arXiv subjects

Rahul Roy

Publications and source records attributed to Rahul Roy.

At least 37 records · Page 2Linked to original sources

arXiv2024

Localization renormalization and quantum Hall systems

The obstruction to constructing localized degrees of freedom is a signature of several interesting condensed matter phases. We introduce a localization renormalization procedure that harnesses this property, and apply our method to distinguish between topological and trivial phases in quantum Hall and Chern insulators. By iteratively removing a fraction of maximally-localized orthogonal basis states, we find that the localization length in the residual Hilbert space exhibits a power-law divergence as the fraction of remaining states approaches zero, with an exponent of $ν=0.5$. In sharp contrast, the localization length converges to a system-size-independent constant in the trivial phase. We verify this scaling using a variety of algorithms to truncate the Hilbert space, and show that it corresponds to a statistically self-similar expansion of the real-space projector. This result accords with a renormalization group picture and motivates the use of localization renormalization as a versatile numerical diagnostic for quantum Hall systems.

cond-mat.mes-hall↗

arXiv2024

Compact Wannier Functions in One Dimension

Wannier functions have widespread utility in condensed matter physics and beyond. Topological physics, on the other hand, has largely involved the related notion of compactly-supported Wannier-type functions, which arise naturally in flat bands. In this paper, we establish a connection between these two notions, by finding the necessary and sufficient conditions under which compact Wannier functions exist in one dimension. We present an exhaustive construction of models with compact Wannier functions and show that the Wannier functions are unique, and in general, distinct from the corresponding maximally-localized Wannier functions.

cond-mat.mes-hall↗

arXiv2024

Phase transitions for a unidirectional elephant random walk with a power law memory

For the standard elephant random walk, Laulin (2022) studied the case when the increment of the random walk is not uniformly distributed over the past history instead has a power law distribution. We study such a problem for the unidirectional elephant random walk introduced by Harbola, Kumar and Lindenberg (2014). Depending on the memory parameter $p$ and the power law exponent $β$, we obtain three distinct phases in one such phase the elephant travels only a finite distance almost surely, and the other two phases are distinguished by the speed at which the elephant travels.

math.PR↗

arXiv2024

Light-induced electronic polarization in antiferromagnetic Cr2O3

In a solid, the electronic subsystem can exhibit incipient order with lower point group symmetry than the crystal lattice. External fields that couple to electronic order parameters have rarely been investigated, however, despite their potential importance to inducing exotic effects. Here, we show that when inversion symmetry is broken by the antiferromagnetic (AFM) order in Cr2O3, transmitting a linearly polarized light pulse through the crystal gives rise to an in-plane rotational symmetry breaking (from C3 to C1) via optical rectification. Using interferometric time-resolved second harmonic generation, we show that the ultrafast timescale of the symmetry reduction is indicative of a purely electronic response; the underlying spin and crystal structures remain unaffected. The symmetry-broken state exhibits a dipole moment, and its polar axis can be controlled with the incident light. Our results establish a coherent nonlinear optical protocol by which to break electronic symmetries and produce unconventional electronic effects in solids.

cond-mat.str-el↗

arXiv2023

Topological Triviality of Flat Hamiltonians

Landau levels play a key role in theoretical models of the quantum Hall effect. Each Landau level is degenerate, flat and topologically non-trivial. Motivated by Landau levels, we study tight-binding Hamiltonians whose energy levels are all flat. We demonstrate that in two dimensions, for such Hamiltonians, the flat bands must be topologically trivial. To that end, we show that the projector onto each flat band is necessarily strictly local. Our conclusions do not need the assumption of lattice translational invariance.

cond-mat.mes-hall↗

arXiv2023

Large-scale adaptive multiple testing for sequential data controlling false discovery and nondiscovery rates

In modern scientific experiments, we frequently encounter data that have large dimensions, and in some experiments, such high dimensional data arrive sequentially rather than full data being available all at a time. We develop multiple testing procedures with simultaneous control of false discovery and nondiscovery rates when $m$-variate data vectors $\mathbf{X}_1, \mathbf{X}_2, \dots$ are observed sequentially or in groups and each coordinate of these vectors leads to a hypothesis testing. Existing multiple testing methods for sequential data uses fixed stopping boundaries that do not depend on sample size, and hence, are quite conservative when the number of hypotheses $m$ is large. We propose sequential tests based on adaptive stopping boundaries that ensure shrinkage of the continue sampling region as the sample size increases. Under minimal assumptions on the data sequence, we first develop a test based on an oracle test statistic such that both false discovery rate (FDR) and false nondiscovery rate (FNR) are nearly equal to some prefixed levels with strong control. Under a two-group mixture model assumption, we propose a data-driven stopping and decision rule based on local false discovery rate statistic that mimics the oracle rule and guarantees simultaneous control of FDR and FNR asymptotically as $m$ tends to infinity. Both the oracle and the data-driven stopping times are shown to be finite (i.e., proper) with probability 1 for all finite $m$ and converge to a finite constant as $m$ grows to infinity. Further, we compare the data-driven test with the existing gap rule proposed in He and Bartroff (2021) and show that the ratio of the expected sample sizes of our method and the gap rule tends to zero as $m$ goes to infinity. Extensive analysis of simulated datasets as well as some real datasets illustrate the superiority of the proposed tests over some existing methods.

stat.ME↗

arXiv2023

Evidence for bootstrap percolation dynamics in a photo-induced phase transition

Upon intense femtosecond photo-excitation, a many-body system can undergo a phase transition through a non-equilibrium route, but understanding these pathways remains an outstanding challenge. Here, we use time-resolved second harmonic generation to investigate a photo-induced phase transition in Ca$_3$Ru$_2$O$_7$ and show that mesoscale inhomogeneity profoundly influences the transition dynamics. We observe a marked slowing down of the characteristic time, $τ$, that quantifies the transition between two structures. $τ$ evolves non-monotonically as a function of photo-excitation fluence, rising from below 200~fs to $\sim$1.4~ps, then falling again to below 200~fs. To account for the observed behavior, we perform a bootstrap percolation simulation that demonstrates how local structural interactions govern the transition kinetics. Our work highlights the importance of percolating mesoscale inhomogeneity in the dynamics of photo-induced phase transitions and provides a model that may be useful for understanding such transitions more broadly.

cond-mat.str-el↗

arXiv2023

Scaling limit of a drainage network model on perturbed lattice

Study of random networks generally requires the nodes to be independently and uniformly distributed such as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate a stochastic forest obtained from a drainage network model constructed on a randomly perturbed subset of $\mathbb{Z}^2$, where both horizontal and vertical perturbations are given by exponentially decaying unbounded discrete random variables and vertical perturbations are allowed in the upward direction only. We show that the resultant stochastic network is a single tree a.s. We further establish that as a collection of paths, under diffusive scaling the resultant network converges to the Brownian web.

math.PR↗

arXiv2022

Asymptotic bayes optimality under sparsity for equicorrelated multivariate normal test statistics

Here we address dependence among the test statistics in connection with asymptotically Bayes' optimal tests in presence of sparse alternatives. Extending the setup in Bogdan et.al. (2011) we consider an equicorrelated ( with equal correlation $ρ$ ) multivariate normal assumption on the joint distribution of the test statistics, while conditioned on the mean vector $\boldsymbolμ$. Rest of the set up is identical to Bogdan et.al. (2011) with a slight modification in the asymptotic framework. We exploit an well known result on equicorrelated multivariate normal variables with equal marginal variances to decompose the test statistics into independent random variables. We then identify a set of independent yet unobservable gaussian random variables sufficient for the multiple testing problem and chalk out the necessary and sufficient conditions for single cutoff tests to be ABOS based on those dummy variables following Bogdan et.al. (2011). Further we replaced the dummy variables with deviations of the statistics from their arithmetic means which were easily calculable from the observations due to the decomposition used earlier. Additional assumptions are then derived so that the necessary and sufficient conditions for single cutoff tests to be ABOS using the independent dummy variables plays the same role with the replacement variable as well (with a deviation of order $o(1)$). Next with the same additional assumption, necessary and sufficient conditions for single cutoff tests to control the Bayesian FDRs are derived and as a consequence under various sparsity assumptions we proved that the classical Bonferroni and Benjamini-Hochberg methods of multiple testing are ABOS if the same conditions are satisfied.

stat.ME↗

arXiv2022

A drainage network with dependence and the Brownian web

We study a system of coalescing random walks on the integer lattice $\mathbb{Z}^{d}$ in which the walk is oriented in the $d$-th direction and follows certain specified rules. We first study the geometry of the paths and show that, almost surely, the paths from a graph consisting of just one tree for dimentions $d=2,3$ and infinitely many disjoint trees for dimensions $d\geq 4$. Also, there is no bi-infinite path in the graph almost surely for $d\geq 2$. Subsequently, we prove that for $d=2$ the diffusive scaling of this system converges in distribution to the Brownian web.

math.PR↗

arXiv2022

Fractional Chern insulators with a non-Landau level continuum limit

Recent developments in fractional quantum Hall (FQH) physics highlight the importance of studying FQH phases of particles partially occupying energy bands that are not Landau levels. FQH phases in the regime of strong lattice effects, called fractional Chern insulators, provide one setting for such studies. As the strength of lattice effects vanishes, the bands of generic lattice models asymptotically approach Landau levels. In this article, we construct lattice models for single-particle bands that are distinct from Landau levels even in this continuum limit. We describe how the distinction between such bands and Landau levels is quantified by band geometry over the magnetic Brillouin zone and reflected in the electromagnetic response. We analyze the localization-delocalization transition in one such model and compute a localization length exponent of 2.57(3). Moreover, we study interactions projected to these bands and find signatures of bosonic and fermionic Laughlin states. Most pertinently, our models allow us to isolate conditions for optimal band geometry and gain further insight into the stability of FQH phases on lattices.

cond-mat.str-el↗

arXiv2022

Criticality and covered area fraction in confetti and Voronoi percolation

Using the randomized algorithm method developed by Duminil-Copin, Raoufi and Tassion (2019b), we exhibit sharp phase transition for the confetti percolation model. This provides an alternate proof, than that of Ahlberg, Tassion and Texeira (2018), for the critical parameter for percolation in this model to be $1/2$ when the radius of the underlying shapes for the distinct colours arise from the same distribution. In addition, we study the covered area fraction for this model, which is akin to the covered volume fraction in continuum percolation. Modulo a certain `transitivity condition', this study allows us to calculate exact critical parameter for percolation when the underlying shapes for different colours may be of different sizes. Similar results are also obtained for the Poisson Voronoi percolation model when different coloured points have different growth speeds.

math.PR↗

arXiv2021

Appropriate transient thermal analysis of an absorber plate in flat-plate solar collectors from beginning to end operational conditions

This work establishes a closed-form analysis for two-dimensional transient heat transfer in an absorber plate based on the thermal wave model when the collector starts to work. The method of separation of variables is employed to determine the exact thermal response during the starting of a solar collector. The thermal field is represented by 2-D thermal contours and 3-D surface plots to provide an accurate prediction compared to the 1-D analysis using the time-lag theory. An influence of Fourier number on the heat flow in the absorber plate is studied for different thermal relaxation times. The present analysis highlights that the magnitude of plate temperature depends significantly on the physical geometry. Differences in two models of heat propagation, viz. classical and thermal wave, in the absorber plate have an alteration in predicted collector performances. The present study also develops another design situation for heat transfer in the absorber plate when the collector shutdowns to the ambient state from its steady condition. Laplace Transform Method (LTM) in combination with the product solution method uses to determine the temperature with the initial condition represented as a steady case. Due to the lagging nature of thermal behavior, a significant difference between the classical and thermal wave models for the propagation of heat was observed, and also this study determines the exact time to be taken to reach the dead state for the complete shutdown of the collector.

physics.flu-dyn↗

arXiv2021

Compactly Supported Wannier Functions and Strictly Local Projectors

Wannier functions that are maximally localized help in understanding many properties of crystalline materials. In the absence of topological obstructions, they are at least exponentially localized. In some cases such as flat-band Hamiltonians, it is possible to construct Wannier functions that are even more localized, so that they are compactly supported thus having zero support outside their corresponding locations. Under what general conditions is it possible to construct compactly supported Wannier functions? We answer this question in this paper. Specifically, we show that in 1d non-interacting tight-binding models, strict locality of the projection operator is a necessary and sufficient condition for a subspace to be spanned by a compactly supported orthogonal basis, independent of lattice translation symmetry. For any strictly local projector, we provide a procedure for obtaining such a basis. For higher dimensional systems, we discuss some additional conditions under which an occupied subspace is spanned by a compactly supported orthogonal basis, and show that the corresponding projectors are topologically trivial in many cases. We also show that a projector in arbitrary dimensions is strictly local if and only if for any chosen axis, its image is spanned by hybrid Wannier functions that are compactly supported along that axis.

cond-mat.mes-hall↗

arXiv2021

Understanding controlled EV charging impacts using scenario-based forecasting models

Electrification of transport is a key strategy in reducing carbon emissions. Many countries have adopted policies of complete but gradual transformation to electric vehicles (EVs). However, mass EV adoption also means a spike in load (kW), which in turn can disrupt existing electricity infrastructure. Smart or controlled charging is widely seen as a potential solution to alleviate this stress on existing networks. Learning from the recent EV trials in the UK and elsewhere we take into account two key aspects which are largely ignored in current research: EVs actually charging at any given time and wide range of EV types, especially battery capacity-wise. Taking a minimalistic scenario-based approach, we study forecasting models for mean number of active chargers and mean EV consumption for distinct scenarios. Focusing on residential charging the models we consider range from simple regression models to more advanced machine and deep learning models such as XGBoost and LSTMs. We then use these models to evaluate the impacts of different levels of future EV penetration on a specimen distribution transformer that captures typical real-world scenarios. In doing so, we also initiate the study of different types of controlled charging when fully controlled charging is not possible. This aligns with the outcomes from recent trials which show that a sizeable proportion of EV owners may not prefer fully controlled centralized charging. We study two possible control regimes and show that one is more beneficial from load-on-transformer point of view, while the other may be preferred for other objectives. We show that a minimum of 60% control is required to ensure that transformers are not overloaded during peak hours.

eess.SP↗

arXiv2020

Voter and Majority Dynamics with Biased and Stubborn Agents

We study binary opinion dynamics in a fully connected network of interacting agents. The agents are assumed to interact according to one of the following rules: (1) Voter rule: An updating agent simply copies the opinion of another randomly sampled agent; (2) Majority rule: An updating agent samples multiple agents and adopts the majority opinion in the selected group. We focus on the scenario where the agents are biased towards one of the opinions called the {\em preferred opinion}. Using suitably constructed branching processes, we show that under both rules the mean time to reach consensus is $Θ(\log N)$, where $N$ is the number of agents in the network. Furthermore, under the majority rule model, we show that consensus can be achieved on the preferred opinion with high probability even if it is initially the opinion of the minority. We also study the majority rule model when stubborn agents with fixed opinions are present. We find that the stationary distribution of opinions in the network in the large system limit using mean field techniques.

math.PR↗

arXiv2020

Asymptotically optimal test for dependent multiple testing set up

In this paper we explore the behaviour of dependent test statistics for testing of multiple hypothesis . To keep simplicity, we have considered a mixture normal model with equicorrelated correlation set up. With a simple linear transformation,the test statistics were decomposed into independent components, which, when conditioned appropriately generated independent variables. These were used to construct conditional tests , which were shown to be asymptotically optimal with power as large as that obtained using N.P.Lemma. We have pursued extensive simulation to support the claim.

math.ST↗

arXiv2020

On a model of evolution of subspecies

Ben-Ari and Schinazi (2016) introduced a stochastic model to study `virus-like evolving population with high mutation rate'. This model is a birth and death model with an individual at birth being either a mutant with a random fitness parameter in $[0,1]$ or having one of the existing fitness parameters with uniform probability; whereas a death event removes the entire population of the least fit site. We change this to incorporate the notion of `survival of the fittest', by requiring that a non-mutant individual, at birth, has a fitness according to a preferential attachment mechanism, i.e., it has a fitness $f$ with a probability proportional to the size of the population of fitness $f$. Also death just removes one individual at the least fit site. This preferential attachment rule leads to a power law behaviour in the asymptotics, unlike the exponential behaviour obtained by Ben-Ari and Schinazi (2016).

math.PR↗