SearcharxivSearch

arXiv subjects

Aalok Pandya

Publications and source records attributed to Aalok Pandya.

9 recordsLinked to original sources

Loops, Loop Sequences and Loop Surfaces in Statistical Geodesics, and Quantum Information

The locus of probability flow in Quantum Mechanics and information is explored. We explore loops, loop sequences and loop surfaces in the statistical geodesics. Having known about the loop character of the statistical geodesics in probability space, we discuss wider physical aspects of consequences of the geometry of the probabilities in the form of loop sequences and loop surfaces. These are interpreted as the locus of probability flow. A deeper philosophical observation reveals that these loops, loop sequences and loop surfaces are the information grids. These investigations in many ways could be significant not only in the research in Statistics, but also in Mathematics, and Physics in general, and entropy, gravity and information theory in specific.

physics.gen-ph

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-II

The geometry of Quantum Mechanics in the context of uncertainty and complementarity, and probability is explored. We extend the discussion of geometry of uncertainty relations in wider perspective. Also, we discuss the geometry of probability in Quantum Mechanics and its interpretations. We give yet another interpretation to the notion of Faraday lines and loops as the locus of probability flow. Also, the possibilities of visualization of spectra of area operators by means of classical geometric forms and conventional Quantum Mechanics are explored.

physics.gen-ph

Background Independent Quantum Mechanics, Classical Geometric Forms and Geometric Quantum Mechanics-I

The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert space has been discussed for the chosen Quantum states. Since the theory of classical gravity is basically geometric in nature and Quantum Mechanics is in no way devoid of geometry, the explorations pertaining to more and more geometry in Quantum Mechanics could prove to be valuable for larger objectives such as understanding of gravity.

physics.gen-ph

Dark Energy, Background Independent Quantum Mechanics and the Origin of Cosmological Constant

We explore the extended framework of the generalized quantum mechanics and discuss various aspects of neighborhood in the construction of space in search of origin of cosmological constant. We propose to expand definition of the volume of the phase space in eight dimensions with an overall constraint in the form of uncertainty relation as: $(Δp_{x}Δp_{y}Δp_{z}ΔE)(ΔxΔyΔzΔt)\sim h^{4}$. We argue that the phase space volume in the eight dimensions is an appropriate representation that it should be, and the relation $(ΔΛ)(ΔV)\sim h$ again brings it down to the reduced phase space.

physics.gen-ph

The Metric of Quantum States Revisited

A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised definition. The metric of quantum states in the configuration space and its possible geometrical framework is explored. Also, invariance of the metric of quantum states under local gauge transformations, coordinate transformations, and the relativistic transformations is discussed.

quant-ph

Spherical Manifold in Quantum Evolution

In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space. Geometrically, the evolution is represented as a closed curve in the projective Hilbert space. In recent times many attempts have been made to describe 'length', 'distance', and 'geometric phases' and also 'parallel transport'and symplectic geometry in various ways in the projective Hilbert space, during quantum evolution. It is shown in this paper that for the quantum evolution in ray space, spherical manifold and features of discreteness can be described geometrically.

quant-ph

On Metric of Quantum States with Lorentzian Signature

In this note we comment on yet another way of describing metric of quantum states with the Lorentzian signature. For this, we consider the metric of quantum states and make successive transformations, exploiting the relationship between S3 and SU(2).

quant-ph

General Topology of the Universe

General topology of the universe is descibed. It is concluded that topology of the present universe is greater or stronger than the topology of the universe in the past and topology of the future universe will be stronger or greater than the present topology of the universe. Consequently, the universe remains unbounded.

astro-ph

Search for Gravity in Quantum Evolution

The possibilities of curvature of space-time in the metric of quantum states are investigated. The curvature of the metric corresponding to a wave function of Hydrogen atom is determined. Also, Einstein tensor is described for a given quantum state.

quant-ph