Lie algebraic noncommuting structures from reparametrisation symmetry

We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our paper \cite{sg}) that for some special choices of the reparametrisation parameter $\epsilon$, one can obtain space-space noncommuting structures which are Lie-algebraic in form even in the case of the relativistic free particle. The connection of these structures with the existing models in the literature is also briefly discussed. Further, there exists some values of $\epsilon$ for which the noncommutativity in the space-space sector can be made to vanish. As a matter of internal consistency of our approach, we also study the angular momentum algebra in details.Comment: 9 pages Latex, some references adde

Relations Between Quantum Maps and Quantum States

The relation between completely positive maps and compound states is investigated in terms of the notion of quantum conditional probability

Gravity and Yang-Mills theory

Three of the four forces of Nature are described by quantum Yang-Mills theories with remarkable precision. The fourth force, gravity, is described classically by the Einstein-Hilbert theory. There appears to be an inherent incompatibility between quantum mechanics and the Einstein-Hilbert theory which prevents us from developing a consistent quantum theory of gravity. The Einstein-Hilbert theory is therefore believed to differ greatly from Yang-Mills theory (which does have a sensible quantum mechanical description). It is therefore very surprising that these two theories actually share close perturbative ties. This article focuses on these ties between Yang-Mills theory and the Einstein-Hilbert theory. We discuss the origin of these ties and their implications for a quantum theory of gravity.Comment: 6 pages, based on contribution to GRF 2010, to appear in a special edition of IJMP

Zeno dynamics and constraints

We investigate some examples of quantum Zeno dynamics, when a system undergoes very frequent (projective) measurements that ascertain whether it is within a given spatial region. In agreement with previously obtained results, the evolution is found to be unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. By using a new approach to this problem, this result is found to be valid in an arbitrary $N$-dimensional compact domain. We then propose some preliminary ideas concerning the algebra of observables in the projected region and finally look at the case of a projection onto a lower dimensional space: in such a situation the Zeno ansatz turns out to be a procedure to impose constraints.Comment: 21 page

One qubit almost completely reveals the dynamics of two

From the time dependence of states of one of them, the dynamics of two interacting qubits is determined to be one of two possibilities that differ only by a change of signs of parameters in the Hamiltonian. The only exception is a simple particular case where several parameters in the Hamiltonian are zero and one of the remaining nonzero parameters has no effect on the time dependence of states of the one qubit. The mean values that describe the initial state of the other qubit and of the correlations between the two qubits also are generally determined to within a change of signs by the time dependence of states of the one qubit, but with many more exceptions. An example demonstrates all the results. Feedback in the equations of motion that allows time dependence in a subsystem to determine the dynamics of the larger system can occur in both classical and quantum mechanics. The role of quantum mechanics here is just to identify qubits as the simplest objects to consider and specify the form that equations of motion for two interacting qubits can take.Comment: 6 pages with new and updated materia

Packing Density Approach for Sustainable Development of Concrete

This paper deals with the details of optimized mix design for normal strength concrete using particle packing density method. Also the concrete mixes were designed as per BIS: 10262-2009. Different water-cement ratios were used and kept same in both design methods. An attempt has been made to obtain sustainable and cost effective concrete product by use of particle packing density method. The parameters such as workability, compressive strength, cost analysis and carbon di oxide emission were discussed. The results of the study showed that, the compressive strength of the concrete produced by packing density method are closer to that of design compressive strength of BIS code method. By adopting the packing density method for design of concrete mixes, resulted in 11% cost saving with 12% reduction in carbon di oxide emission

Derivation of reduced two-dimensional fluid models via Dirac's theory of constrained Hamiltonian systems

We present a Hamiltonian derivation of a class of reduced plasma two-dimensional fluid models, an example being the Charney-Hasegawa-Mima equation. These models are obtained from the same parent Hamiltonian model, which consists of the ion momentum equation coupled to the continuity equation, by imposing dynamical constraints. It is shown that the Poisson bracket associated with these reduced models is the Dirac bracket obtained from the Poisson bracket of the parent model