quantitative explication of a wide range of spectral and transport responses in both normal and CDW phases provides strong support for our scenario, and suggests that soft excitonic liquid fluctuations mediate superconductivity in a broad class of transition-metal dichalcogenides on the border of CDW. This brings the transition-metal dichalcogenides closer to the bad actors (where the metallic state is clearly not a Fermi liquid) in d and f band systems, where anomalously soft fluctuations of electronic origin are believed to mediate unconventional superconductivity on the border of magnetism. Restricted Access Wed, 01 Jan 2014 00:00:00 GMT https://libjncir.jncasr.ac.in/xmlui/handle/10572/2581 2014-01-01T00:00:00Z