arXiv subjects

Chandan Dasgupta

Publications and source records attributed to Chandan Dasgupta.

87 records · Page 5Linked to original sources

arXiv2003

Mound formation and coarsening from a nonlinear instability in surface growth

We study a class of one-dimensional, nonequilibrium, conserved growth equations for both nonconserved and conserved noise statistics using numerical integration. An atomistic version of these growth equations is also studied using stochastic simulation. The models with nonconserved noise statistics are found to exhibit mound formation and power-law coarsening with slope selection for a range of values of the model parameters. Unlike previously proposed models of mound formation, the Ehrlich-Schwoebel step-edge barrier, usually modeled as a linear instability in growth equations, is absent in our models. Mound formation in our models occurs due to a nonlinear instability in which the height (depth) of spontaneously generated pillars (grooves) increases rapidly if the initial height (depth) is sufficiently large. When this instability is controlled by the introduction of an infinite number of higher-order gradient nonlinearities, the system exhibits a first-order dynamical phase transition from a rough self-affine phase to a mounded one as the value of the parameter that measures the effectiveness of control is decreased. We define a new ``order parameter'' that may be used to distinguish between these two phases. In the mounded phase, the system exhibits power-law coarsening of the mounds in which a selected slope is retained at all times. The coarsening exponents for the continuum equation and the discrete model are found to be different. An explanation of this difference is proposed and verified by simulations. In the growth equation with conserved noise, we find the curious result that the kinetically rough and mounded phases are both locally stable in a region of parameter space. In this region, the initial configuration of the system determines its steady-state behavior.

cond-mat.stat-mech↗

arXiv2003

Structure and Magnetization of Two-Dimensional Vortex Arrays in the Presence of Periodic Pinning

Ground-state properties of a two-dimensional system of superconducting vortices in the presence of a periodic array of strong pinning centers are studied analytically and numerically. The ground states of the vortex system at different filling ratios are found using a simple geometric argument under the assumption that the penetration depth is much smaller than the spacing of the pin lattice. The results of this calculation are confirmed by numerical studies in which simulated annealing is used to locate the ground states of the vortex system. The zero-temperature equilibrium magnetization as a function of the applied field is obtained by numerically calculating the energy of the ground state for a large number of closely spaced filling ratios. The results show interesting commensurability effects such as plateaus in the B-H diagram at simple fractional filling ratios.

cond-mat.supr-con↗

arXiv2002

Vortices in layered superconductors with columnar pins: A density functional study

We use numerical minimization of a model free energy functional to study the effects of columnar pinning centers on the structure and thermodynamics of a system of pancake vortices in the mixed phase of highly anisotropic layered superconductors. The magnetic field and the columnar pins are assumed to be perpendicular to the layers. Our methods allow us to study in detail the density distribution of vortices in real space. We present results for the dependence of the average number of vortices trapped at a pinning center on temperature and pinning strength, and for the effective interaction between nearby pinned vortices arising from short-range correlations in the vortex liquid. For a commensurate, periodic array of pinning centers, we find a line of first order vortex lattice melting transitions in the temperature $T$ vs. pin concentration $c$ plane, which terminates at an experimentally accessible critical point as $c$ is increased. Beyond this point, the transition is replaced by a crossover. Our results should also apply, with little change, to thin-film superconductors with strong point pinning.

cond-mat.supr-con↗

arXiv2001

Vortex lattice melting in layered superconductors with periodic columnar pins

The melting transition of the vortex lattice in highly anisotropic, layered superconductors with commensurate, periodic columnar pins is studied in a geometry where magnetic field and columnar pins are normal to the layers. Thermodynamic properties and equilibrium density distributions are obtained from numerical minimizations of an appropriate free-energy functional. We find a line of first-order transitions that ends at a critical point as the pin concentration is increased. A simple Landau theory providing a semi-quantitative explanation of the numerical results is proposed.

cond-mat.supr-con↗

arXiv2000

Equilibrium and dynamical properties of the ANNNI chain at the multiphase point

We study the equilibrium and dynamical properties of the ANNNI (axial next-nearest-neighbor Ising) chain at the multiphase point. An interesting property of the system is the macroscopic degeneracy of the ground state leading to finite zero-temperature entropy. In our equilibrium study we consider the effect of softening the spins. We show that the degeneracy of the ground state is lifted and there is a qualitative change in the low temperature behaviour of the system with a well defined low temperature peak of the specific heat that carries the thermodynamic ``weight'' of the ground state entropy. In our study of the dynamical properties, the stochastic Kawasaki dynamics is considered. The Fokker-Planck operator for the process corresponds to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with constraints on allowed states. This leads to a number of differences in its properties which are obtained through exact numerical diagonalization, simulations and by obtaining various analytic bounds.

cond-mat.stat-mech↗

arXiv2000

Phase Diagram Of A Hard-sphere System In A Quenched Random Potential: A Numerical Study

We report numerical results for the phase diagram in the density-disorder plane of a hard sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.

cond-mat.dis-nn↗

arXiv2000

Free Energy Landscape Of Simple Liquids Near The Glass Transition

Properties of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form are investigated numerically. A considerable number of glassy local minima of the free energy are located and the distribution of an appropriately defined ``overlap'' between minima is calculated. The process of transition from the basin of attraction of a minimum to that of another one is studied using a new ``microcanonical'' Monte Carlo procedure, leading to a determination of the effective height of free energy barriers that separate different glassy minima. The general appearance of the free energy landscape resembles that of a putting green: deep minima separated by a fairly flat structure. The growth of the effective free-energy barriers with increasing density is consistent with the Vogel-Fulcher law, and this growth is primarily driven by an entropic mechanism.

cond-mat.dis-nn↗

arXiv2000

Phase Diagram of a Classical Fluid in a Quenched Random Potential

We consider the phase diagram of a classical fluid in the presence of a random pinning potential of arbitrary strength. Introducing replicas for averaging over the quenched disorder, we use the hypernetted chain approximation to calculate the correlations in the replicated liquid. The freezing transition of the liquid into a nearly crystalline state is studied using a density functional approach, and the liquid-to-glass transition is studied using a phenomenological replica symmetry breaking approach introduced by Mezard and Parisi. The first-order liquid-to-crystal transition is found to change to a continuous liquid-to-glass transition as the strength of the disorder is increased above a threshold value.

cond-mat↗

arXiv1999

The triangular Ising antiferromagnet in a staggered field

We study the equilibrium properties of the nearest-neighbor Ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states. Using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice, we classify the ground states into sectors specified by the number of ``strings''. We show that the effect of the staggered field is to generate long-range interactions between strings. In the limiting case of the antiferromagnetic coupling constant J becoming infinitely large, we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature. For finite J, we study the equilibrium properties of the system using Monte Carlo simulations with three different dynamics. We find that in all the three cases, equilibration times for low field values increase rapidly with system size at low temperatures. Due to this difficulty in equilibrating sufficiently large systems at low temperatures, our finite-size scaling analysis of the numerical results does not permit a definite conclusion about the existence of a phase transition for finite values of J. A surprising feature in the system is the fact that unlike usual glassy systems, a zero-temperature quench almost always leads to the ground state, while a slow cooling does not.

cond-mat.stat-mech↗

arXiv1999

Muon-Spin Rotation Spectra in the Mixed Phase of High-T_c Superconductors : Thermal Fluctuations and Disorder Effects

We study muon-spin rotation (muSR) spectra in the mixed phase of highly anisotropic layered superconductors, specifically Bi_2+xSr_2-xCaCu_2O_8+delta (BSCCO), by modeling the fluid and solid phases of pancake vortices using liquid-state and density functional methods. The role of thermal fluctuations in causing motional narrowing of muSR lineshapes is quantified in terms of a first-principles theory of the flux-lattice melting transition. The effects of random point pinning are investigated using a replica treatment of liquid state correlations and a replicated density functional theory. Our results indicate that motional narrowing in the pure system, although substantial, cannot account for the remarkably small linewidths obtained experimentally at relatively high fields and low temperatures. We find that satisfactory agreement with the muSR data for BSCCO in this regime can be obtained through the ansatz that this ``phase'' is characterized by frozen short-range positional correlations reflecting the structure of the liquid just above the melting transition. This proposal is consistent with recent suggestions of a ``pinned liquid'' or ``glassy'' state of pancake vortices in the presence of pinning disorder. Our results for the high-temperature liquid phase indicate that measurable linewidths may be obtained in this phase as a consequence of density inhomogeneities induced by the pinning disorder. The results presented here comprise a unified, first-principles theoretical treatment of muSR spectra in highly anisotropic layered superconductors in terms of a controlled set of approximations.

cond-mat.supr-con↗

arXiv1998

Free energy landscape in a dense hard sphere system

The topography of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form is investigated numerically using a ``microcanonical'' Monte Carlo procedure. We locate a considerable number of glassy local minima of the free energy and analyze the distributions of the free energy at a minimum and an appropriately defined phase-space ``distance'' between different minima. We find evidence for the existence of pairs of closely related glassy minima (``two-level systems''). We also investigate the way the system makes transitions as it moves from the basin of attraction of a minimum to that of another one after a start under nonequilibrium conditions. This allows us to determine the effective height of free energy barriers that separate a glassy minimum from the others. The dependence of the height of free energy barriers on the density is investigated in detail. The general appearance of the free energy landscape resembles that of a putting green: relatively deep minima separated by a fairly flat structure. We discuss the connection of our results with the Vogel-Fulcher law and relate our observations to other work on the glass transition.

cond-mat.dis-nn↗

arXiv1998

Extended Self-similarity in Kinetic Surface Roughening

We show from numerical simulations that a limited mobility solid-on-solid model of kinetically rough surface growth exhibits extended self-similarity analogous to that found in fluid turbulence. The range over which scale-independent power-law behavior is observed is significantly enhanced if two correlation functions of different order, such as those representing two different moments of the difference in height between two points, are plotted against each other. This behavior, found in both one and two dimensions, suggests that the `relative' exponents may be more fundamental than the `absolute' ones.

cond-mat.stat-mech↗

arXiv1997

Entropic Origin of the Growth of Relaxation Times in Simple Glassy Liquids

Transitions between ``glassy'' local minima of a model free-energy functional for a dense hard-sphere system are studied numerically using a ``microcanonical'' Monte Carlo method that enables us to obtain the transition probability as a function of the free energy and the Monte Carlo ``time''. The growth of the height of the effective free energy barrier with density is found to be consistent with a Vogel-Fulcher law. The dependence of the transition probability on time indicates that this growth is primarily due to entropic effects arising from the difficulty of finding low-free-energy saddle points connecting glassy minima.

cond-mat.soft↗

arXiv1996

Time Scales for transitions between free energy minima of a hard sphere system

Time scales associated with activated transitions between glassy metastable states of a free energy functional appropriate for a dense hard sphere system are calculated by using a new Monte Carlo method for the local density variables. We calculate the time the system,initially placed in a shallow glassy minimum of the free energy, spends in the neighborhood of this minimum before making a transition to the basin of attarction of another free energy minimum. This time scale is found to increase with the average density. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This scale shows no evidence of dependence on sample size.

cond-mat↗

arXiv1993

Nonlinear Hydrodynamics of a Hard Sphere Fluid Near the Glass Transition

We conduct a numerical study of the dynamic behavior of a dense hard sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free energy functional of the Ramakrishnan-Yussouff form. We find that the system exhibits glassy behavior as evidenced through stretched exponential decay and two-stage relaxation of the density correlation function. The characteristic times grow with increasing density according to the Vogel-Fulcher law. The wavenumber dependence of the kinetics is extensively explored. The connection of our results with experiment, mode coupling theory, and molecular dynamics results is discussed.

cond-mat↗