We present an analytical study of bent twisted ribbons. We first describe the elastic response of... more We present an analytical study of bent twisted ribbons. We first describe the elastic response of a ribbon within a purely mechanical framework. We then study the role of thermal fluctuations in modifying its elastic response. We predict the moment angle relation of bent and twisted ribbons. Such a study is expected to shed light on the role of twist in the "J factor" for DNA looping and on bending elasticity of twisted graphene ribbons.
From the principle of equivalence, Einstein predicted that clocks slow down in a gravitational fi... more From the principle of equivalence, Einstein predicted that clocks slow down in a gravitational field. Since the general theory of relativity is based on the principle of equivalence, it is essential to test this prediction accurately. Muller, Peters and Chu claim that a reinterpretation of decade old experiments with atom interferometers leads to a sensitive test of this gravitational redshift effect at the Compton frequency. Wolf et al dispute this claim and adduce arguments against it. In this article, we distill these arguments to a single fundamental objection: an atom is NOT a clock ticking at the Compton frequency. We conclude that atom interferometry experiments conducted to date do not yield such sensitive tests of the gravitational redshift. Finally, we suggest a new interferometric experiment to measure the gravitational redshift, which realises a quantum version of the classical clock "paradox".
We present an exact solution of the Worm-Like Chain (WLC) model for semi-flexible polymers valid ... more We present an exact solution of the Worm-Like Chain (WLC) model for semi-flexible polymers valid over the entire range of polymer lengths. Our results are in excellent agreement with recent computer simulations and reproduces important qualitatively interesting features observed in simulations of polymers of intermediate lengths. We also make a number of predictions that can be tested in a variety of concrete experimental realizations. The expected level of finite size fluctuations in force-extension curves is also estimated. This study is relevant to mechanical properties of biological molecules.
We present an interesting connection between Brownian motion and magnetism. We use this to determ... more We present an interesting connection between Brownian motion and magnetism. We use this to determine the distribution of areas enclosed by the path of a particle diffusing on a sphere. In addition, we find a bound on the free energy of an arbitrary system of spinless bosons in a magnetic field. The work presented here is expected to shed light on polymer entanglement, depolarized light scattering, and magnetic behavior of spinless bosons.
In a recent study of Thomas precession of electron spin in the context of the Dirac equation, Sha... more In a recent study of Thomas precession of electron spin in the context of the Dirac equation, Shankar and Mathur identify the non-Abelian Berry potential (arising from Kramers degeneracy) with the meron. We point out that there is a global mathematical subtlety which prevents such an identification. We go on to clarify the physical context in which merons do arise as Berry potentials.
This is a very interesting and well-written expository paper on the Hamiltonian formulation for c... more This is a very interesting and well-written expository paper on the Hamiltonian formulation for constrained systems and its symmetry from the geometrical point of view. Coordinate-free and coordinate-based methods are both used throughout the paper, making both geometrical and physical concepts transparent. The paper is divided into two parts. Part I is devoted to dynamics while part II deals with symmetries, and contains three appendices where some calculations and proofs are exhibited. Both the mathematically as well as the physically inclined reader will certainly find enough motivation to read this paper.
We describe a non-Abelian Berry phase in polarisation optics, suggested by an analogy due to Nity... more We describe a non-Abelian Berry phase in polarisation optics, suggested by an analogy due to Nityananda between boosts in special relativity and the effect of elliptic dichroism on polarised light. The analogy permits a simple optical realization of the non-Abelian gauge field describing Thomas rotation. We also show how Thomas rotation can be understood geometrically on the Poincaré sphere in terms of the Pancharatnam phase.
We study the behaviour of the geometric phase under isometries of the ray space. This leads to a ... more We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner's proof is best viewed as an use of the Pancharatnam connection to "lift" a ray space isometry to the Hilbert space.
A manifestly covariant Lagrangian is presented which leads to the reformulation of canonical gene... more A manifestly covariant Lagrangian is presented which leads to the reformulation of canonical general relativity using new variables recently discovered by Ashtekar.
We respond to a recent paper by Rindler on the "Anti-Machian" nature of the Lense-Thirring effect... more We respond to a recent paper by Rindler on the "Anti-Machian" nature of the Lense-Thirring effect. We remark that his conclusion depends crucially on the particular formulation of Mach's principle used.
We present a novel setup that allows the observation of the geometric phase that accompanies pola... more We present a novel setup that allows the observation of the geometric phase that accompanies polarization changes in monochromatic light beams for which the initial and final states are different (so-called non-cyclic changes). This Pancharatnam-Berry phase can depend in a linear or in a nonlinear fashion on the orientation of the optical elements, and sometimes the dependence is singular. Experimental results that confirm these three types of behavior are presented. The observed singular behavior may be applied in the design of optical switches.
We present an analytical study of the role of thermal fluctuations in shaping molecular elastic p... more We present an analytical study of the role of thermal fluctuations in shaping molecular elastic properties of semiflexible polymers. Our study interpolates between mechanics and statistical mechanics in a controlled way and shows how thermal fluctuations modify the elastic properties of biopolymers. We present a study of the minimum-energy configurations with explicit expressions for their energy and writhe and plots of the extension versus link for these configurations and a study of fluctuations around the local minima of energy and approximate analytical formulas for the free energy of stretched twisted polymers. The central result of our study is a closed-form expression for the leading thermal fluctuation correction to the free energy around the nonperturbative writhing family solution for the configuration of a biopolymer. From the derived formulas, the predictions of the wormlike chain model for molecular elasticity can be worked out for a comparison against numerical simulations and experiments.
We make two observations about Holst's derivation of Barbero's ... more We make two observations about Holst's derivation of Barbero's Hamiltonian formulation from a covariant Lagrangian. While Holst's derivation does appear to be correct, there are two points in the derivation which may be worth clarifying. These concern the choice of time gauge ...
We propose a polarised intensity interferometry experiment, which measures the nonlocal Pancharat... more We propose a polarised intensity interferometry experiment, which measures the nonlocal Pancharatnam phase acquired by a pair of Hanbury Brown-Twiss photons. The setup involves two polarised thermal sources illuminating two polarised detectors. Varying the relative polarisation angle of the detectors introduces a two photon geometric phase. Local measurements at either detector do not reveal the effects of the phase, which is an optical analog of the multiparticle Aharonov-Bohm effect. The geometric phase sheds light on the three slit experiment and suggests ways of tuning entanglement.
We present an analytical study of ribbons subjected to an external torque. We first describe the ... more We present an analytical study of ribbons subjected to an external torque. We first describe the elastic response of a ribbon within a purely mechanical framework. We then study the role of thermal fluctuations in modifying its elastic response. We predict the moment-angle relation of bent and twisted ribbons. Such a study is expected to shed light on the role of twist in DNA looping and on bending elasticity of twisted graphene ribbons. Our quantitative predictions can be tested against future single molecule experiments.
Journal of Physics A: Mathematical and General, 2000
Fermi Transport is useful for describing the behaviour of spins or gyroscopes following nongeodes... more Fermi Transport is useful for describing the behaviour of spins or gyroscopes following nongeodesic, timelike world lines. However, Fermi Transport breaks down for null world lines. We introduce a transport law for polarisation vectors along non-geodesic null curves. We show how this law emerges naturally from the geometry of null directions by comparing polarisation vectors associated with two distinct null directions. We then give a spinorial treatment of this topic and make contact with the geometric phase of quantum mechanics. There are two significant differences between the null and timelike cases. In the null case (i) The transport law does not approach a unique smooth limit as the null curve approaches a null geodesic. (ii) The transport law for vectors is integrable, i.e the result depends only on the local properties of the curve and not on the entire path taken. However, the transport of spinors is not integrable: there is a global sign of topological origin.
We present an analytical study of bent twisted ribbons. We first describe the elastic response of... more We present an analytical study of bent twisted ribbons. We first describe the elastic response of a ribbon within a purely mechanical framework. We then study the role of thermal fluctuations in modifying its elastic response. We predict the moment angle relation of bent and twisted ribbons. Such a study is expected to shed light on the role of twist in the "J factor" for DNA looping and on bending elasticity of twisted graphene ribbons.
From the principle of equivalence, Einstein predicted that clocks slow down in a gravitational fi... more From the principle of equivalence, Einstein predicted that clocks slow down in a gravitational field. Since the general theory of relativity is based on the principle of equivalence, it is essential to test this prediction accurately. Muller, Peters and Chu claim that a reinterpretation of decade old experiments with atom interferometers leads to a sensitive test of this gravitational redshift effect at the Compton frequency. Wolf et al dispute this claim and adduce arguments against it. In this article, we distill these arguments to a single fundamental objection: an atom is NOT a clock ticking at the Compton frequency. We conclude that atom interferometry experiments conducted to date do not yield such sensitive tests of the gravitational redshift. Finally, we suggest a new interferometric experiment to measure the gravitational redshift, which realises a quantum version of the classical clock "paradox".
We present an exact solution of the Worm-Like Chain (WLC) model for semi-flexible polymers valid ... more We present an exact solution of the Worm-Like Chain (WLC) model for semi-flexible polymers valid over the entire range of polymer lengths. Our results are in excellent agreement with recent computer simulations and reproduces important qualitatively interesting features observed in simulations of polymers of intermediate lengths. We also make a number of predictions that can be tested in a variety of concrete experimental realizations. The expected level of finite size fluctuations in force-extension curves is also estimated. This study is relevant to mechanical properties of biological molecules.
We present an interesting connection between Brownian motion and magnetism. We use this to determ... more We present an interesting connection between Brownian motion and magnetism. We use this to determine the distribution of areas enclosed by the path of a particle diffusing on a sphere. In addition, we find a bound on the free energy of an arbitrary system of spinless bosons in a magnetic field. The work presented here is expected to shed light on polymer entanglement, depolarized light scattering, and magnetic behavior of spinless bosons.
In a recent study of Thomas precession of electron spin in the context of the Dirac equation, Sha... more In a recent study of Thomas precession of electron spin in the context of the Dirac equation, Shankar and Mathur identify the non-Abelian Berry potential (arising from Kramers degeneracy) with the meron. We point out that there is a global mathematical subtlety which prevents such an identification. We go on to clarify the physical context in which merons do arise as Berry potentials.
This is a very interesting and well-written expository paper on the Hamiltonian formulation for c... more This is a very interesting and well-written expository paper on the Hamiltonian formulation for constrained systems and its symmetry from the geometrical point of view. Coordinate-free and coordinate-based methods are both used throughout the paper, making both geometrical and physical concepts transparent. The paper is divided into two parts. Part I is devoted to dynamics while part II deals with symmetries, and contains three appendices where some calculations and proofs are exhibited. Both the mathematically as well as the physically inclined reader will certainly find enough motivation to read this paper.
We describe a non-Abelian Berry phase in polarisation optics, suggested by an analogy due to Nity... more We describe a non-Abelian Berry phase in polarisation optics, suggested by an analogy due to Nityananda between boosts in special relativity and the effect of elliptic dichroism on polarised light. The analogy permits a simple optical realization of the non-Abelian gauge field describing Thomas rotation. We also show how Thomas rotation can be understood geometrically on the Poincaré sphere in terms of the Pancharatnam phase.
We study the behaviour of the geometric phase under isometries of the ray space. This leads to a ... more We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner's proof is best viewed as an use of the Pancharatnam connection to "lift" a ray space isometry to the Hilbert space.
A manifestly covariant Lagrangian is presented which leads to the reformulation of canonical gene... more A manifestly covariant Lagrangian is presented which leads to the reformulation of canonical general relativity using new variables recently discovered by Ashtekar.
We respond to a recent paper by Rindler on the "Anti-Machian" nature of the Lense-Thirring effect... more We respond to a recent paper by Rindler on the "Anti-Machian" nature of the Lense-Thirring effect. We remark that his conclusion depends crucially on the particular formulation of Mach's principle used.
We present a novel setup that allows the observation of the geometric phase that accompanies pola... more We present a novel setup that allows the observation of the geometric phase that accompanies polarization changes in monochromatic light beams for which the initial and final states are different (so-called non-cyclic changes). This Pancharatnam-Berry phase can depend in a linear or in a nonlinear fashion on the orientation of the optical elements, and sometimes the dependence is singular. Experimental results that confirm these three types of behavior are presented. The observed singular behavior may be applied in the design of optical switches.
We present an analytical study of the role of thermal fluctuations in shaping molecular elastic p... more We present an analytical study of the role of thermal fluctuations in shaping molecular elastic properties of semiflexible polymers. Our study interpolates between mechanics and statistical mechanics in a controlled way and shows how thermal fluctuations modify the elastic properties of biopolymers. We present a study of the minimum-energy configurations with explicit expressions for their energy and writhe and plots of the extension versus link for these configurations and a study of fluctuations around the local minima of energy and approximate analytical formulas for the free energy of stretched twisted polymers. The central result of our study is a closed-form expression for the leading thermal fluctuation correction to the free energy around the nonperturbative writhing family solution for the configuration of a biopolymer. From the derived formulas, the predictions of the wormlike chain model for molecular elasticity can be worked out for a comparison against numerical simulations and experiments.
We make two observations about Holst's derivation of Barbero's ... more We make two observations about Holst's derivation of Barbero's Hamiltonian formulation from a covariant Lagrangian. While Holst's derivation does appear to be correct, there are two points in the derivation which may be worth clarifying. These concern the choice of time gauge ...
We propose a polarised intensity interferometry experiment, which measures the nonlocal Pancharat... more We propose a polarised intensity interferometry experiment, which measures the nonlocal Pancharatnam phase acquired by a pair of Hanbury Brown-Twiss photons. The setup involves two polarised thermal sources illuminating two polarised detectors. Varying the relative polarisation angle of the detectors introduces a two photon geometric phase. Local measurements at either detector do not reveal the effects of the phase, which is an optical analog of the multiparticle Aharonov-Bohm effect. The geometric phase sheds light on the three slit experiment and suggests ways of tuning entanglement.
We present an analytical study of ribbons subjected to an external torque. We first describe the ... more We present an analytical study of ribbons subjected to an external torque. We first describe the elastic response of a ribbon within a purely mechanical framework. We then study the role of thermal fluctuations in modifying its elastic response. We predict the moment-angle relation of bent and twisted ribbons. Such a study is expected to shed light on the role of twist in DNA looping and on bending elasticity of twisted graphene ribbons. Our quantitative predictions can be tested against future single molecule experiments.
Journal of Physics A: Mathematical and General, 2000
Fermi Transport is useful for describing the behaviour of spins or gyroscopes following nongeodes... more Fermi Transport is useful for describing the behaviour of spins or gyroscopes following nongeodesic, timelike world lines. However, Fermi Transport breaks down for null world lines. We introduce a transport law for polarisation vectors along non-geodesic null curves. We show how this law emerges naturally from the geometry of null directions by comparing polarisation vectors associated with two distinct null directions. We then give a spinorial treatment of this topic and make contact with the geometric phase of quantum mechanics. There are two significant differences between the null and timelike cases. In the null case (i) The transport law does not approach a unique smooth limit as the null curve approaches a null geodesic. (ii) The transport law for vectors is integrable, i.e the result depends only on the local properties of the curve and not on the entire path taken. However, the transport of spinors is not integrable: there is a global sign of topological origin.
Uploads
Papers by Joseph Samuel