Generation of new classes of integrable quantum and statistical models

A scheme based on a unifying q-deformed algebra and associated with a generalized Lax operator is proposed for generating integrable quantum and statistical models. As important applications we derive known as well as novel quantum models and obtain new series of vertex models related to q-spin, q-boson and their hybrid combinations. Generic q, q roots of unity and q -> 1 yield different classes of integrable models. Exact solutions through algebraic Bethe ansatz is formulated for all models in a unified way.Comment: Latex, 9 pages + 1 figure (eps), Invited talk at Statphys-Kolkata I

Unifying scheme for generating discrete integrable systems including inhomogeneous and hybrid models

A unifying scheme based on an ancestor model is proposed for generating a wide range of integrable discrete and continuum as well as inhomogeneous and hybrid models. They include in particular discrete versions of sine-Gordon, Landau-Lifshitz, nonlinear Schr\"odinger (NLS), derivative NLS equations, Liouville model, (non-)relativistic Toda chain, Ablowitz-Ladik model etc. Our scheme introduces the possibility of building a novel class of integrable hybrid systems including multi-component models like massive Thirring, discrete self trapping, two-mode derivative NLS by combining different descendant models. We also construct inhomogeneous systems like Gaudin model including new ones like variable mass sine-Gordon, variable coefficient NLS, Ablowitz-Ladik, Toda chains etc. keeping their flows isospectral, as opposed to the standard approach. All our models are generated from the same ancestor Lax operator (or its q -> 1 limit) and satisfy the classical Yang-Baxter equation sharing the same r-matrix. This reveals an inherent universality in these diverse systems, which become explicit at their action-angle level.Comment: Latex, 20 pages, 2 figures, v3, final version to be published in J. Math Phy

Holographic Entanglement in a Noncommutative Gauge Theory

In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties.Comment: 28 pages, multiple figures; minor changes, conclusions unchange

Globalization and Exclusionary Urban rowth in Asian Countries

This paper overviews the debate on the relationship between the measures of globalization, economic growth and pace of urbanization, and speculates on its impact on the quality of life and poverty in the context of Asian countries. After experiencing moderate to high urban growth for three to four decades since the 1950s, most of these countries have reported a significant deceleration. This questions the postulate of the epicentre of urbanization shifting to Asia. It also lends credence to the thesis of exclusionary urban growth, which is linked with the formal or informal denial of entry to poor migrants and increased unaffordability of urban space of the rural people. An analysis of the policies and programmes at the national and regional levels shows that these have contributed to the ushering in of this era of urban exclusion. The process of elite capture in the global cities has led to ‘sanitization’ and cleaning up of the micro environment by pushing out the current and prospective migrants and informal activities out of the city boundaries. Given the political economy of urban growth and the need to attract global and domestic capital into cities, governments would not interfere with ‘elitist interests’. Asia, thus, is unlikely to go the same way as Latin America did in the second half of the last century. To absorb incremental labourforce outside agriculture, many of the large countries may, however, promote the small and medium towns that have unfortunately reported economic stagnation and deceleration in population growth. Furthermore, a few among the small and less developed countries are likely to experience high urban growth, largely due to foreign investment. This would impact on the geopolitical balance on the continent despite the fact that expansion in the urban and industrial base in these countries would not make a dent on macro-level aggregates.globalization, urbanization, urban growth, URGD, exclusionary urbanization, inequality, poverty, small towns, small Asian countries economic resiliency, Liberia

Exact Bethe ansatz solution of nonultralocal quantum mKdV model

A lattice regularized Lax operator for the nonultralocal modified Korteweg de Vries (mKdV) equation is proposed at the quantum level with the basic operators satisfying a $q$-deformed braided algebra. Finding further the associated quantum $R$ and $Z$-matrices the exact integrability of the model is proved through the braided quantum Yang--Baxter equation, a suitably generalized equation for the nonultralocal models. Using the algebraic Bethe ansatz the eigenvalue problem of the quantum mKdV model is exactly solved and its connection with the spin-\ha XXZ chain is established, facilitating the investigation of the corresponding conformal properties.Comment: 12 pages, latex, no figure