arXiv subjects

Sayan Roy

Publications and source records attributed to Sayan Roy.

9 recordsLinked to original sources

arXiv2026

Phase transitions in first-detection statistics of monitored long-range quantum walks

In a quantum walk, the first-detection return probability (FDRP) characterizes salient features, determining whether the quantum walk is transient or recurrent. We study the FDRP of quantum walks on a chain where the initial site is stroboscopically monitored by a detector and the walker performs long-range hopping between sites. We assume that the hopping strength decays with the distance $d$ as $d^{-\alpha}$ and $\alpha\geq 0$ and show that the power-law exponent $\alpha$ critically determines the behavior of the FDRP. The value $\alpha=1$ separates recurrent ($\alpha<1$) from transient ($\alpha>1$) quantum walks through a continuous phase transition in the total detection probability. For $\alpha<1$, strong long-range hopping induces localization, resulting in unit total detection probability. Instead, for $\alpha>1$ the long-range walk is transient and the return probability decays algebraically as a function of time as $t^{-\beta}$. The associated decay exponent $\beta$ features nonanalytic points as a function of $\alpha$. Such singularities are not exclusively determined by the low-energy spectrum, but are caused by the interference between infrared and ultraviolet energy modes induced by projective measurements, signalling the emergence of critical behavior intrinsic to the non-unitary dynamics. These dynamics are solely controlled by tuning the long-range exponent $\alpha$ and can thus be experimentally probed in atomic and molecular systems.

quant-ph↗

arXiv2026

A spectral viewpoint on the single defect tight-binding chain

We analyze the time evolution of the nearest-neighbour tight-binding chain in the presence of a single onsite defect. Such a defect was shown to generate non-trivial transport behavior recently in the article \textit{Acharya et al J. Stat. Mech. (2026) 043102}. The authors have used a defect technique inspired by classical random walk methods to obtain exact analytical expressions for the occupation probability and subsequently the mean and mean-squared displacement (MSD). Here we derive the same results using a spectral decomposition approach. Starting from the secular equation, we obtain the self-consistency condition for the eigenvalues and construct the corresponding normalized eigenvectors. This approach naturally separates the Hilbert space into dark subspace, whose states have zero amplitude at the defect site and remain unaffected, and bright subspaces, whose states get modified because of the defect. Using this eigenvalue decomposition, we provide a spectral origin of non-monotonicity in the MSD. Numerical calculations for finite chains show that the analytically estimated critical defect strength is in excellent agreement with the defect strength that minimizes the MSD.

quant-ph↗

arXiv2026

Time complexity of a monitored quantum search with resetting

Searching a database is a central task in computer science and is paradigmatic of transport and optimization problems in physics. For an unstructured search, Grover's algorithm predicts a quadratic speedup, with the search time $\tau(N)=\Theta(\sqrt{N})$ and $N$ the database size. Numerical studies suggest that the time complexity can change in the presence of feedback, injecting information during the search. Here, we determine the time complexity of the quantum analog of a randomized algorithm, which implements feedback in a simple form. The search is a continuous-time quantum walk on a complete graph, where the target is continuously monitored by a detector. Additionally, the quantum state is reset if the detector does not click within a specified time interval. This yields a non-unitary, non-Markovian dynamics. We optimize the search time as a function of the hopping amplitude, detection rate, and resetting rate, and identify the conditions under which time complexity could outperform Grover's scaling. The overall search time does not violate Grover's optimality bound when including the time budget of the physical implementation of the measurement. For databases of finite sizes monitoring can warrant rapid convergence and provides a promising avenue for fault-tolerant quantum searches.

quant-ph↗

arXiv2025

Causality, localization, and universality of monitored quantum walks with long-range hopping

A powerful strategy to accelerate quantum-walk-based search algorithms leverages on resetting protocols, where a detector monitors a target site and the evolution of the walker is restarted if no detection occurs within a fixed time interval. The optimal resetting rate can be extracted from the time evolution of the probability $S(t)$ that the detector has not clicked up to time $t$. We analyze $S(t)$ for a quantum walk on a one-dimensional lattice when the coupling between sites decays algebraically as $d^{-\alpha}$ with the distance $d$, for $\alpha\in(0,\infty)$. At long times, $S(t)$ decays with a universal power-law exponent that is independent of $\alpha$. At short times, $S(t)$ exhibits a plethora of phase transitions as a function of $\alpha$. From this, we provide a strategy to determine the optimal resetting rate. We identify two regimes: for $\alpha>1$, the resetting rate $r$ is bounded from below by the velocity with which information propagates causally across the lattice; for $\alpha<1$, instead, the long-range hopping tends to localize the walker: The optimal resetting rate depends on the size of the lattice and diverges as $\alpha\to 0$. Our strategy directly connects local measurement outcomes with the global dynamics encoded in $S(t)$. We derive simple models explaining our numerical results, shedding light on the interplay of long-range coherent dynamics, symmetries, and local quantum measurement processes in determining equilibrium. Our findings offer experimentally testable predictions and provide new physical insights on optimizing quantum search through resetting.

quant-ph↗

arXiv2023

Rise and fall of entanglement between two qubits in a non-Markovian bath

We analyse the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The chain mediates interactions between the qubits and acts as a non-Markovian reservoir. The the model is amenable to an analytical solution when the initial state of the chain is Gaussian}. We study the dynamics of the qubits concurrence starting from a separable state and assuming that the chain spectrum is gapped {and the chain is initially in a thermal state. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak coupling regime, where the qubits are entangled at the asymptotics; (ii) the strong coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude; and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitations. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study unravels the basic mechanisms leading to entanglement in a non-Markovian bath and allows to identify the key resources for realising quantum coherent dynamics of open systems.

quant-ph↗

arXiv2020

Machine Learning in Nonlinear Dynamical Systems

In this article, we discuss some of the recent developments in applying machine learning (ML) techniques to nonlinear dynamical systems. In particular, we demonstrate how to build a suitable ML framework for addressing two specific objectives of relevance: prediction of future evolution of a system and unveiling from given time-series data the analytical form of the underlying dynamics. This article is written in a pedagogical style appropriate for a course in nonlinear dynamics or machine learning.

nlin.AO↗

arXiv2019

Enhancement of Photovoltaic Current Generation through Dark States in Donor-Acceptor Pairs of Tungsten-based Transition Metal Di-Chalcogenides (TMDCs)

As several photovoltaic materials experimentally approach the Shockley-Queisser limit, there has been a growing interest in unconventional materials and approaches with the potential to cross this efficiency barrier. One such candidate is dark state protection induced by the dipole-dipole interaction between molecular excited states. This phenomenon has been shown to significantly reduce carrier recombination rate and enhance photon-to-current conversion, in elementary models consisting of few interacting chromophore centers. Atomically thin 2D transition metal di-chalcogenides (TMDCs) have shown great potential for use as ultra-thin photovoltaic materials in solar cells due to their favorable photon absorption and electronic transport properties. TMDC alloys exhibit tunable direct bandgaps and significant dipole moments. In this work, we introduce the dark state protection mechanism to a TMDC based photovoltaic system with pure tungsten diselenide (WSe2) as the acceptor material and the TMDC alloy tungsten sulfo-selenide (WSeS) as the donor material. Our numerical model demonstrates the first application of the dark state protection mechanism to a photovoltaic material with a photon current enhancement of up to 35% and an ideal photon-to-current efficiency exceeding the Shockley-Queisser limit.

physics.app-ph↗

arXiv2018

Reconstructing bifurcation behavior of a nonlinear dynamical system by introducing weak noise

For a model nonlinear dynamical system, we show how one may obtain its bifurcation behavior by introducing noise into the dynamics and then studying the resulting Langevin dynamics in the weak-noise limit. A suitable quantity to capture the bifurcation behavior in the noisy dynamics is the conditional probability to observe a microscopic configuration at one time, conditioned on the observation of a given configuration at an earlier time. For our model system, this conditional probability is studied by using two complementary approaches, the Fokker-Planck and the path-integral approach. The latter has the advantage of yielding exact closed-form expressions for the conditional probability. All our predictions are in excellent agreement with direct numerical integration of the dynamical equations of motion.

nlin.AO↗

arXiv2008

A Statistical Approach to Modeling Indian Classical Music Performance

A raga is a melodic structure with fixed notes and a set of rules characterizing a certain mood endorsed through performance. By a vadi swar is meant that note which plays the most significant role in expressing the raga. A samvadi swar similarly is the second most significant note. However, the determination of their significance has an element of subjectivity and hence we are motivated to find some truths through an objective analysis. The paper proposes a probabilistic method of note detection and demonstrates how the relative frequency (relative number of occurrences of the pitch) of the more important notes stabilize far more quickly than that of others. In addition, a count for distinct transitory and similar looking non-transitory (fundamental) frequency movements (but possibly embedding distinct emotions!) between the notes is also taken depicting the varnalankars or musical ornaments decorating the notes and note sequences as rendered by the artist. They reflect certain structural properties of the ragas. Several case studies are presented.

cs.SD↗