We explore the role of exceptional points and complex eigenvalues on the occurrence of the quantum Mpemba effect. To this end, we study a two-level driven dissipative system subjected to an oscillatory electric field and dissipative coupling with the environment. We find that both exceptional points and complex eigenvalues can lead to $multiple$ quantum Mpemba effect. It occurs in an observable when time evolved copies corresponding to two different initial conditions, one initially having higher observable value compared to the other and both relaxing towards the same steady state, intersect each other more than once during their relaxation process. Each of the intersections denotes a quantum Mpemba effect and marks the reversal of identities between the two copies i.e. the copy with higher observable value before the intersection becomes the lower valued copy (and vice versa) after the intersection. Such multiple intersections originate from additional algebraic time dependence at the exceptional points and due to oscillatory relaxation in the case of complex eigenvalues. We provide analytical results for quantum Mpemba effect in the density matrix in presence of coherence. Depending on the control parameters (drive and dissipation), observables such as energy, von Neumann entropy, temperature etc. exhibit either single or multiple quantum Mpemba effect. However, the distance from steady state measured in terms of the Kullback-Leibler divergence shows only single quantum Mpemba effect although the corresponding speed gives rise to either single or multiple quantum Mpemba effect.

We analyze the cluster formation in a non-ergodic stochastic system as a result of counter-flow, with the aid of an exactly solvable model. To illustrate the clustering, a two species asymmetric simple exclusion process with impurities on a periodic lattice is considered, where the impurity can activate flips between the two non-conserved species. Exact analytical results, supported by Monte Carlo simulations, show two distinct phases, free flowing phase and clustering phase. The clustering phase is characterized by constant density and vanishing current of the non-conserved species, whereas the free flowing phase is identified with non-monotonic density and non-monotonic finite current of the same. The $n$-point spatial correlation between $n$ consecutive vacancies grows with increasing $n$ in the clustering phase, indicating the formation of two macroscopic clusters in this phase, one of the vacancies and the other consisting of all the particles. We define a rearrangement parameter that permutes the ordering of particles in the initial configuration, keeping all the input parameters fixed. This rearrangement parameter reveals the significant effect of non-ergodicity on the onset of clustering. For a special choice of the microscopic dynamics, we connect the present model to a system of run and tumble particles used to model active matter, where the two species having opposite net bias manifest the two possible run directions of the run and tumble particles, and the impurities act as tumbling reagents that enable the tumbling process.

We demonstrate the quantum Mpemba effect in a quantum dot coupled to two reservoirs, described by the Anderson model. We show that the system temperatures starting from two different initial values (hot and cold) cross each other at finite time (and thereby reverse their identities; i.e., hot becomes cold and vice versa) to generate thermal quantum Mpemba effect. The slowest relaxation mode believed to play the dominating role in Mpemba effect in Markovian systems does not contribute to such anomalous relaxation in the present model. In this connection, our analytical result provides necessary condition for producing quantum Mpemba effect in the density matrix elements of the quantum dot, as a combined effect of the remaining relaxation modes.

We demonstrate exciting similarities between classical and quantum many body systems whose microscopic dynamics are composed of non-reciprocal three-site facilitated exclusion processes. We show that the quantum analogue of the classical facilitated process engineers an interesting $quantum$ $absorbing$ $transition$ where the quantum particles transit from an unentangled direct-product absorbing phase to an entangled steady state with a finite current at density $\rho=1/2$. In the generalised classical facilitated exclusion process, which includes independent hopping of particles with rate $p$, our analytical and Monte-Carlo results establish emergence of a special density $\rho^*=1/3$ that demarcates two regimes in the steady state, based on the competition between two current carrying modes (facilitated and independent). The corresponding quantum system also displays similar qualitative behaviours with striking non-monotonic features in the bipartite entanglement. Our work ties the two sub-fields of classically interacting exclusion processes, and interacting non-Hermitian quantum Hamiltonians to show common themes in the non-equilibrium phases they realise.

We obtain an exact matrix product steady state for a class of multi species asymmetric simple exclusion process with impurities, under periodic boundary condition. Alongside the usual hopping dynamics, an additional flip dynamics is activated only in the presence of impurities. Although the microscopic dynamics renders the system to be non-ergodic, exact analytical results for observables are obtained in steady states for a specific class of initial configurations. Interesting physical features including negative differential mobility and transition of correlations from negative to positive with changing vacancy density, have been observed. We discuss plausible connections of this exactly solvable model with multi lane asymmetric simple exclusion processes as well as enzymatic chemical reactions.

We show that the one-dimensional discrete nonlinear Schrödinger chain (DNLS) at finite temperature has three different dynamical regimes (ultralow-, low-, and high-temperature regimes). This has been established via (i) one-point macroscopic thermodynamic observables (temperature T, energy density ε, and the relationship between them), (ii) emergence and disappearance of an additional almost conserved quantity (total phase difference), and (iii) classical out-of-time-ordered correlators and related quantities (butterfly speed and Lyapunov exponents). The crossover temperatures T_{l-ul} (between low- and ultra-low-temperature regimes) and T_{h-l} (between the high- and low-temperature regimes) extracted from these three different approaches are consistent with each other. The analysis presented here is an important step forward toward the understanding of DNLS which is ubiquitous in many fields and has a nonseparable Hamiltonian form. Our work also shows that the different methods used here can serve as important tools to identify dynamical regimes in other interacting many-body systems.

Out-of-time-ordered correlators (OTOC) have been extensively used as a major tool for exploring quantum chaos and also recently, there has been a classical analogue. Studies have been limited to closed systems. In this work, we probe an open classical many-body system, more specifically, a spatially extended driven dissipative chain of coupled Duffing oscillators using the classical OTOC to investigate the spread and growth (decay) of an initially localized perturbation in the chain. Correspondingly, we find three distinct types of dynamical behavior, namely the sustained chaos, transient chaos and non-chaotic region, as clearly exhibited by different geometrical shapes in the heat map of OTOC. To quantify such differences, we look at instantaneous speed (IS), finite time Lyapunov exponents (FTLE) and velocity dependent Lyapunov exponents (VDLE) extracted from OTOC. Introduction of these quantities turn out to be instrumental in diagnosing and demarcating different regimes of dynamical behavior. To gain control over open nonlinear systems, it is important to look at the variation of these quantities with respect to parameters. As we tune drive, dissipation and coupling, FTLE and IS exhibit transition between sustained chaos and non-chaotic regimeswith intermediate transient chaos regimes and highly intermittent sustained chaos points. In the limit of zero nonlinearity, we present exact analytical results for the driven dissipative harmonic system and we find that our analytical results can very well describe the non-chaotic regime as well as the late time behavior in the transient regime of the Duffing chain. We believe, this analysis is an important step forward towards understanding nonlinear dynamics, chaos and spatio-temporal spread of perturbations in many-particle open systems.

The present study was conducted during 2016-17 to assess the knowledge level of farmers about Brinjal production technology. A total of 120 Brinjal growers were selected randomly from 10 villages of Gohad block of Bhind district (M.P.). For data collection, the respondents were interviewed with the help of a structure interview schedule containing questions on Brinjal production technology. Each component has been assigned a particular score to assess knowledge level of Brinjal growing farmers. The collected data were analyzed with suitable statistical methods. The study concludes that more than fifty percent (62.50%) respondents had medium level of knowledge while only 19.17% falls in the category of high level of knowledge about recommended Brinjal production of technology. This may be due lack of exposure towards agricultural messages from interpersonal and mass media channels.

Out-of-time-ordered correlators (OTOCs) have been extensively used as a major tool for exploring quantum chaos, and recently there has been a classical analog. Studies have been limited to closed systems. In this work, we probe an open classical many-body system, more specifically, a spatially extended driven dissipative chain of coupled Duffing oscillators using the classical OTOC to investigate the spread and growth (decay) of an initially localized perturbation in the chain. Correspondingly, we find three distinct types of dynamical behavior: the sustained chaos, transient chaos, and nonchaotic region, as clearly exhibited by different geometrical shapes in the OTOC heat map. To quantify such differences, we look at instantaneous speed (IS), finite-time Lyapunov exponents (FTLEs), and velocity-dependent Lyapunov exponents (VDLEs) extracted from OTOCs. Introduction of these quantities turns out to be instrumental in diagnosing and demarcating different regimes of dynamical behavior. To gain control over open nonlinear systems, it is important to look at the variation of these quantities with respect to parameters. As we tune drive, dissipation, and coupling, FTLEs and IS exhibit transition between sustained chaos and nonchaotic regimes with intermediate transient chaos regimes and highly intermittent sustained chaos points. In the limit of zero nonlinearity, we present exact analytical results for the driven dissipative harmonic system, and we find that our analytical results can very well describe the nonchaotic regime as well as the late-time behavior in the transient regime of the Duffing chain. We believe that this analysis is an important step forward towards understanding nonlinear dynamics, chaos, and spatiotemporal spread of perturbations in many-particle open systems.

We introduce an assisted exchange model (AEM) on a one dimensional periodic lattice with (K+1) different species of hard core particles, where the exchange rate depends on the pair of particles which undergo exchange and their immediate left neighbor. We show that this stochastic process has a pair factorized steady state for a broad class of exchange dynamics. We calculate exactly the particle current and spatial correlations (K+1)-species AEM using a transfer matrix formalism. Interestingly the current in AEM exhibits density dependent current reversal and negative differential mobility- both of which have been discussed elaborately by using a two species exchange model which resembles the partially asymmetric conserved lattice gas model in one dimension. Moreover, multi-species version of AEM exhibits additional features like multiple points of current reversal, and unusual response of particle current.

Driven particles in the presence of crowded environment, obstacles, or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. Based on the empirical studies of conserved lattice gas model, two species exclusion model and other interacting particle systems we propose a new mechanism for complex many-particle systems where slowing down of certain non-driven degrees of freedom by the external field can give rise to NDM. To prove that the slowing down of the non-driven degrees is indeed the underlying cause, we consider several driven diffusive systems including two species exclusion models, misanthrope process, and show from the exact steady state results that NDM indeed appears when some non-driven modes are slowed down deliberately. For clarity, we also provide a simple pedagogical example of two interacting random walkers on a ring which conforms to the proposed scenario.

We construct matrix product steady states for a class of interacting particle systems where particles do not obey hardcore exclusion, meaning each site can occupy any number of particles subjected to the global conservation of the total number of particles in the system. To represent the arbitrary occupancy of the sites, the matrix product ansatz here requires an infinite set of matrices which in turn leads to an algebra involving an infinite number of matrix equations. We show that these matrix equations, in fact, can be reduced to a single functional relation when the matrices are parametric functions of the representative occupation number. We demonstrate this matrix formulation in a class of stochastic particle hopping processes on a one dimensional periodic lattice where hop rates depend on the occupation numbers of the departure site and its neighbors within a finite range; this includes some well known stochastic processes like, the totally or partially asymmetric zero range process, misanthrope process and finite range process.

We introduce and solve exactly a class of interacting particle systems in one dimension where particles hop asymmetrically. In its simplest form, namely asymmetric zero range process (AZRP), particles hop on a one dimensional periodic lattice with asymmetric hop rates; the rates for both right and left moves depend only on the occupation at the departure site but their functional forms are different. We show that AZRP leads to a factorized steady state (FSS) when its rate-functions satisfy certain constraints. We demonstrate with explicit examples that AZRP exhibits certain interesting features which were not possible in usual zero range process. Firstly, it can undergo a condensation transition depending on how often a particle makes a right move compared to a left one and secondly, the particle current in AZRP can reverse its direction as the density is changed. We show that these features are common in other asymmetric models which have FSS, like the asymmetric misanthrope process where rate functions for right and left hops are different, and depend on occupation of both the departure and the arrival site. We also derive sufficient conditions for having cluster-factorized steady states for finite range process with such asymmetric rate functions and discuss the possibility of condensation there.

This unique book presents an in-depth analysis of all the emerging ironmaking processes, supplementing the conventional blast furnace method. Various processes for producing solid and liquid iron are discussed, including important features such as process outline, techno-economics, and process fundamentals. The present global status of each process is examined, projections for the future are made, and processes are compared.Beyond the Blast Furnace is valuable reading for process developers, because it gives them a complete picture of various process options. Conventional iron- and steelmakers as well as researchers and practitioners working in the area of alternative processes of ironmaking will also benefit from this ready reference. The book is an ideal text for undergraduate and postgraduate students in metallurgy.

During a 28-year field survey in India (1988–2016), groundwater arsenic contamination and its health effects were registered in the states of West Bengal, Jharkhand, Bihar and Uttar Pradesh in the Ganga River flood plain, and the states of Assam and Manipur in the flood plain of Brahamaputra and Imphal rivers. Groundwater of Rajnandgaon village in Chhattisgarh state, which is not in a flood plain, is also arsenic contaminated. More than 170,000 tubewell water samples from the affected states were analyzed and half of the samples had arsenic >10 μg/L (maximum concentration 3,700 μg/L). Chronic exposure to arsenic through drinking water causes various health problems, like dermal, neurological, reproductive and pregnancy effects, cardiovascular effects, diabetes mellitus, diseases of the respiratory and gastrointestinal systems, and cancers, typically involving the skin, lungs, liver, bladder, etc. About 4.5% of the 8,000 children from arsenic-affected villages of affected states were registered with mild to moderate arsenical skin lesions. In the preliminary survey, more than 10,000 patients were registered with different types of arsenic-related signs and symptoms, out of more than 100,000 people screened from affected states. Elevated levels of arsenic were also found in biological samples (urine, hair, nails) of the people living in affected states. The study reveals that the population who had severe arsenical skin lesions may suffer from multiple Bowens/cancers in the long term. Some unusual symptoms, such as burning sensation, skin itching and watering of eyes in the presence of sun light, were also noticed in arsenicosis patients.

In reconstituting k-mer models, extended objects that occupy several sites on a one-dimensional lattice undergo directed or undirected diffusion, and reconstitute-when in contact-by transferring a single monomer unit from one k-mer to the other; the rates depend on the size of participating k-mers. This polydispersed system has two conserved quantities, the number of k-mers and the packing fraction. We provide a matrix product method to write the steady state of this model and to calculate the spatial correlation functions analytically. We show that for a constant reconstitution rate, the spatial correlation exhibits damped oscillations in some density regions separated, from other regions with exponential decay, by a disorder surface. In a specific limit, this constant-rate reconstitution model is equivalent to a single dimer model and exhibits a phase coexistence similar to the one observed earlier in totally asymmetric simple exclusion process on a ring with a defect.

During our last 27 years of field survey in India, we have studied the magnitude of groundwater arsenic and fluoride contamination and its resulting health effects from numerous states. India is the worst groundwater fluoride and arsenic affected country in the world. Fluoride results the most prevalent groundwater related diseases in India. Out of a total 29 states in India, groundwater of 20 states is fluoride affected. Total population of fluoride endemic 201 districts of India is 411 million (40% of Indian population) and more than 66 million people are estimated to be suffering from fluorosis including 6 million children below 14 years of age. Fluoride may cause a crippling disease. In 6 states of the Ganga-Brahmaputra Plain (GB-Plain), 70.4 million people are potentially at risk from groundwater arsenic toxicity. Three additional states in the non GB-Plain are mildly arsenic affected. For arsenic with substantial cumulative exposure can aggravate the risk of cancers along with various other diseases. Clinical effects of fluoride includes abnormal tooth enamel in children; adults had joint pain and deformity of the limbs, spine etc. The affected population chronically exposed to arsenic and fluoride from groundwater is in danger and there is no available medicine for those suffering from the toxicity. Arsenic and fluoride safe water and nutritious food are suggested to prevent further aggravation of toxicity. The World Health Organization (WHO) points out that social problems arising from arsenic and fluoride toxicity eventually create pressure on the economy of the affected areas. In arsenic and fluoride affected areas in India, crisis is not always having too little safe water to satisfy our need, it is the crisis of managing the water.

We study a class of nonequilibrium lattice models on a ring where particles hop in a particular direction, from a site to one of its (say, right) nearest neighbors, with a rate that depends on the occupation of all the neighboring sites within a range R. This finite-range process (FRP) for R=0 reduces to the well-known zero-range process (ZRP), giving rise to a factorized steady state (FSS) for any arbitrary hop rate. We show that, provided the hop rates satisfy a specific condition, the steady state of FRP can be written as a product of a cluster-weight function of (R+1) occupation variables. We show that, for a large class of cluster-weight functions, the cluster-factorized steady state admits a finite dimensional transfer-matrix formulation, which helps in calculating the spatial correlation functions and subsystem mass distributions exactly. We also discuss a criterion for which the FRP undergoes a condensation transition.