arXiv subjects

Rahul Roy

Publications and source records attributed to Rahul Roy.

At least 55 records · Page 3Linked to original sources

arXiv2020

Finite-wavevector Electromagnetic Response in Lattice Quantum Hall Systems

In a quantum Hall system, the finite-wavevector Hall conductivity displays an intriguing dependence on the Hall viscosity, a coefficient that describes the non-dissipative response of the fluid to a velocity gradient. In this paper, we pursue this connection in detail for quantum Hall systems on a lattice, noting that the neat continuum relation breaks down and develops corrections due to the broken rotational symmetry. In the process, we introduce a new, quantum mechanical derivation of the finite-wavevector Hall conductivity for the integer quantum Hall effect, which allows terms to arbitrary order in the wavevector expansion to be calculated straightforwardly. We also develop a universal formalism for studying quantum Hall physics on a lattice, and find that at weak applied magnetic fields, generic lattice wavefunctions connect smoothly to the Landau levels of the continuum. At moderate field strengths, the lattice corrections can be significant and perturb the wavefunctions, energy levels, and transport properties from their continuum values. Our approach allows the finite-field behaviour of a system to be inferred directly from the zero-field band structure.

cond-mat.str-el↗

arXiv2020

Majorana Braiding in Realistic Nanowire Y-Junctions and Tuning Forks

Majorana fermions are predicted to arise at the ends of nanowire devices which combine superconductivity, strong spin-orbit coupling and an external magnetic field. By manipulating networks of these devices with suitable gating, it has been suggested that braiding operations may be performed which act as logic operations, suitable for quantum computation. However, the unavoidable misalignment of the magnetic field in any realistic device geometry has raised questions about the feasibility of such braiding. In this paper, we numerically simulate braiding operations in devices with Y-junction and tuning fork geometries using an experimentally motivated nanowire model. We study how the static and dynamical features vary with geometric parameters and identify parameter choices that optimise the probability of a successful braid. Notably, we find that there is an optimal Y-junction half-angle (about 20 degrees for our parameter values), which balances two competing mechanisms that reduce the energy gap to excitations. In addition, we find that a tuning fork geometry has significant advantages over a Y-junction geometry, as it substantially reduces the effect of dynamical phase oscillations that complicate the braiding process. Our results suggest that performing a successful braid is in principle possible with such devices, and lies within experimental reach.

cond-mat.mes-hall↗

arXiv2019

Streaming Potential in Bio-mimetic Microvessels Mediated by Capillary Glycocalyx

Implantable medical devices and biosensors are pivotal in revolutionizing the field of medical technology by opening new dimensions in the field of disease detection and cure. These devices need to harness a biocompatible and physiologically sustainable safe power source instead of relying on external stimuli, overcoming the constraints on their applicability in-vivo. Here, by appealing to the interplay of electromechanics and hydrodynamics in physiologically relevant microvessels, we bring out the role of charged Endothelial Glycocalyx layer (EGL) towards establishing a streaming potential across physiological fluidic conduits. We account for the complex rheology of blood-mimicking fluid by appealing to Newtonian fluid model representing the blood plasma and a viscoelastic fluid model representing the whole blood. We model the EGL as a poroelastic layer with volumetric charge distribution. Our results reveal that for physiologically relevant microflows, the streaming potential induced is typically of the order of 0.1 V/mm, which may turn out to be substantial towards energizing biosensors and implantable medical devices whose power requirements are typically in the range of micro to milli Watt. We also bring out the specific implications of the relevant physiological parameters towards establishment of the streaming potential, with a vision of augmenting the same within plausible functional limits. We further unveil that the dependence of streaming potential on EGL thickness might be one of the key aspects in unlocking the mystery behind the angiogenesis pattern. Our results may open up novel bio-sensing and actuating possibilities in medical diagnostics as well as may provide a possible alternative regarding the development of physiologically safe and biocompatible power sources within the human body.

physics.flu-dyn↗

arXiv2019

Topology and Broken Symmetry in Floquet Systems

Floquet systems are governed by periodic, time-dependent, Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite temperature. However this unhappy state of affairs can be avoided in many ways. Instead, as has become clear from much recent work, they can exhibit a variety of nontrivial behavior---some of it impossible in undriven systems. In this review we describe the main ideas and themes of this work: novel Floquet drives which exhibit nontrivial topology in single-particle systems, the existence and classification of exotic Floquet drives in interacting systems, and the attendant notion of many-body Floquet phases and arguments for their stability to heating.

cond-mat.str-el↗

arXiv2019

Mixed Uncertainty Sets for Robust Combinatorial Optimization

In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only recently it has been recognized that the process of building useful uncertainty sets is in itself a challenging task that requires mathematical support. In this paper, we propose an approach to go beyond the classic setting, by assuming multiple uncertainty sets to be prepared, each with a weight showing the degree of belief that the set is a "true" model of uncertainty. We consider theoretical aspects of this approach and show that it is as easy to model as the classic setting. In an extensive computational study using a shortest path problem based on real-world data, we auto-tune uncertainty sets to the available data, and show that with regard to out-sample performance, the combination of multiple sets can give better results than each set on its own.

math.OC↗

arXiv2018

On rumour propagation among sceptics

Junior, Machado and Zuluaga (2011) studied a model to understand the spread of a rumour. Their model consists of individuals situated at the integer points of the line $\N$. An individual at the origin $0$ starts a rumour and passes it to all individuals in the interval $[0,R_0]$, where $R_0$ is a non-negative random variable. An individual located at $i$ in this interval receives the rumour and transmits it further among individuals in $[i, i+R_i]$ where $R_0$ and $R_i$ are i.i.d. random variables. The rumour spreads in this manner. An alternate model considers individuals seeking to find the rumour from individuals who have already heard it. For this s/he asks individuals to the left of her/him and lying in an interval of a random size. We study these two models, when the individuals are more sceptical and they transmit or accept the rumour only if they receive it from at least two different sources. In stochastic geometry the equivalent of this rumour process is the study of coverage of the space $\N^d$ by random sets. Our study here extends the study of coverage of space and considers the case when each vertex of $\N^d$ is covered by at least two distinct random sets.

math.ST↗

arXiv2018

A six-factor asset pricing model

The present study introduce the human capital component to the Fama and French five-factor model proposing an equilibrium six-factor asset pricing model. The study employs an aggregate of four sets of portfolios mimicking size and industry with varying dimensions. The first set consists of three set of six portfolios each sorted on size to B/M, size to investment, and size to momentum. The second set comprises of five index portfolios, third, a four-set of twenty-five portfolios each sorted on size to B/M, size to investment, size to profitability, and size to momentum, and the final set constitute thirty industry portfolios. To estimate the parameters of six-factor asset pricing model for the four sets of variant portfolios, we use OLS and Generalized method of moments based robust instrumental variables technique (IVGMM). The results obtained from the relevance, endogeneity, overidentifying restrictions, and the Hausman's specification, tests indicate that the parameter estimates of the six-factor model using IVGMM are robust and performs better than the OLS approach. The human capital component shares equally the predictive power alongside the factors in the framework in explaining the variations in return on portfolios. Furthermore, we assess the t-ratio of the human capital component of each IVGMM estimates of the six-factor asset pricing model for the four sets of variant portfolios. The t-ratio of the human capital of the eighty-three IVGMM estimates are more than 3.00 with reference to the standard proposed by Harvey et al. (2016). This indicates the empirical success of the six-factor asset-pricing model in explaining the variation in asset returns.

q-fin.ST↗

arXiv2018

Chiral Flow in One-dimensional Floquet Topological Insulators

We propose a bulk topological invariant for one-dimensional Floquet systems with chiral symmetry which quantifies the particle transport on each sublattice during the evolution. This chiral flow is physically motivated, locally computable, and improves on existing topological invariants by being applicable to systems with disorder. We derive a bulk-edge correspondence which relates the chiral flow to the number of protected dynamical edge modes present on a boundary at the end of the evolution. In the process, we introduce two real-space edge invariants which classify the dynamical topological boundary behavior at various points during the evolution. Our results provide the first explicit bulk-boundary correspondence for Floquet systems in this symmetry class.

cond-mat.str-el↗

arXiv2018

Interacting Floquet topological phases in three dimensions

In two dimensions, interacting Floquet topological phases may arise even in the absence of any protecting symmetry, exhibiting chiral edge transport that is robust to local perturbations. We explore a similar class of Floquet topological phases in three dimensions, with translational invariance but no other symmetry, which also exhibit anomalous transport at a boundary surface. By studying the space of local 2D unitary operators, we show that the boundary behavior of such phases falls into equivalence classes, each characterized by an infinite set of reciprocal lattice vectors. In turn, this provides a classification of the 3D bulk, which we argue is complete. We demonstrate that such phases may be generated by exactly-solvable `exchange drives' in the bulk. In the process, we show that the edge behavior of a general exchange drive in two or three dimensions can be deduced from the geometric properties of its action in the bulk, a form of bulk-boundary correspondence.

cond-mat.str-el↗

arXiv2017

Floquet Topological Order in Interacting Systems of Bosons and Fermions

Periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We find that these drives have surprising many-body analogs, corresponding to class A, which exhibit anomalous charge and information transport at the boundary. Drives of this form are applicable to generic systems of bosons, fermions, and spins, and may be characterized by the anomalous unitary operator that acts at the edge of an open system. We find that these operators are robust to all local perturbations and may be classified by a pair of coprime integers. This defines a notion of dynamical topological order that may be applied to general time-dependent systems, including many-body localized phases or time crystals.

cond-mat.str-el↗

arXiv2016

Floquet topological phases with symmetry in all dimensions

Dynamical systems may host a number of remarkable symmetry-protected phases that are qualitatively different from their static analogs. In this work, we consider the phase space of symmetry-respecting unitary evolutions in detail and identify several distinct classes of evolution that host novel dynamical order. Using ideas from group cohomology, we construct a set of interacting Floquet drives that generate dynamical symmetry-protected topological order for each nontrivial cohomology class in every dimension, illustrating our construction with explicit two-dimensional examples. We also identify a set of symmetry-protected Floquet drives that lie outside of the group cohomology construction, and a further class of symmetry-respecting topological drives which host chiral edge modes. We use these special drives to define a notion of phase (stable to a class of local perturbations in the bulk) and the concepts of relative and absolute topological order, which can be applied to many different classes of unitary evolutions. These include fully many-body localized unitary evolutions and time crystals.

cond-mat.str-el↗

arXiv2016

Isotropic-nematic behaviour of hard rigid rods: a percolation theoretic approach

Needles at different orientations are placed in an i.i.d. manner at points of a Poisson point process on $\mathbb R^2$ of density $λ$. Needles at the same direction have the same length, while needles at different directions maybe of different lengths. We study the geometry of a finite cluster when needles have only two possible orientations and when needles have only three possible orientations. In both these cases the asymptotic shape of the finite cluster as $λ\to \infty$ is shown to consists of needles only in two directions. In the two orientations case the shape does not depend on the orientation but just on the i.i.d. structure of the orientations, while in the three orientations case the shape depend on all the parameters, i.e. the i.i.d. structure of the orientations, the lengths and the orientations of the needles.

math-ph↗

arXiv2016

Abelian Floquet symmetry-protected topological phases in one dimension

Time-dependent systems have recently been shown to support novel types of topological order that cannot be realised in static systems. In this paper, we consider a range of time-dependent, interacting systems in one dimension that are protected by an Abelian symmetry group. We classify the distinct topological phases that can exist in this setting and find that they may be described by a bulk invariant associated with the unitary evolution of the closed system. In the open system, nontrivial phases correspond to the appearance of edge modes in the many-body quasienergy spectrum, which relate to the bulk invariant through a form of bulk-edge correspondence. We introduce simple models which realise nontrivial dynamical phases in a number of cases, and outline a loop construction that can be used to generate such phases more generally.

cond-mat.str-el↗

arXiv2016

Periodic Table for Floquet Topological Insulators

Dynamical phases with novel topological properties are known to arise in driven systems of free fermions. In this paper, we obtain a `periodic table' to describe the phases of such time-dependent systems, generalizing the periodic table for static topological insulators. Using K-theory, we systematically classify Floquet topological insulators from the ten Altland-Zirnbauer symmetry classes across all dimensions. We find that the static classification scheme described by a group $G$ becomes $G\times G$ in the time-dependent case, and interpret the two factors as arising from the bipartite decomposition of the unitary time-evolution operator. Topologically protected edge modes may arise at the boundary between two Floquet systems, and we provide a mapping between the number of such edge modes and the topological invariant of the bulk.

cond-mat.str-el↗

arXiv2016

Hack's law in a drainage network model: A Brownian web approach

Hack [Studies of longitudinal stream profiles in Virginia and Maryland (1957). Report], while studying the drainage system in the Shenandoah valley and the adjacent mountains of Virginia, observed a power law relation $l\sim a^{0.6}$ between the length $l$ of a stream from its source to a divide and the area $a$ of the basin that collects the precipitation contributing to the stream as tributaries. We study the tributary structure of Howard's drainage network model of headward growth and branching studied by Gangopadhyay, Roy and Sarkar [Ann. Appl. Probab. 14 (2004) 1242-1266]. We show that the exponent of Hack's law is $2/3$ for Howard's model. Our study is based on a scaling of the process whereby the limit of the watershed area of a stream is area of a Brownian excursion process. To obtain this, we define a dual of the model and show that under diffusive scaling, both the original network and its dual converge jointly to the standard Brownian web and its dual.

math.PR↗

arXiv2016

Firm Growth and Innovation in the ERP Industry: A Systems Thinking Approach

Achievement and sustenance of growth are essential themes in organizational literature. In our paper, we develop models using systems thinking approach to understand how firms achieve and sustain growth in a technology-intensive product domain. We augment these to explain the possible impact of a disruptive technological innovation. We use enterprise software industry as the context where SAP has been acknowledged as the market leader. We find that product differentiation and learning effects helped SAP establish itself, and this growth was further sustained through networks and complementors. Introducing cloud computing as the disruptive innovation, we explain its impact on a firm. Analysis reveals that for the next wave of growth to occur, and to tap into newer markets, it would be imperative for SAP to create attractive cloud based offerings. We also discuss how the model can be enhanced by considering competitor dynamics.

cs.CY↗

arXiv2016

On the Universality of the Non-singularity of General Ginibre and Wigner Random Matrices

We prove the universal asymptotically almost sure non-singularity of general Ginibre and Wigner ensembles of random matrices when the distribution of the entries are independent but not necessarily identically distributed and may depend on the size of the matrix. These models include adjacency matrices of random graphs and also sparse, generalized, universal and banded random matrices. We find universal rates of convergence and precise estimates for the probability of singularity which depend only on the size of the biggest jump of the distribution functions governing the entries of the matrix and not on the range of values of the random entries. Moreover, no moment assumptions are made about the distributions governing the entries. Our proofs are based on a concentration function inequality due to Kolmogorov, Rogozin and Kesten, which allows us to improve universal rates of convergence for the Wigner case when the distribution of the entries do not depend on the size of the matrix.

math.PR↗

arXiv2015

Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model

We study how the stability of the fractional quantum Hall effect (FQHE) is influenced by the geometry of band structure in lattice Chern insulators. We consider the Hofstadter model, which converges to continuum Landau levels in the limit of small flux per plaquette. This gives us a degree of analytic control not possible in generic lattice models, and we are able to obtain analytic expressions for the relevant geometric criteria. These may be differentiated by whether they converge exponentially or polynomially to the continuum limit. We demonstrate that the latter criteria have a dominant effect on the physics of interacting particles in Hofstadter bands in this low flux density regime. In particular, we show that the many-body gap depends monotonically on a band-geometric criterion related to the trace of the Fubini-Study metric.

cond-mat.str-el↗