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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., Comment: To appear in Phys. Rev. A

This work proposes a switched model reference adaptive control (S-MRAC) architecture for a multi-input multi-output (MIMO) switched linear system with memory for enhanced learning. A salient feature of the proposed method that separates it from most previous results is the use of memory that store the estimator states at switching and facilitate parameter learning during both active and inactive phases of a subsystem, thereby improving the tracking performance of the overall switched system. Specifically, the learning experience from the previous active duration of a subsystem is retained in the memory and reused when the subsystem is inactive and when the subsystem becomes active again. Parameter convergence is shown based on an intermittent initial excitation (IIE), which is significantly relaxed than the classical persistence of excitation (PE) condition. A common Lyapunov function is considered to ensure closed-loop stability with S-MRAC. Further under IIE, the exponential stability of tracking and parameter estimation error dynamics are guaranteed., Comment: arXiv admin note: text overlap with arXiv:2204.03338

This paper proposes a composite adaptive control architecture using dual adaptation scheme for dynamical systems comprising time-varying uncertain parameters. While majority of the adaptive control schemes in literature address the case of constant parameters, recent research has conceptualized improved adaptive control techniques for time-varying systems with rigorous stability proofs. The proposed work is an effort towards a similar direction, where a novel dual adaptation mechanism is introduced to efficiently tackle the time-varying nature of the parameters. Projection and $\sigma$-modification algorithms are strategically combined using congelation of variables to claim a global result for the tracking error space. While the classical adaptive systems demand a restrictive condition of persistence of excitation (PE) for accurate parameter estimation, the proposed work relies on a milder condition, called initial excitation (IE) for the same. A rigorous Lyapunov stability analysis is carried out to establish uniformly ultimately bounded (UUB) stability of the closed-loop system. Further it is analytically shown that the proposed work can recover the performance of previously designed IE-based adaptive controller in case of time invariant systems., Comment: 6 pages

This work proposes an online adaptive identification method for multi-input multi-output (MIMO) switched affine systems with guaranteed parameter convergence. A family of online parameter estimators is used that is equipped with a dual-layer low pass filter architecture to facilitate parameter learning and identification of each subsystem. The filters capture information about the unknown parameters in the form of a prediction error which is used in the parameter estimation algorithm. A salient feature of the proposed method that distinguishes it from most previous results is the use of a memory bank that stores filter values and promotes parameter learning during both active and inactive phases of a subsystem. Specifically, the learnt experience from the previous active phase of a subsystem is retained in the memory and leveraged for parameter learning in its subsequent active and inactive phases. Further, a new notion of intermittent initial excitation (IIE) is introduced that extends the previously established initial excitation (IE) condition to the switched system framework. IIE is shown to be sufficient to ensure exponential convergence of the switched system parameters.

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., Comment: 13 pages, 9 figures , Accepted in Resonance - Journal of Science Education

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.

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., Comment: v1: 8 pages, 8 figures; v2: added results, close to the published version

This work proposes a new adaptive-robust control (ARC) architecture for a class of uncertain Euler-Lagrange (EL) systems where the upper bound of the uncertainty satisfies linear in parameters (LIP) structure. Conventional ARC strategies either require structural knowledge of the system or presume that the overall uncertainties or its time derivative are norm bounded by a constant. Due to unmodelled dynamics and modelling imperfection, true structural knowledge of the system is not always available. Further, for the class of systems under consideration, prior assumption regarding the uncertainties (or its time derivative) being upper bounded by a constant, puts a restriction on states beforehand. Conventional ARC laws invite overestimation-underestimation problem of switching gain. Towards this front, Adaptive Switching-gain based Robust Control (ASRC) is proposed which alleviates the overestimation-underestimation problem of switching gain. Moreover, ASRC avoids any presumption of constant upper bound on the overall uncertainties and can negotiate uncertainties regardless of being linear or nonlinear in parameters. Experimental results of ASRC using a wheeled mobile robot notes improved control performance in comparison to adaptive sliding mode control., Comment: 10 pages, 9 figures

Convergence of controller parameters in standard model reference adaptive control (MRAC) requires the system states to be persistently exciting (PE), a restrictive condition to be verified online. A recent data-driven approach, concurrent learning, uses information-rich past data concurrently with the standard parameter update laws to guarantee parameter convergence without the need of the PE condition. This method guarantees exponential convergence of both the tracking and the controller parameter estimation errors to zero, whereas, the classical MRAC merely ensures asymptotic convergence of tracking error to zero. However, the method requires knowledge of the state derivative, at least at the time instances when the state values are stored in memory. The method further assumes knowledge of the control allocation matrix. This paper addresses these limitations by using a memory-based finite-time system identifier in conjunction with a data-driven approach, leading to convergence of both the tracking and the controller parameter estimation errors without the PE condition and knowledge of the system matrices and the state derivative. A Lyapunov based stability proof is included to justify the validity of the proposed data-driven approach. Simulation results demonstrate the efficacy of the suggested method.

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., Comment: 24 pages,11 figures;a replacement paper is being uploaded because the the nyas swars of Yaman were not correctly given;some typos have been corrected