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Joseph Samuel

Publications and source records attributed to Joseph Samuel.

At least 19 recordsLinked to original sources
arXiv2026

Unified Hydrodynamic Analogue of Aharonov-Bohm and Lense-Thirring Effects

We show that surface waves in a draining-bathtub vortex provide a hydrodynamic realization of both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging within a single system. A static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, yielding an effective vector potential set by the background flow. In this geometry, the circulation defines a global phase holonomy that controls wave structure. Traveling waves exhibit wavefront dislocations characteristic of Aharonov-Bohm scattering, while standing-wave superpositions produce nodal patterns that rotate at an angular velocity fixed by the circulation, providing a direct analogue of frame dragging. For noninteger circulation, the problem is naturally defined on the universal cover, ensuring single-valued partial-wave solutions. Experiments on a controlled vortex confirm these predictions and establish a laboratory platform in which topological phase and inertial effects, central to gauge and gravitational physics, emerge from a measurable velocity field.

physics.flu-dyn↗
arXiv2024

Closure invariants for polarised radio interferometric observations: a graph theoretical approach

Aperture synthesis observations with full polarisation have long been used to study the magnetic fields of synchrotron emitting sources. Recently proposed closure invariants give us a powerful method for extracting information from measured visibilities which are corrupted by antenna and polarisation dependent gains. In this paper, a formalism developed earlier for complete graphs (where all visibilities are available) is extended to incomplete graphs. The formalism provides a complete and independent set of closure invariants from the measured visibilities in a general situation where not all visibilities are available. We then show in a simulated, quasi-realistic case that the invariants developed here contain usable information even in the presence of noise.

astro-ph.IM↗
arXiv2022

Born-Oppenheimer and the Geometry of Ray Space

It is known that, within the Born-Oppenheimer approximation, the slow modes of the nuclear motion are altered by three effects that emerge from integrating out the fast modes of the electronic motion. The first is an effective scalar potential $V_{\mathrm dyn}$ coming from the eigenvalue of the electronic state, the second is an effective magnetic field coming from the Berry phase vector potential $A$. The third term is an additional potential $V_{\mathrm geom}$ originating in the geometry of ray space and the Fubini-Study metric. In this article, we illustrate these effects and their geometric origin in the context of a simple toy model of a slow neutron interacting with a strong, spatially varying magnetic field. Regarding the neutron spin as a fast degree of freedom, we work out the slow dynamics of the motion of the neutron. Our treatment is geometrical and brings out the effects originating in the K\"ahler geometry of ray space and the Fubini-Study metric. We then give examples of magnetic field configurations which isolate these three separate effects. Finally we apply these ideas to the trapping of cold atoms. Our main result is that the geometric electric potential $V_{\mathrm geom}$ dominates for smaller traps and can be used to confine cold atoms in static traps. This observation could result in better and smaller atomic clocks. This paper is dedicated to Michael Berry on his 80th Birthday.

quant-ph↗
arXiv2021

Invariants in Co-polar Interferometry: an Abelian Gauge Theory

An $N$-element interferometer measures correlations among pairs of array elements. Closure invariants associated with closed loops among array elements are immune to multiplicative, element-based ("local") corruptions that occur in these measurements. Till recently, it has been unclear how a complete set of independent invariants can be analytically determined. We view the local, element-based corruptions in co-polar correlations as gauge tranformations belonging to the gauge group $\textrm{GL}(1,\mathbb{C})$. Closure quantities are then naturally gauge invariant. We use this to provide a simple and effective formalism, and identify the complete set of independent closure invariants from co-polar interferometric correlations using only quantities defined on $(N-1)(N-2)/2$ elementary and independent triangular loops. The $(N-1)(N-2)/2$ closure phases and $N(N-3)/2$ closure amplitudes (totaling $N^2-3N+1$ real invariants), familiar in astronomical interferometry, naturally emerge from this formalism, which unifies what has required separate treatments until now. We do not require auto-correlations, but can easily include them if reliably measured. This unified view clarifies issues relating to noise and inference of object model parameters. It also allows us to extend the rule of parallel transport associated with Pancharatnam phase in optics to apply to amplitudes as well. The framework presented here extends to $\textrm{GL}(2,\mathbb{C}$) for full polarimetric interferometry as presented in a companion paper, which generalizes and clarifies earlier work. Our findings are relevant to state of the art co-polar and full polarimetric very long baseline interferometry measurements to determine features very near the event horizons of blackholes at the centers of M87, Centaurus~A, and the Milky Way.

astro-ph.IM↗
arXiv2021

Invariants in Polarimetric Interferometry: a non-Abelian Gauge Theory

The discovery of magnetic fields close to the M87 black hole using Very Long Baseline Interferometry (VLBI) by the Event Horizon Telescope collaboration utilized the novel concept of "closure traces", that are immune to element-based aberrations. We take a fundamentally new approach to this promising tool of polarimetric VLBI, using ideas from the geometric phase and gauge theories. The multiplicative distortion of polarized signals at the individual elements are represented as gauge transformations by general $2\times 2$ complex matrices, so the closure traces now appear as gauge-invariant quantities. We apply this formalism to polarimetric interferometry and generalize it to any number of interferometer elements. Our approach goes beyond existing studies in the following respects: (1) we use triangular combinations of correlations as basic building blocks of invariants, (2) we use well-known symmetry properties of the Lorentz group to transparently identify a complete and independent set of invariants, and (3) we do not need auto-correlations, which are susceptible to large systematic biases, and therefore unreliable. This set contains all the information, immune to corruption, available in the interferometer measurements, thus providing important robust constraints for interferometric studies.

gr-qc↗
arXiv2021

Coadjoint orbits and K\"ahler structure: examples from coherent states

Do co-adjoint orbits of Lie groups support a K\"{a}hler structure? We study this question from a point of view derived from coherent states. We examine three examples of Lie groups: the Weyl-Heisenberg group, $\mathrm{SU(2)}$ and $\mathrm{SU(1,1)}$. In cases, where the orbits admit a K\"{a}hler structure, we show that coherent states give us a K\"{a}hler embedding of the orbit into projective Hilbert space. In contrast, squeezed states, (which like coherent states, also saturate the uncertainty bound) only give us a symplectic embedding. We also study geometric quantisation of the co-adjoint orbits of the group $\mathrm{SUT(2,\mathbb{R})}$ of real, special, upper triangular matrices in two dimensions. We glean some general insights from these examples. Our presentation is semi-expository and accessible to physicists.

math-ph↗
arXiv2020

Of Light and Shadows: Raychaudhuri's equation, the Big Bang and Black Holes

Einstein's genius and penetrating physical intuition led to the general theory of relativity, which incorporates gravity into the geometry of spacetime. However, the theory of general relativity leads to perspectives which go far beyond the vision of its creator. Many of these insights came to light only after Einstein's death in 1955. These developments were due to a new breed of relativists, like Penrose, Hawking and Geroch, who approached the subject with a higher degree of mathematical sophistication than earlier workers. Some of these insights were made possible because of work by Amal Kumar Raychaudhuri (AKR) who derived an equation which turned out to be a key ingredient in the singularity theorems of general relativity. This article explains AKR's work in elementary terms.

physics.pop-ph↗
arXiv2020

Precursors of the El Ni\~no Phenomenon: A climate network analysis

The identification of precursors of climatic phenomena has enormous practical importance. Recent work constructs a climate network based on surface air temperature data to analyze the El Ni\~no phenomena. We utilize microtransitions which occur before the discontinuous percolation transition in the network as well as other network quantities to identify a set of reliable precursors of El Ni\~no episodes. These precursors identify nine out of twelve El Ni\~no episodes occurring in the period of 1979 to 2018 with a lead time varying from six to ten months. We also find indicators of tipping events in the data.

physics.ao-ph↗
arXiv2019

Likelihood Theory in a Quantum World: tests with Quantum coins and computers

By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix. Given a string of qubits representing a series of trials, one can measure them individually and determine the state with a certain confidence. We show that there is an improved strategy which measures the qubits after entangling them, which leads to a greater confidence. This strategy is demonstrated on the simulation facility of IBM quantum computers.

quant-ph↗
arXiv2018

A Physical Perspective on Classical Cloning

The celebrated quantum no-cloning theorem states that an arbitrary quantum state cannot be cloned perfectly. This raises questions about cloning of classical states, which have also attracted attention. Here, we present a physical approach to the classical cloning process showing how cloning can be realised using Hamiltonians. After writing down a canonical transformation that clones classical states, we show how this can be implemented by Hamiltonian evolution. We then propose an experiment using the tools of nonlinear optics to realise the ideas presented here. Finally, to understand the cloning process in a more realistic context, we introduce statistical mechanical noise to the system and study how this affects the cloning process. While most of our work deals with linear systems and harmonic oscillators, we give some examples of cloning maps on manifolds and show that any system whose configuration space is a group manifold admits a cloning canonical transformation.

quant-ph↗
arXiv2018

Lorentzian geometry of qubit entanglement

We study the relation between qubit entanglement and Lorentzian geometry. In an earlier paper, we had given a recipe for detecting two qubit entanglement. The entanglement criterion is based on Partial Lorentz Transformations (PLT) on individual qubits. The present paper gives the theoretical framework underlying the PLT test. The treatment is based physically, on the causal structure of Minkowski spacetime, and mathematically, on a Lorentzian Singular Value Decomposition. A surprising feature is the natural emergence of "Energy conditions" used in Relativity. All states satisfy a "Dominant Energy Condition" (DEC) and separable states satisfy the Strong Energy Condition(SEC), while entangled states violate the SEC. Apart from testing for entanglement, our approach also enables us to construct a separable form for the density matrix in those cases where it exists. Our approach leads to a simple graphical three dimensional representation of the state space which shows the entangled states within the set of all states.

quant-ph↗
arXiv2017

Detecting qubit entanglement : an alternative to the PPT test

We propose a Partial Lorentz Transformation (PLT) test for detecting entanglement in a two qubit system. One can expand the density matrix of a two qubit system in terms of a tensor product of $(\mathbb{I}, \vec{\sigma})$. The matrix $A$ of the coefficients that appears in such an expansion can be "squared" to form a $4\times4$ matrix $B$. It can be shown that the eigenvalues $\lambda_0, \lambda_1, \lambda_2, \lambda_3$ of $B$ are positive. With the choice of $\lambda_0$ as the dominant eigenvalue, the separable states satisfy $\sqrt{\lambda_1}+\sqrt{\lambda_2}+\sqrt{\lambda_3}\leq \sqrt{\lambda_0}$. Violation of this inequality is a test of entanglement. Thus, this condition is both necessary and sufficient and serves as an alternative to the celebrated Positive Partial Transpose (PPT) test for entanglement detection. We illustrate this test by considering some explicit examples.

quant-ph↗
arXiv2017

Boundaries without boundaries

Starting with a quantum particle on a closed manifold without boundary, we consider the process of generating boundaries by modding out by a group action with fixed points, and we study the emergent quantum dynamics on the quotient manifold. As an illustrative example, we consider a free nonrelativistic quantum particle on the circle and generate the interval via parity reduction. A free particle with Neumann and Dirichlet boundary conditions on the interval is obtained, and, by changing the metric near the boundary, Robin boundary conditions can also be accommodated. We also indicate a possible method of generating non-local boundary conditions. Then, we explore an alternative generation mechanism which makes use of a folding procedure and is applicable to a generic Hamiltonian through the emergence of an ancillary spin degree of freedom.

quant-ph↗
arXiv2017

IITMSAT Communications System : A LeanSat Design Approach

IITMSAT is a student-built nano satellite mission of Indian Institute of Technology Madras, Chennai, India. The objective is to study the precipitation of high energy electrons and protons from Van-Allen radiation belts to lower altitude of 600-900 km due to resonance interaction with low frequency EM waves. The unique communications system design of IITMSAT evolves from the challenging downlink data requirement of 1 MB per day in the UHF band posed by the mission and the satellite's payload, SPEED (Space based Proton and Electron Energy Detector). To ensure continuous downlink data stream in the short Low earth Orbit passes, a robust physical layer protocol was designed to counter time-varying aspects of a Space-Earth telecom link. For the on-board communications system, two types of design alternatives exist for each module. The first option is a custom design wherein a module is developed from scratch using discrete components.The other option is an integrated design wherein an electronics COTS module can be directly plugged into the subsystem. This module is evaluated by carrying out vibration and thermal tests. If an integrated module is low-cost and meets the design requirements, it is preferred over a custom design. In order to carry out performance tests under simulated link conditions, an RF attenuation test setup was designed that can work at extreme temperatures. Burn-In tests for 72 hours at ambient and extreme temperatures were carried out. Integrated tests indicate all IITMSAT design requirements have been met. Hence a robust communications system has been validated. The time taken for development of on-board telecom and GS was less than a year and was achieved at a low cost which agrees to a LeanSat approach.

astro-ph.IM↗
arXiv2017

Gravity and decoherence: the double slit experiment revisited

The double slit experiment is iconic and widely used in classrooms to demonstrate the fundamental mystery of quantum physics. The puzzling feature is that the probability of an electron arriving at the detector when both slits are open is not the sum of the probabilities when the slits are open separately. The superposition principle of quantum mechanics tells us to add amplitudes rather than probabilities and this results in interference. This experiment defies our classical intuition that the probabilities of exclusive events add. In understanding the emergence of the classical world from the quantum one, there have been suggestions by Feynman, Diosi and Penrose that gravity is responsible for suppressing interference. This idea has been pursued in many different forms ever since, predominantly within Newtonian approaches to gravity. In this paper, we propose and theoretically analyse two `gedanken' or thought experiments which lend strong support to the idea that gravity is responsible for decoherence. The first makes the point that thermal radiation can suppress interference. The second shows that in an accelerating frame, Unruh radiation plays the same role. Invoking the Einstein equivalence principle to relate acceleration to gravity, we support the view that gravity is responsible for decoherence.

gr-qc↗
arXiv2016

Boundary and Corner Terms in the Action for General Relativity

We revisit the action principle for general relativity motivated by the path integral approach to quantum gravity. We consider a spacetime region whose boundary has piecewise $C^2$ components, each of which can be spacelike, timelike or null and consider metric variations in which only the pullback of the metric to the boundary is held fixed. Allowing all such metric variations we present a unified treatment of the spacelike, timelike and null boundary components using Cartan's tetrad formalism. Apart from its computational simplicity, this formalism gives us a simple way of identifying corner terms. We also discuss "creases" which occur when the boundary is the event horizon of a black hole. Our treatment is geometric and intrinsic and we present our results both in the computationally simpler tetrad formalism as well as the more familiar metric formalism. We recover known results from a simpler and more general point of view and find some new ones.

gr-qc↗
arXiv2016

Entropy and Geometry of Quantum States

We compare the roles of the Bures-Helstrom (BH) and Bogoliubov-Kubo-Mori (BKM) metrics in the subject of quantum information geometry. We note that there are two limits involved in state discrimination, which we call the "thermodynamic" limit (of $N$, the number of realizations going to infinity) and the infinitesimal limit (of the separation of states tending to zero). We show that these two limits do not commute in the quantum case. Taking the infinitesimal limit first leads to the BH metric and the corresponding Cram\'er-Rao bound, which is widely accepted in this subject. Taking limits in the opposite order leads to the BKM metric, which results in a weaker Cram\'er-Rao bound. This lack of commutation of limits is a purely quantum phenomenon arising from quantum entanglement. We can exploit this phenomenon to gain a quantum advantage in state discrimination and get around the limitation imposed by the Bures-Helstrom Cram\'er-Rao (BHCR) bound. We propose a technologically feasible experiment with cold atoms to demonstrate the quantum advantage in the simple case of two qubits.

quant-ph↗