arXiv subjects

Supurna Sinha

Publications and source records attributed to Supurna Sinha.

At least 37 records · Page 2Linked to original sources

arXiv2018

Quantum Brownian motion in a magnetic field: Transition from monotonic to oscillatory behaviour

We investigate the Brownian motion of a charged particle in a magnetic field. We study this in the high temperature classical and low temperature quantum domains. In both domains, we observe a transition of the mean square displacement from a monotonic behaviour to a damped oscillatory behaviour as one increases the strength of the magnetic field. When the strength of the magnetic field is negligible, the mean square displacement grows linearly with time in the classical domain and logarithmically with time in the quantum domain. We notice that these features of the mean square displacement are robust and remain essentially the same for an Ohmic dissipation model and a single relaxation time model for the memory kernel. The predictions stemming from our analysis can be tested against experiments in trapped cold ions.

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 $(\mathbb{I}, \vecσ)$. 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 $λ_0, λ_1, λ_2, λ_3$ of $B$ are positive. With the choice of $λ_0$ as the dominant eigenvalue, the separable states satisfy $\sqrt{λ_1}+\sqrt{λ_2}+\sqrt{λ_3}\leq \sqrt{λ_0}$. 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

A quantum diffusion law

We analyse diffusion at low temperature by bringing the fluctuation-dissipation theorem (FDT) to bear on a physically natural, viscous response-function R(t). The resulting diffusion-law exhibits several distinct regimes of time and temperature, each with its own characteristic rate of spreading. As with earlier analyses, we find logarithmic spreading in the quantum regime, indicating that this behavior is robust. A consistent R(t) must satisfy the key physical requirements of Wightman positivity and passivity, and we prove that ours does so. We also prove in general that these two conditions are equivalent when the FDT holds. Given current technology, our diffusion law can be tested in a laboratory with ultra cold atoms.

cond-mat.stat-mech↗

arXiv2017

Ring closure in actin polymers

We present an analysis for the ring closure probability of semiflexible polymers within the pure bend Worm Like Chain (WLC) model. The ring closure probability predicted from our analysis can be tested against fluorescent actin cyclization experiments.We also discuss the effect of ring closure on bend angle fluctuations in actin polymers.

cond-mat.soft↗

arXiv2016

Coarse Quantum Measurement: An analysis of the Stern Gerlach experiment

We study the Quantum Measurement Process in a Stern-Gerlach setup with the spin of a silver atom as the quantum system and the position as the apparatus. The system and the apparatus are treated quantum-mechanically using unitary evolution. The new ingredient in our analysis is the idea that the probes determining the position of the silver atom are limited in resolution. We show using a Wigner matrix that due to the coarseness of the detection process, the pure density matrix appears to evolve to an impure one. We quantify the information gained about the spin in a coarse position measurement.

quant-ph↗

arXiv2014

Non-classical paths in interference experiments

In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well known text books in quantum mechanics implicitly and/or explicitly use this assumption which is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from non-classical paths in quantum interference experiments which provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these non-classical paths is hard. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.

quant-ph↗

arXiv2014

Quantum Limit on Stability of Clocks in a Gravitational Field

Good clocks are of importance both to fundamental physics and for applications in astronomy, metrology and global positioning systems. In a recent technological breakthrough, researchers at NIST have been able to achieve a stability of 1 part in $10^{18}$ using an Ytterbium clock. This naturally raises the question of whether there are fundamental limits to the stability of clocks. In this paper we point out that gravity and quantum mechanics set a fundamental limit on the stability of clocks. This limit comes from a combination of the uncertainty relation, the gravitational redshift and the relativistic time dilation effect. For example, a single ion hydrogen maser clock in a terrestrial gravitational field cannot achieve a stability better than one part in $10^{22}$. This observation has implications for laboratory experiments involving both gravity and quantum theory.

gr-qc↗

arXiv2013

Statistical mechanics of bent twisted ribbons

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.

cond-mat.stat-mech↗

arXiv2013

A "Gaussian" for diffusion on the sphere

We present an analytical closed form expression, which gives a good approximate propagator for diffusion on the sphere. Our formula is the spherical counterpart of the Gaussian propagator for diffusion on the plane. While the analytical formula is derived using saddle point methods for short times, it works well even for intermediate times. Our formula goes beyond conventional "short time heat kernel expansions" in that it is nonperturbative in the spatial coordinate, a feature that is ideal for studying large deviations. Our work suggests a new and efficient algorithm for numerical integration of the diffusion equation on a sphere. We perform Monte Carlo simulations to compare the numerical efficiency of the new algorithm with the older Gaussian one.

cond-mat.stat-mech↗

arXiv2013

Bending elasticity of macromolecules: analytic predictions from the wormlike chain model

We present a study of the bend angle distribution of semiflexible polymers of short and intermediate lengths within the wormlike chain model. This enables us to calculate the elastic response of a stiff molecule to a bending moment. Our results go beyond the Hookean regime and explore the nonlinear elastic behaviour of a single molecule. We present analytical formulae for the bend angle distribution and for the moment-angle relation. Our analytical study is compared against numerical Monte Carlo simulations. The functional forms derived here can be applied to fluorescence microscopic studies on actin and DNA. Our results are relevant to recent studies in "kinks" and cyclization in short and intermediate length DNA strands.

cond-mat.soft↗

arXiv2012

Classical light analogue of the nonlocal Aharonov-Bohm effect

We demonstrate the existence of a non-local geometric phase in the intensity-intensity correlations of classical incoherent light, that is not seen in the lower order correlations. This two-photon Pancharatnam phase was observed and modulated in a Mach-Zehnder interferometer. Using acousto-optic interaction, independent phase noise was introduced to light in the two arms of the interferometer to create two independent incoherent classical sources from laser light. The experiment is the classical optical analogue of the multi-particle Aharonov-Bohm effect. As the trajectory of light over the Poincare sphere introduces a phase shift observable only in the intensity-intensity correlation, it provides a means of deflecting the two-photon wavefront, while having no effect on single photons.

quant-ph↗

arXiv2012

Non-local geometric phase in two-photon interferometry

We report the experimental observation of the nonlocal geometric phase in Hanbury Brown-Twiss polarized intensity interferometry. The experiment involves two independent, polar- ized, incoherent sources, illuminating two polarized detectors. Varying the relative polarization angle between the detectors introduces a geometric phase equal to half the solid angle on the Poincaré sphere traced out by a pair of single photons. Local measurements at either detector do not reveal the effect of the geometric phase, which appears only in the coincidence counts between the two detectors, showing a genuinely nonlocal effect. We show experimentally that coincidence rates of photon arrival times at separated detectors can be controlled by the two photon geometric phase. This effect can be used for manipulating and controlling photonic entanglement.

quant-ph↗

arXiv2011

Atom Interferometers and the Gravitational Redshift

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".

gr-qc↗

arXiv2010

DNA Twist Elasticity: Mechanics and Thermal Fluctuations

The elastic properties of semiflexible polymers are of great importance in biology. There are experiments on biopolymers like double stranded DNA, which twist and stretch single molecules to probe their elastic properties. It is known that thermal fluctuations play an important role in determining molecular elastic properties, but a full theoretical treatment of the problem of twist elasticity of fluctuating ribbons using the simplest worm like chain model (WLC) remains elusive. In this paper, we approach this problem by taking first a mechanical approach and then incorporating thermal effects in a quadratic approximation applying the Gelfand-Yaglom (GY) method for computing fluctuation determinants. Our study interpolates between mechanics and statistical mechanics in a controlled way and shows how profoundly thermal fluctuations affect the elasticity of semiflexible polymers. The new results contained here are: 1) a detailed study of the minimum energy configurations with explicit expressions for their energy and writhe and plots of the extension versus Link for these configurations. 2) a study of fluctuations around the local minima of energy and approximate analytical formulae for the free energy of stretched twisted polymers derived by the Gelfand Yaglom method. We use insights derived from our mechanical approach to suggest calculational schemes that lead to an improved treatment of thermal fluctuations. From the derived formulae, predictions of the WLC model for molecular elasticity can be worked out for comparison against numerical simulations and experiments.

cond-mat.soft↗

arXiv2010

Tops and Writhing DNA

The torsional elasticity of semiflexible polymers like DNA is of biological significance. A mathematical treatment of this problem was begun by Fuller using the relation between link, twist and writhe, but progress has been hindered by the non-local nature of the writhe. This stands in the way of an analytic statistical mechanical treatment, which takes into account thermal fluctuations, in computing the partition function. In this paper we use the well known analogy with the dynamics of tops to show that when subjected to stretch and twist, the polymer configurations which dominate the partition function admit a local writhe formulation in the spirit of Fuller and thus provide an underlying justification for the use of Fuller's "local writhe expression" which leads to considerable mathematical simplification in solving theoretical models of DNA and elucidating their predictions. Our result facilitates comparison of the theoretical models with single molecule micromanipulation experiments and computer simulations.

cond-mat.soft↗

arXiv2010

The Nonlocal Pancharatnam Phase in Two-Photon Interferometry

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.

quant-ph↗