arXiv subjects

Debarshee Bagchi

Publications and source records attributed to Debarshee Bagchi.

18 recordsLinked to original sources

arXiv2023

Unusual ergodic and chaotic properties of trapped hard rods

We investigate ergodicity, chaos and thermalization for a one-dimensional classical gas of hard rods confined to an external quadratic or quartic trap, which breaks microscopic integrability. To quantify the strength of chaos in this system, we compute its maximal Lyapunov exponent numerically. The approach to thermal equilibrium is studied by considering the time evolution of particle position and velocity distributions and comparing the late-time profiles with the Gibbs state. Remarkably, we find that quadratically trapped hard rods are highly non-ergodic and do not resemble a Gibbs state even at extremely long times, despite compelling evidence of chaos for four or more rods. On the other hand, our numerical results reveal that hard rods in a quartic trap exhibit both chaos and thermalization, and equilibrate to a Gibbs state as expected for a nonintegrable many-body system.

cond-mat.stat-mech↗

arXiv2022

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 inter-particle 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 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 inter-particle repulsion is weak and particle trajectories can cross. In this case, we find that a field theoretic description is ill-suited due to the lack of a thermodynamic length scale. The density profiles for the Toda model obtained from Monte-Carlo simulations can be understood by studying the analytically tractable harmonic chain model (Hessian approximation of the Toda model). For the harmonic chain model one can derive an exact expression for the density that shines light on some of the qualitative features of the Toda model in a quadratic trap. Our work provides an analytical approach towards understanding the equilibrium properties for interacting integrable systems in confining traps.

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arXiv2022

Macroscopic charge segregation in driven polyelectrolyte solutions

Understanding the behavior of charged complex fluids is crucial for a plethora of important industrial, technological, and medical applications. Using coarse-grained molecular dynamics simulations, here we investigate the properties of a polyelectrolyte solution, with explicit counterions and implicit solvent, that is driven by a steady electric field. By properly tuning the interplay between interparticle electrostatics and the applied electric field, we uncover two nonequilibrium continuous phase transitions as a function of the driving field. The first transition occurs from a homogeneously mixed phase to a macroscopically charge segregated phase, in which the polyelectrolyte solution self-organizes to form two lanes of like-charges, parallel to the applied field. We show that the fundamental underlying factor responsible for the emergence of this charge segregation in the presence of electric field is the excluded volume interactions of the drifting polyelectrolyte chains. As the drive is increased further, a re-entrant transition is observed from a charge segregated phase to a homogeneous phase. The re-entrance is signaled by the decrease in mobility of the monomers and counterions, as the electric field is increased. Furthermore, with multivalent counterions, a counterintuitive regime of negative differential mobility is observed, in which the charges move progressively slower as the driving field is increased. We show that all these features can be consistently explained by an intuitive trapping mechanism that operates between the oppositely moving charges, and present numerical evidence to support our claims. Parameter dependencies and phase diagrams are studied to better understand charge segregation in such driven polyelectrolyte solutions.

cond-mat.soft↗

arXiv2021

Heat transport in long-ranged anharmonic oscillator models

In this work, we perform a detailed study of heat transport in one dimensional long-ranged anharmonic oscillator systems, such as the long-ranged Fermi-Pasta-Ulam-Tsingou model. For these systems, the long-ranged anharmonic potential decays with distance as a power-law, controlled by an exponent $δ\geq 0$. For such a non-integrable model, one of the recent results that has captured quite some attention is the puzzling ballistic-like transport observed for $δ= 2$, reminiscent of integrable systems. Here, we first employ the reverse nonequilibrium molecular dynamics simulations to look closely at the $δ= 2$ transport in three long-ranged models, and point out a few problematic issues with this simulation method. Next, we examine the process of energy relaxation, and find that relaxation can be appreciably slow for $δ= 2$ in some situations. We invoke the concept of nonlinear localized modes of excitation, also known as discrete breathers, and demonstrate that the slow relaxation and the ballistic-like transport properties can be consistently explained in terms of a novel depinning of the discrete breathers that makes them highly mobile at $δ= 2$. Finally, in the presence of quartic pinning potentials we find that the long-ranged model exhibits Fourier (diffusive) transport at $δ= 2$, as one would expect from short-ranged interacting systems with broken momentum conservation. Such a diffusive regime is not observed for harmonic pinning.

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arXiv2020

Dynamics of a driven confined polyelectrolyte solution

The transport of polyelectrolytes confined by oppositely charged surfaces and driven by a constant electric field is of interest in studies of DNA separation according to size. Using molecular dynamics simulations that include surface polarization effect, we find that the mobilities of the polyelectrolytes and their counterions change non-monotonically with the confinement surface charge density. For an optimum value of the confinement charge density, efficient separation of polyelectrolytes can be achieved over a wide range of polyelectrolyte charge due to the differential friction imparted by the oppositely charged confinement on the polyelectrolyte chains. Furthermore, by altering the placement of the charged confinement counterions, enhanced polyelectrolyte separation can be achieved by utilizing surface polarization effect due to dielectric mismatch between the media inside and outside the confinement.

cond-mat.soft↗

arXiv2019

Polyelectrolyte solution under spatial and dielectric confinement

Polyelectrolytes under confinement are crucial for energy storage and for understanding biomolecular functions. Using molecular dynamics simulations, we analyze a polyelectrolyte solution confined between two oppositely charged planar dielectric surfaces and include surface polarization effects due to dielectric mismatch at the two electrodes. Although the effect of polarization on the charge distribution seems minor, we find that surface polarization enhances energy storage and also leads to the emergence of negative differential capacitance in confined polyelectrolyte solutions.

cond-mat.stat-mech↗

arXiv2017

Energy transport in the presence of long-range interactions

We study energy transport in the paradigmatic Hamiltonian mean-field (HMF) model and other related long-range interacting models using molecular dynamics simulations. We show that energy diffusion in the HMF model is subdiffusive in nature, which confirms a recently obtained intriguing result that, despite being globally interacting, this model is a thermal insulator in the thermo- dynamic limit. Surprisingly, when additional nearest neighbor interactions are introduced to the HMF model, an energy superdiffusion is observed. We show that these results can be consistently explained by studying energy localization due to thermally generated intrinsic localized excitation modes (discrete breathers) in nonlinear discrete systems. Our analysis for the HMF model can also be readily extended to more generic long-range interacting models where the interaction strength decays algebraically with the (shortest) distance between two lattice sites. This reconciles many of the apparently counter-intuitive results presented recently [C. Olivares and C. Anteneodo, Phys. Rev. E 94, 042117 (2016); D. Bagchi, Phys. Rev. E 95, 032102 (2017)] concerning energy transport in two such long-range interacting models.

cond-mat.stat-mech↗

arXiv2017

Fermi--Pasta--Ulam--Tsingou problems: Passage from Boltzmann to $q$-statistics

The Fermi-Pasta-Ulam (FPU) one-dimensional Hamiltonian includes a quartic term which guarantees ergodicity of the system in the thermodynamic limit. Consistently, the Boltzmann factor $P(ε) \sim e^{-βε}$ describes its equilibrium distribution of one-body energies, and its velocity distribution is Maxwellian, i.e., $P(v) \sim e^{- βv^2/2}$. We consider here a generalized system where the quartic coupling constant between sites decays as $1/d_{ij}^α$ $(α\ge 0; d_{ij} = 1,2,\dots)$. Through {\it first-principle} molecular dynamics we demonstrate that, for large $α$ (above $α\simeq 1$), i.e., short-range interactions, Boltzmann statistics (based on the {\it additive} entropic functional $S_B[P(z)]=-k \int dz P(z) \ln P(z)$) is verified. However, for small values of $α$ (below $α\simeq 1$), i.e., long-range interactions, Boltzmann statistics dramatically fails and is replaced by q-statistics (based on the {\it nonadditive} entropic functional $S_q[P(z)]=k (1-\int dz [P(z)]^q)/(q-1)$, with $S_1 = S_B$). Indeed, the one-body energy distribution is q-exponential, $P(ε) \sim e_{q_ε}^{-β_ε ε} \equiv [1+(q_ε - 1) β_εε]^{-1/(q_ε-1)}$ with $q_ε > 1$, and its velocity distribution is given by $P(v) \sim e_{q_v}^{ - β_v v^2/2}$ with $q_v > 1$. Moreover, within small error bars, we verify $q_ε = q_v = q$, which decreases from an extrapolated value q $\simeq$ 5/3 to q=1 when $α$ increases from zero to $α\simeq 1$, and remains q = 1 thereafter.

cond-mat.stat-mech↗

arXiv2017

Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions

We study the thermal transport properties of the one dimensional Fermi-Pasta-Ulam model ($β$-type) with long-range interactions. The strength of the long-range interaction decreases with the (shortest) distance between the lattice sites as ${distance}^{-δ}$, where $δ\ge 0$.Two Langevin heat baths at unequal temperatures are connected to the ends of the one dimensional lattice via short-range harmonic interactions that drive the system away from thermal equilibrium. In the nonequilibrium steady state the heat current, thermal conductivity and temperature profiles are computed by solving the equations of motion numerically. It is found that the conductivity $κ$ has an interesting non-monotonic dependence with $δ$ with a maximum at $δ= 2.0$ for this model. Moreover, at $δ= 2.0$, $κ$ diverges almost linearly with system size $N$ and the temperature profile has a negligible slope, as one expects in ballistic transport for an integrable system. We demonstrate that the non-monotonic behavior of the conductivity and the nearly ballistic thermal transport at $δ= 2.0$ obtained under nonequilibrium conditions can be explained consistently by studying the variation of largest Lyapunov exponent $λ_{max}$ with $δ$, and excess energy diffusion in the equilibrium microcanonical system.

cond-mat.stat-mech↗

arXiv2016

Sensitivity to initial conditions of a $d$-dimensional long-range-interacting quartic Fermi-Pasta-Ulam model: Universal scaling

We introduce a generalized $d$-dimensional Fermi-Pasta-Ulam (FPU) model in presence of long-range interactions, and perform a first-principle study of its chaos for $d=1,2,3$ through large-scale numerical simulations. The nonlinear interaction is assumed to decay algebraically as $d_{ij}^{-α}$ ($α\ge 0$), $\{d_{ij}\}$ being the distances between $N$ oscillator sites. Starting from random initial conditions we compute the maximal Lyapunov exponent $λ_{max}$ as a function of $N$. Our $N>>1$ results strongly indicate that $λ_{max}$ remains constant and positive for $α/d>1$ (implying strong chaos, mixing and ergodicity), and that it vanishes like $N^{-κ}$ for $0 \le α/d < 1$ (thus approaching weak chaos and opening the possibility of breakdown of ergodicity). The suitably rescaled exponent $κ$ exhibits universal scaling, namely that $(d+2) κ$ depends only on $α/d$ and, when $α/d$ increases from zero to unity, it monotonically decreases from unity to zero, remaining so for all $α/d >1$. The value $α/d=1$ can therefore be seen as a critical point separating the ergodic regime from the anomalous one, $κ$ playing a role analogous to that of an order parameter. This scaling law is consistent with Boltzmann-Gibbs statistics for $α/d > 1$, and possibly with $q$-statistics for $0 \le α/d < 1$.

cond-mat.stat-mech↗

arXiv2016

On the connection between linear combination of entropies and linear combination of extremizing distributions

We analyze the distribution that extremizes a linear combination of the Boltzmann--Gibbs entropy and the nonadditive $q$-entropy. We show that this distribution can be expressed in terms of a Lambert function. Both the entropic functional and the extremizing distribution can be associated with a nonlinear Fokker--Planck equation obtained from a master equation with nonlinear transition rates. Also, we evaluate the entropy extremized by a linear combination of a Gaussian distribution (which extremizes the Boltzmann--Gibbs entropy) and a $q$-Gaussian distribution (which extremizes the $q$-entropy). We give its explicit expression for $q=0$, and discuss the other cases numerically. The entropy that we obtain can be expressed, for $q=0$, in terms of Lambert functions, and exhibits a discontinuity in the second derivative for all values of $q<1$. The entire discussion is closely related to recent results for type-II superconductors and for the statistics of the standard map.

cond-mat.stat-mech↗

arXiv2015

A microscopic model of ballistic-diffusive crossover

Several low-dimensional systems show a crossover from diffusive to ballistic heat transport when system size is decreased. Although there is some phenomenological understanding of this crossover phenomena in the coarse grained level, a microscopic picture that consistently describes both the ballistic and the diffusive transport regimes has been lacking. In this work we derive a scaling from for the thermal current in a class of one dimensional systems attached to heat baths at boundaries, and show rigorously that the crossover occurs when the characteristic length scale of the system competes with the system size.

cond-mat.stat-mech↗

arXiv2014

Thermally driven classical Heisenberg chain with a spatially varying magnetic field: Thermal rectification and Negative differential thermal resistance

Thermal rectification and negative differential thermal resistance are two important features that have direct technological relevance. In this paper, we study the classical one dimensional Heisenberg model, thermally driven by heat baths attached at the two ends of the system, and in presence of an external magnetic field that varies monotonically in space. Heat conduction in this system is studied using a local energy conserving dynamics. It is found that, by suitably tuning the spatially varying magnetic field, the homogeneous symmetric system exhibits both thermal rectification and negative differential thermal resistance. Thermal rectification, in some parameter ranges, shows interesting dependences on the average temperature T and the system size N - rectification improves as T and N is increased. Using the microscopic dynamics of the spins we present a physical picture to explain the features observed in rectification as exhibited by this system and provide supporting numerical evidences. Emergence of NDTR in this system can be controlled by tuning the external magnetic field alone which can have possible applications in the fabrication of thermal devices.

cond-mat.stat-mech↗

arXiv2013

Thermal Rectification and Negative Differential Thermal Resistance in a driven two segment classical Heisenberg chain

We investigate thermal transport in a two segment classical Heisenberg spin chain with nearest neighbor interaction and in presence of external magnetic field using computer simulation. The system is thermally driven by heat baths attached at the two ends and transport properties are studied using an energy conserving dynamics. We demonstrate that by properly tuning the parameters thermal rectification can be achieved - the system behaves as a good conductor of heat along one direction but becomes a bad conductor when the thermal gradient is reversed and crucially depends on nonlinearity and spatial asymmetry. Moreover, suitable tuning of the system parameters gives rise to the counterintuitive and technologically important feature known as the negative differential thermal resistance (NDTR). We find that the crucial factor responsible for the emergence of NDTR is a suitable mechanism to impede the current in the bulk of the system.

cond-mat.stat-mech↗

arXiv2013

Thermally driven classical Heisenberg model in one dimension with a local time-varying field

We study thermal transport in the one dimensional classical Heisenberg model driven by boundary heat baths in presence of a local time varying magnetic field that acts at one end of the system. The system is studied numerically using an energy conserving discrete-time odd even dynamics. We find that the steady state energy current shows thermal resonance as the frequency of the time- periodic forcing is varied. When the amplitude of the forcing field is increased the system exhibits multiple resonance peaks instead of a single peak. Both single and multiresonance survive in the thermodynamic limit and their magnitudes increase as the average temperature of the system is decreased. Finally we show that, although a reversed thermal current can be made to flow through the bulk for a certain range of the forcing frequency, the system fails to behave as a heat pump, thus revalidating the fact that thermal pumping is generically absent in such force-driven lattices.

cond-mat.stat-mech↗

arXiv2012

Thermally driven classical Heisenberg model in one dimension

We study thermal transport in a classical one-dimensional Heisenberg model employing a discrete time odd even precessional update scheme. This dynamics equilibrates a spin chain for any arbitrary temperature and finite value of the integration time step $Δt$. We rigorously show that in presence of driving the system attains local thermal equilibrium which is a strict requirement of Fourier law. In the thermodynamic limit heat current for such a system obeys Fourier law for all temperatures, as has been recently shown [A. V. Savin, G. P. Tsironis, and X. Zotos, Phys. Rev. B 72, 140402(R) (2005)]. Finite systems, however, show an apparent ballistic transport which crosses over to a diffusive one as the system size is increased. We provide exact results for current and energy profiles in zero- and infinite-temperature limits.

cond-mat.stat-mech↗

arXiv2012

Spin diffusion in one-dimensional classical Heisenberg mode

The problem of spin diffusion is studied numerically in one-dimensional classical Heisenberg model using a deterministic odd even spin precession dynamics. We demonstrate that spin diffusion in this model, like energy diffusion, is normal and one obtains a long time diffusive tail in the decay of autocorrelation function (ACF). Some variations of the model with different coupling schemes and with anisotropy are also studied and we find normal diffusion in all of them. A systematic finite size analysis of the Heisenberg model also suggests diffusive spreading of fluctuation, contrary to previous claims of anomalous diffusion.

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arXiv2011

Phase Transition in an Exactly Solvable Extinction Model

We introduce a model of biological evolution where species evolve in response to biotic interactions and a fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective stress level is greater than their individual fitness. The model exhibits a phase transition to a completely extinct phase as the environmental stress or the mutation rate is varied. We discuss the generic conditions for which this transition is continuous. The model is exactly solvable and the critical behavior is characterized by an unusual dynamic exponent z=1/3. Apart from predicting large scale evolution, the model can be applied to understand the trends in the available fossil data.

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