Phase transitions with finite atom number in the Dicke Model

Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are the number of photons inside the cavity and the number of excited atoms. Coherent states provide a mean field description, which becomes exact in the thermodynamic limit. Employing symmetry adapted (SA) SU(2) coherent states (SACS) the critical behavior can be described for a finite number of atoms. A variation after projection treatment, involving a numerical minimization of the SA energy surface, associates the finite number phase transition with a discontinuity in the order parameters, which originates from a competition between two local minima in the SA energy surface.Comment: 8 pages, 10 figures, Conference Proceedings of CEWQO-2012, to be published as a Topical Issue of the journal Physica Script

Geometric Satake, Springer correspondence, and small representations

For a simply-connected simple algebraic group $G$ over \C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of $G$, generalizing a well-known fact about $GL_n$. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number of known facts (mostly due to Broer and Reeder) about small representations of the dual group.Comment: Version 2: minor revisions, 33 page

High Speed Machining for Enhancing the AZ91 Magnesium Alloy Surface Characteristics Influence and Optimisation of Machining Parameters

In this study, optimum machining parameters are evaluated for enhancing the surface roughness and hardness of AZ91 alloy using Taguchi design of experiments with Grey Relational Analysis. Dry face milling is performed using cutting conditions determined using Taguchi L9 design and Grey Relational Analysis has been used for the optimization of multiple objectives. Taguchi’s signal-to-noise ratio analysis is also performed individually for both characteristics and grey relational grade to identify the most influential machining parameter affecting them. Further, Analysis of Variance is carried to see the contribution of factors on both surface roughness and hardness. Finally, the predicted trends obtained from the signal-to-noise ratio are validated using confirmation experiments. The study showed the effectiveness of Taguchi design combined with Grey Relational Analysis for the multi-objective problems such as surface characteristics studies

Analytic Approximation of the Tavis-Cummings Ground State via Projected States

We show that an excellent approximation to the exact quantum solution of the ground state of the Tavis-Cummings model is obtained by means of a semi-classical projected state. This state has an analytical form in terms of the model parameters and, in contrast to the exact quantum state, it allows for an analytical calculation of the expectation values of field and matter observables, entanglement entropy between field and matter, squeezing parameter, and population probability distributions. The fidelity between this projected state and the exact quantum ground state is very close to 1, except for the region of classical phase transitions. We compare the analytical results with those of the exact solution obtained through the direct Hamiltonian diagonalization as a function of the atomic separation energy and the matter-field coupling.Comment: 22 pages, 13 figures, accepted for publication in Physics Script

Coherent State Description of the Ground State in the Tavis-Cummings Model and its Quantum Phase Transitions

Quantum phase transitions and observables of interest of the ground state in the Tavis-Cummings model are analyzed, for any number of atoms, by using a tensorial product of coherent states. It is found that this "trial" state constitutes a very good approximation to the exact quantum solution, in that it globally reproduces the expectation values of the matter and field observables. These include the population and dipole moments of the two-level atoms and the squeezing parameter. Agreement in the field-matter entanglement and in the fidelity measures, of interest in quantum information theory, is also found.The analysis is carried out in all three regions defined by the separatrix which gives rise to the quantum phase transitions. It is argued that this agreement is due to the gaussian structure of the probability distributions of the constant of motion and the number of photons. The expectation values of the ground state observables are given in analytic form, and the change of the ground state structure of the system when the separatrix is crossed is also studied.Comment: 38 pages, 16 figure

Mass and Spin of Poincare Gauge Theory

We discuss two expressions for the conserved quantities (energy momentum and angular momentum) of the Poincar\'e Gauge Theory. We show, that the variations of the Hamiltonians, of which the expressions are the respective boundary terms, are well defined, if we choose an appropriate phase space for asymptotic flat gravitating systems. Furthermore, we compare the expressions with others, known from the literature.Comment: 16 pages, plain-tex; to be published in Gen. Rel. Gra

Kerr-Schild Symmetries

We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized and that they constitute a Lie algebra if the null deformation direction is fixed. The properties of these Lie algebras are briefly analyzed and we show that they are generically finite-dimensional but that they may have infinite dimension in some relevant situations. The most general vector fields of the above type are explicitly constructed for the following cases: any two-dimensional metric, the general spherically symmetric metric and deformation direction, and the flat metric with parallel or cylindrical deformation directions.Comment: 15 pages, no figures, LaTe