Finite-temperature equilibrium density profiles of integrable systems in confining potentials.

We study the equilibrium density profile of particles in two one-dimensional classical integrable models, namely hard rods and the hyperbolic Calogero model, placed in confining potentials. For both of these models the interparticle repulsion is strong enough to prevent particle trajectories from intersecting. We use field theoretic techniques to compute the density profile and their scaling with system size and temperature, and we compare them with results from Monte Carlo simulations. In both cases we find good agreement between the field theory and simulations. We also consider the case of the Toda model in which interparticle repulsion is weak and particle trajectories can cross. In this case, we find that a field theoretic description is ill-suited and instead, in certain parameter regimes, we present an approximate Hessian theory to understand the density profile. Our work provides an analytical approach toward understanding the equilibrium properties for interacting integrable systems in confining traps.

Blast in a One-Dimensional Cold Gas: From Newtonian Dynamics to Hydrodynamics.

A gas composed of a large number of atoms evolving according to Newtonian dynamics is often described by continuum hydrodynamics. Proving this rigorously is an outstanding open problem, and precise numerical demonstrations of the equivalence of the hydrodynamic and microscopic descriptions are rare. We test this equivalence in the context of the evolution of a blast wave, a problem that is expected to be at the limit where hydrodynamics could work. We study a one-dimensional gas at rest with instantaneous localized release of energy for which the hydrodynamic Euler equations admit a self-similar scaling solution. Our microscopic model consists of hard point particles with alternating masses, which is a nonintegrable system with strong mixing dynamics. Our extensive microscopic simulations find a remarkable agreement with Euler hydrodynamics, with deviations in a small core region that are understood as arising due to heat conduction.

Microscopic Theory of Fluctuating Hydrodynamics in Nonlinear Lattices.

The theory of fluctuating hydrodynamics has been an important tool for analyzing macroscopic behavior in nonlinear lattices. However, despite its practical success, its microscopic derivation is still incomplete. In this work, we provide the microscopic derivation of fluctuating hydrodynamics, using the coarse-graining and projection technique; the equivalence of ensembles turns out to be critical. The Green-Kubo (GK)-like formula for the bare transport coefficients are presented in a numerically computable form. Our numerical simulations show that the bare transport coefficients exist for a sufficiently large but finite coarse-graining length in the infinite lattice within the framework of the GK-like formula. This demonstrates that the bare transport coefficients uniquely exist for each physical system.

COVID-19: Analytic results for a modified SEIR model and comparison of different intervention strategies.

The Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is one of the standard models of disease spreading. Here we analyse an extended SEIR model that accounts for asymptomatic carriers, believed to play an important role in COVID-19 transmission. For this model we derive a number of analytic results for important quantities such as the peak number of infections, the time taken to reach the peak and the size of the final affected population. We also propose an accurate way of specifying initial conditions for the numerics (from insufficient data) using the fact that the early time exponential growth is well-described by the dominant eigenvector of the linearized equations. Secondly we explore the effect of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number, R 0 , to a target value R 0 target < 1 , but in distinct ways, which we implement in our model equations. We find that for the same R 0 target < 1 , TQ is more efficient in controlling the pandemic than SD. However, for TQ to be effective, it has to be based on contact tracing and our study quantifies the required ratio of tests-per-day to the number of new cases-per-day. Our analysis shows that the largest eigenvalue of the linearised dynamics provides a simple understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. We apply our results to the COVID data for India to obtain heuristic projections for the course of the pandemic, and note that the predictions strongly depend on the assumed fraction of asymptomatic carriers.

Transport, correlations, and chaos in a classical disordered anharmonic chain.

We explore transport properties in a disordered nonlinear chain of classical harmonic oscillators, and thereby identify a regime exhibiting behavior analogous to that seen in quantum many-body-localized systems. Through extensive numerical simulations of this system connected at its ends to heat baths at different temperatures, we computed the heat current and the temperature profile in the nonequilibrium steady state as a function of system size N, disorder strength Δ, and temperature T. The conductivity κ_{N}, obtained for finite length (N), saturates to a value κ_{∞}>0 in the large N limit, for all values of disorder strength Δ and temperature T>0. We show evidence that for any Δ>0 the conductivity goes to zero faster than any power of T in the (T/Δ)→0 limit, and find that the form κ_{∞}∼e^{-B|ln(CΔ/T)|^{3}} fits our data. This form has earlier been suggested by a theory based on the dynamics of multioscillator chaotic islands. The finite-size effect can be κ_{N}<κ_{∞} due to boundary resistance when the bulk conductivity is high (the weak disorder case), or κ_{N}>κ_{∞} due to direct bath-to-bath coupling through bulk localized modes when the bulk is weakly conducting (the strong disorder case). We also present results on equilibrium dynamical correlation functions and on the role of chaos on transport properties. Finally, we explore the differences in the growth and propagation of chaos in the weak and strong chaos regimes by studying the classical version of the out-of-time-ordered commutator.

Universal scaling in active single-file dynamics.

We study the single-file dynamics of three classes of active particles: run-and-tumble particles, active Brownian particles and active Ornstein-Uhlenbeck particles. At high activity values, the particles, interacting via purely repulsive and short-ranged forces, aggregate into several motile and dynamical clusters of comparable size, and do not display bulk phase-segregation. In this dynamical steady-state, we find that the cluster size distribution of these aggregates is a scaled function of the density and activity parameters across the three models of active particles with the same scaling function. The velocity distribution of these motile clusters is non-Gaussian. We show that the effective dynamics of these clusters can explain the observed emergent scaling of the mean-squared displacement of tagged particles for all the three models with identical scaling exponents and functions. Concomitant with the clustering seen at high activities, we observe that the static density correlation function displays rich structures, including multiple peaks that are reminiscent of particle clustering induced by effective attractive interactions, while the dynamical variant shows non-diffusive scaling. Our study reveals a universal scaling behavior in the single-file dynamics of interacting active particles.

Aging effects on thermal conductivity of glass-forming liquids.

Thermal conductivity of a model glass-forming system in the liquid and glass states is studied using extensive numerical simulations. We show that near the glass transition temperature, where the structural relaxation time becomes very long, the measured thermal conductivity decreases with increasing age. Second, the thermal conductivity of the disordered solid obtained at low temperatures is found to depend on the cooling rate with which it was prepared. For the cooling rates accessible in simulations, lower cooling rates lead to lower thermal conductivity. Our analysis links this decrease of the thermal conductivity with increased exploration of lower-energy inherent structures of the underlying potential energy landscape. Further, we show that the lowering of conductivity for lower-energy inherent structures is related to the high-frequency harmonic modes associated with the inherent structure being less extended. Possible effects of considering relatively small systems and fast cooling rates in the simulations are discussed.

Steady state of an active Brownian particle in a two-dimensional harmonic trap.

We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions in the presence of translational diffusion. This series solution allows us to efficiently explore the behavior of the system in different parameter regimes. Identifying "active" and "passive" regimes, we predict a surprising re-entrant active-to-passive transition with increasing trap stiffness. Our numerical simulations validate this finding. We discuss various interesting limiting cases wherein closed-form expressions for the distributions can be obtained.

Silica-immobilized ionic liquid Brønsted acids as highly effective heterogeneous catalysts for the isomerization of n-heptane and n-octane.

Metal-free imidazolium-based ionic liquid (IL) Brønsted acids 1-methyl imidazolium hydrogen sulphate [HMIM]HSO4 and 1-methyl benzimidazolium hydrogen sulphate [HMBIM]HSO4 were synthesized. Their physicochemical properties were investigated using spectroscopic and thermal techniques, including UV-Vis, FT-IR, 1H NMR, 13C-NMR, mass spectrometry, and TGA. The ILs were immobilized on mesoporous silica gel and characterized by FT-IR spectroscopy, scanning electron microscopy, Brunauer-Emmett-Teller analysis, ammonia temperature-programmed desorption, and thermogravimetric analysis. [HMIM]HSO4@silica and [HMBIM]HSO4@silica have been successfully applied as promising replacements for conventional catalysts for alkane isomerization reactions at room temperature. Isomerization of n-heptane and n-octane was achieved with both catalysts. In addition to promoting the isomerization of n-heptane and n-octane (a quintessential reaction for petroleum refineries), these immobilized catalysts are non-hazardous and save energy.

A brief review on solid lipid nanoparticles: part and parcel of contemporary drug delivery systems.

Drug delivery technology has a wide spectrum, which is continuously being upgraded at a stupendous speed. Different fabricated nanoparticles and drugs possessing low solubility and poor pharmacokinetic profiles are the two major substances extensively delivered to target sites. Among the colloidal carriers, nanolipid dispersions (liposomes, deformable liposomes, virosomes, ethosomes, and solid lipid nanoparticles) are ideal delivery systems with the advantages of biodegradation and nontoxicity. Among them, nano-structured lipid carriers and solid lipid nanoparticles (SLNs) are dominant, which can be modified to exhibit various advantages, compared to liposomes and polymeric nanoparticles. Nano-structured lipid carriers and SLNs are non-biotoxic since they are biodegradable. Besides, they are highly stable. Their (nano-structured lipid carriers and SLNs) morphology, structural characteristics, ingredients used for preparation, techniques for their production, and characterization using various methods are discussed in this review. Also, although nano-structured lipid carriers and SLNs are based on lipids and surfactants, the effect of these two matrixes to build excipients is also discussed together with their pharmacological significance with novel theranostic approaches, stability and storage.

Quantum Brownian motion: Drude and Ohmic baths as continuum limits of the Rubin model.

The motion of a free quantum particle in a thermal environment is usually described by the quantum Langevin equation, where the effect of the bath is encoded through a dissipative and a noise term, related to each other via the fluctuation dissipation theorem. The quantum Langevin equation can be derived starting from a microscopic model of the thermal bath as an infinite collection of harmonic oscillators prepared in an initial equilibrium state. The spectral properties of the bath oscillators and their coupling to the particle determine the specific form of the dissipation and noise. Here we investigate in detail the well-known Rubin bath model, which consists of a one-dimensional harmonic chain with the boundary bath particle coupled to the Brownian particle. We show how in the limit of infinite bath bandwidth, we get the Drude model, and a second limit of infinite system-bath coupling gives the Ohmic model. A detailed analysis of relevant equilibrium correlation functions, such as the mean squared displacement, velocity autocorrelation functions, and response function are presented, with the aim of understanding the various temporal regimes. In particular, we discuss the quantum-to-classical crossover time scales where the mean square displacement changes from a ∼lnt to a ∼t dependence. We relate our study to recent work using linear response theory to understand quantum Brownian motion.

Kardar-Parisi-Zhang scaling for an integrable lattice Landau-Lifshitz spin chain.

Recent studies report on anomalous spin transport for the integrable Heisenberg spin chain at its isotropic point. Anomalous scaling is also observed in the time evolution of nonequilibrium initial conditions, the decay of current-current correlations, and nonequilibrium steady state averages. These studies indicate a space-time scaling with x∼t^{2/3} behavior at the isotropic point, in sharp contrast to the ballistic form x∼t generically expected for integrable systems. In our contribution we study the scaling behavior for the integrable lattice Landau-Lifshitz spin chain. We report on equilibrium spatiotemporal correlations and dynamics with step initial conditions. Remarkably, for the case with zero mean magnetization, we find strong evidence that the scaling function is identical to the one obtained from the stationary stochastic Burgers equation, alias Kardar-Parisi-Zhang equation. In addition, we present results for the easy-plane and easy-axis regimes for which, respectively, ballistic and diffusive spin transport is observed, whereas the energy remains ballistic over the entire parameter regime.

Run-and-tumble particle in one-dimensional confining potentials: Steady-state, relaxation, and first-passage properties.

We study the dynamics of a one-dimensional run-and-tumble particle subjected to confining potentials of the type V(x)=α|x|^{p}, with p>0. The noise that drives the particle dynamics is telegraphic and alternates between ±1 values. We show that the stationary probability density P(x) has a rich behavior in the (p,α) plane. For p>1, the distribution has a finite support in [x_{-},x_{+}] and there is a critical line α_{c}(p) that separates an activelike phase for α>α_{c}(p) where P(x) diverges at x_{±}, from a passivelike phase for α<α_{c}(p) where P(x) vanishes at x_{±}. For p<1, the stationary density P(x) collapses to a delta function at the origin, P(x)=δ(x). In the marginal case p=1, we show that, for α<α_{c}, the stationary density P(x) is a symmetric exponential, while for α>α_{c}, it again is a delta function P(x)=δ(x). For the harmonic case p=2, we obtain exactly the full time-dependent distribution P(x,t), which allows us to study how the system relaxes to its stationary state. In addition, for this p=2 case, we also study analytically the full distribution of the first-passage time to the origin. Numerical simulations are in complete agreement with our analytical predictions.

Light-Cone Spreading of Perturbations and the Butterfly Effect in a Classical Spin Chain.

We find that the effects of a localized perturbation in a chaotic classical many-body system-the classical Heisenberg chain at infinite temperature-spread ballistically with a finite speed even when the local spin dynamics is diffusive. We study two complementary aspects of this butterfly effect: the rapid growth of the perturbation, and its simultaneous ballistic (light-cone) spread, as characterized by the Lyapunov exponents and the butterfly speed, respectively. We connect this to recent studies of the out-of-time-ordered commutators (OTOC), which have been proposed as an indicator of chaos in a quantum system. We provide a straightforward identification of the OTOC with a natural correlator in our system and demonstrate that many of its interesting qualitative features are present in the classical system. Finally, by analyzing the scaling forms, we relate the growth, spread, and propagation of the perturbation with the growth of one-dimensional interfaces described by the Kardar-Parisi-Zhang equation.

Energy Current Cumulants in One-Dimensional Systems in Equilibrium.

A recent theory based on fluctuating hydrodynamics predicts that one-dimensional interacting systems with particle, momentum, and energy conservation exhibit anomalous transport that falls into two main universality classes. The classification is based on behavior of equilibrium dynamical correlations of the conserved quantities. One class is characterized by sound modes with Kardar-Parisi-Zhang scaling, while the second class has diffusive sound modes. The heat mode follows Lévy statistics, with different exponents for the two classes. Here we consider heat current fluctuations in two specific systems, which are expected to be in the above two universality classes, namely, a hard particle gas with Hamiltonian dynamics and a harmonic chain with momentum conserving stochastic dynamics. Numerical simulations show completely different system-size dependence of current cumulants in these two systems. We explain this numerical observation using a phenomenological model of Lévy walkers with inputs from fluctuating hydrodynamics. This consistently explains the system-size dependence of heat current fluctuations. For the latter system, we derive the cumulant-generating function from a more microscopic theory, which also gives the same system-size dependence of cumulants.

Exact Extremal Statistics in the Classical 1D Coulomb Gas.

We consider a one-dimensional classical Coulomb gas of N-like charges in a harmonic potential-also known as the one-dimensional one-component plasma. We compute, analytically, the probability distribution of the position x_{max} of the rightmost charge in the limit of large N. We show that the typical fluctuations of x_{max} around its mean are described by a nontrivial scaling function, with asymmetric tails. This distribution is different from the Tracy-Widom distribution of x_{max} for Dyson's log gas. We also compute the large deviation functions of x_{max} explicitly and show that the system exhibits a third-order phase transition, as in the log gas. Our theoretical predictions are verified numerically.

Driven inelastic Maxwell gas in one dimension.

A lattice version of the driven inelastic Maxwell gas is studied in one dimension with periodic boundary conditions. Each site i of the lattice is assigned with a scalar "velocity," v_{i}. Nearest neighbors on the lattice interact, with a rate τ_{c}^{-1}, according to an inelastic collision rule. External driving, occurring with a rate τ_{w}^{-1}, sustains a steady state in the system. A set of closed coupled equations for the evolution of the variance and the two-point correlation is found. Steady-state values of the variance, as well as spatial correlation functions, are calculated. It is shown exactly that the correlation function decays exponentially with distance, and the correlation length for a large system is determined. Furthermore, the spatiotemporal correlation C(x,t)=〈v_{i}(0)v_{i+x}(t)〉 can also be obtained. We find that there is an interior region -x^{*}x^{*}, the correlation function remains the same as the initial form. C(x,t) exhibits second-order discontinuity at the transition points x=±x^{*}, and these transition points move away from the x=0 with a constant speed.

Dependency of Anion and Chain Length of Imidazolium Based Ionic Liquid on Micellization of the Block Copolymer F127 in Aqueous Solution: An Experimental Deep Insight.

The non-ionic triblock copolymer, Pluronic® F127, has been selected to observe its interaction with ionic liquids (ILs) in aqueous solutions by using DLS, surface tension, and viscosity measurements. The Critical Micelle Concentration (CMC) of F127 increased with the addition of ILs, which appeared logical since it increases the solubility of PPO (and PEO) moiety, making it behaves more like a hydrophilic block copolymer that is micellized at a higher copolymer concentration. The results from DLS data showed good agreement with those obtained from the surface tension measurements. Upon the addition of ILs, the tendency in micellar size reduction was demonstrated by viscosity results, and therefore, intrinsic viscosity decreased compared to pure F127 in aqueous solution. The results were discussed as a function of alkyl chain length and anions of imidazolium based ILs.

Equilibrium dynamical correlations in the Toda chain and other integrable models.

We investigate the form of equilibrium spatiotemporal correlation functions of conserved quantities in the Toda lattice and in other integrable models. From numerical simulations we find that the correlations satisfy ballistic scaling with a remarkable collapse of data from different times. We examine special limiting choices of parameter values, for which the Toda lattice tends to either the harmonic chain or the equal mass hard-particle gas. In both these limiting cases, one can obtain the correlations exactly and we find excellent agreement with the direct Toda simulation results. We also discuss a transformation to "normal mode" variables, as commonly done in hydrodynamic theory of nonintegrable systems, and find that this is useful, to some extent, even for the integrable system. The striking differences between the Toda chain and a truncated version, expected to be nonintegrable, are pointed out.

Pumping single-file colloids: Absence of current reversal.

We consider the single-file motion of colloidal particles interacting via short-range repulsion and placed in a traveling wave potential that varies periodically in time and space. Under suitable driving conditions, a directed time-averaged flow of colloids is generated. We obtain analytic results for the model using a perturbative approach to solve the Fokker-Planck equations. The predictions show good agreement with numerical simulations. We find peaks in the time-averaged directed current as a function of driving frequency, wavelength, and particle density and discuss possible experimental realizations. Surprisingly, unlike a closely related exclusion dynamics on a lattice, the directed current in the present model does not show current reversal with density. A linear response formula relating current response to equilibrium correlations is also proposed.