arXiv subjects

Mehran Kardar

Publications and source records attributed to Mehran Kardar.

At least 145 records · Page 8Linked to original sources

arXiv1999

Collapse of Stiff Polyelectrolytes due to Counterion Fluctuations

The effective elasticity of highly charged stiff polyelectrolytes is studied in the presence of counterions, with and without added salt. The rigid polymer conformations may become unstable due to an effective attraction induced by counterion density fluctuations. Instabilities at the longest, or intermediate length scales may signal collapse to globule, or necklace states, respectively. In the presence of added-salt, a generalized electrostatic persistence length is obtained, which has a nontrivial dependence on the Debye screening length.

cond-mat.soft↗

arXiv1998

Path Integral Approach to the Dynamic Casimir Effect with Fluctuating Boundaries

A path integral formulation is developed for the dynamic Casimir effect. It allows us to study arbitrary deformations in space and time of the perfectly reflecting (conducting) boundaries of a cavity. The mechanical response of the intervening vacuum is calculated to linear order in the frequency-wavevector plane, using which a plethora of interesting phenomena can be studied. For a single corrugated plate we find a correction to mass at low frequencies, and an effective shear viscosity at high frequencies that are both anisotropic. The anisotropy is set by the wavevector of the corrugation. For two plates, the mass renormalization is modified by a function of the ratio between the separation of the plates and the wave-length of corrugations. The dissipation rate is not modified for frequencies below the lowest optical mode of the cavity, and there is a resonant dissipation for all frequencies greater than that. In this regime, a divergence in the response function implies that such high frequency deformation modes of the cavity can not be excited by any macroscopic external forces. This phenomenon is intimately related to resonant particle creation. For particular examples of two corrugated plates that are stationary, or moving uniformly in the lateral directions, Josephson-like effects are observed. For capillary waves on the surface of mercury a renormalization to surface tension, and sound velocity is obtained.

quant-ph↗

arXiv1998

Critical Hysteresis for n-Component Magnets

Earlier work on dynamical critical phenomena in the context of magnetic hysteresis for uniaxial (scalar) spins, is extended to the case of a multicomponent (vector) field. From symmetry arguments and a perturbative renormalization group approach (in the path integral formalism), it is found that the generic behavior at long time and length scales is described by the scalar fixed point (reached for a given value of the magnetic field and of the quenched disorder), with the corresponding Ising-like exponents. By tuning an additional parameter, however, a fully rotationally invariant fixed point can be reached, at which all components become critical simultaneously, with O(n)-like exponents. Furthermore, the possibility of a spontaneous non-equilibrium transverse ordering, controlled by a distinct fixed point, is unveiled and the associated exponents calculated. In addition to these central results, a didactic ``derivation'' of the equations of motion for the spin field are given, the scalar model is revisited and treated in a more direct fashion, and some issues pertaining to time dependences and the problem of multiple solutions within the path integral formalism are clarified.

cond-mat.stat-mech↗

arXiv1998

Ordering Phenomena on Growing Films

In many growth processes particles are highly mobile in an active layer at the surface, but are relatively immobile once incorporated in the bulk. We study models in which atoms are allowed to interact, equilibrate, and order on the surface, but are frozen in the bulk. Order parameter correlations in the resulting bulk material are highly anisotropic, reflecting its growth history. In a flat (layer by layer) growth mode, correlations perpendicular to the growth direction are similar to a two dimensional system in equilibrium, while parallel correlations reflect the dynamics of such a system. When the growing film is rough, various couplings between height and order parameter fluctuations are possible. Such couplings modify the dynamic scaling properties of surface roughness, and may also change the critical behavior of the order parameter. Even the deterministic growth of the surface profile can result in interesting textures for the order parameter.

cond-mat.soft↗

arXiv1998

Melting of Flux Lines in an Alternating Parallel Current

We use a Langevin equation to examine the dynamics and fluctuations of a flux line (FL) in the presence of an {\it alternating longitudinal current} $J_{\parallel}(ω)$. The magnus and dissipative forces are equated to those resulting from line tension, confinement in a harmonic cage by neighboring FLs, parallel current, and noise. The resulting mean-square FL fluctuations are calculated {\it exactly}, and a Lindemann criterion is then used to obtain a nonequilibrium `phase diagram' as a function of the magnitude and frequency of $J_{\parallel}(ω)$. For zero frequency, the melting temperature of the mixed phase (a lattice, or the putative "Bose" or "Bragg Glass") vanishes at a limiting current. However, for any finite frequency, there is a non-zero melting temperature.

cond-mat.stat-mech↗

arXiv1998

Generalizing the O(N)-field theory to N-colored manifolds of arbitrary internal dimension D

We introduce a geometric generalization of the O(N)-field theory that describes N-colored membranes with arbitrary dimension D. As the O(N)-model reduces in the limit N->0 to self-avoiding polymers, the N-colored manifold model leads to self-avoiding tethered membranes. In the other limit, for inner dimension D->1, the manifold model reduces to the O(N)-field theory. We analyze the scaling properties of the model at criticality by a one-loop perturbative renormalization group analysis around an upper critical line. The freedom to optimize with respect to the expansion point on this line allows us to obtain the exponent νof standard field theory to much better precision that the usual 1-loop calculations. Some other field theoretical techniques, such as the large N limit and Hartree approximation, can also be applied to this model. By comparison of low and high temperature expansions, we arrive at a conjecture for the nature of droplets dominating the 3d-Ising model at criticality, which is satisfied by our numerical results. We can also construct an appropriate generalization that describes cubic anisotropy, by adding an interaction between manifolds of the same color. The two parameter space includes a variety of new phases and fixed points, some with Ising criticality, enabling us to extract a remarkably precise value of 0.6315 for the exponent νin d=3. A particular limit of the model with cubic anisotropy corresponds to the random bond Ising problem; unlike the field theory formulation, we find a fixed point describing this system at 1-loop order.

cond-mat↗

arXiv1998

A geometric generalization of field theory to manifolds of arbitrary dimension

We introduce a generalization of the O(N) field theory to N-colored membranes of arbitrary inner dimension D. The O(N) model is obtained for D->1, while N->0 leads to self-avoiding tethered membranes (as the O(N) model reduces to self-avoiding polymers). The model is studied perturbatively by a 1-loop renormalization group analysis, and exactly as N->infinity. Freedom to choose the expansion point D, leads to precise estimates of critical exponents of the O(N) model. Insights gained from this generalization include a conjecture on the nature of droplets dominating the 3d-Ising model at criticality; and the fixed point governing the random bond Ising model.

cond-mat↗

arXiv1998

The `Friction' of Vacuum, and other Fluctuation-Induced Forces

The static Casimir effect describes an attractive force between two conducting plates, due to quantum fluctuations of the electromagnetic (EM) field in the intervening space. {\it Thermal fluctuations} of correlated fluids (such as critical mixtures, super-fluids, liquid crystals, or electrolytes) are also modified by the boundaries, resulting in finite-size corrections at criticality, and additional forces that effect wetting and layering phenomena. Modified fluctuations of the EM field can also account for the `van der Waals' interaction between conducting spheres, and have analogs in the fluctuation--induced interactions between inclusions on a membrane. We employ a path integral formalism to study these phenomena for boundaries of arbitrary shape. This allows us to examine the many unexpected phenomena of the dynamic Casimir effect due to moving boundaries. With the inclusion of quantum fluctuations, the EM vacuum behaves essentially as a complex fluid, and modifies the motion of objects through it. In particular, from the mechanical response function of the EM vacuum, we extract a plethora of interesting results, the most notable being: (i) The effective mass of a plate depends on its shape, and becomes anisotropic. (ii) There is dissipation and damping of the motion, again dependent upon shape and direction of motion, due to emission of photons. (iii) There is a continuous spectrum of resonant cavity modes that can be excited by the motion of the (neutral) boundaries.

cond-mat↗

arXiv1997

Threading dislocation lines in two-sided flux array decorations

Two-sided flux decoration experiments indicate that threading dislocation lines (TDLs), which cross the entire film, are sometimes trapped in metastable states. We calculate the elastic energy associated with the meanderings of a TDL. The TDL behaves as an anisotropic and dispersive string with thermal fluctuations largely along its Burger's vector. These fluctuations also modify the structure factor of the vortex solid. Both effects can in principle be used to estimate the elastic moduli of the material.

cond-mat.supr-con↗

arXiv1997

Nonequilibrium Dynamics of Interfaces and Lines

The lectures examine several problems related to non-equilibrium fluctuations of interfaces and flux lines. The first two introduce the phenomenology of depinning, with particular emphasis on interfaces and contact lines. The role of the anisotropy of the medium in producing different universality classes is elucidated. The last two lectures focus on the dynamics of lines, where transverse fluctuations are also important. We shall demonstrate how various non-linearities appear in the dynamics of driven flux lines. The universality classes of depinning, and also dynamic roughening, are illustrated in the contexts of moving flux lines, advancing crack fronts, and drifting polymers.

cond-mat.stat-mech↗

arXiv1997

The Mechanical Response of Vacuum

quant-ph↗

arXiv1996

Winding Angle Distributions for Directed Polymers

We study analytically and numerically the winding of directed polymers of length $t$ around each other or around a rod. Unconfined polymers in pure media have exponentially decaying winding angle distributions, the decay constant depending on whether the interaction is repulsive or neutral, but not on microscopic details. In the presence of a chiral asymmetry, the exponential tails become non universal. In all these cases the mean winding angle is proportional to $\ln t$. When the polymer is confined to a finite region around the winding center, e.g. due to an attractive interaction, the winding angle distribution is Gaussian, with a variance proportional to $t$. We also examine the windings of polymers in random systems. Our results suggest that randomness reduces entanglements, leading to a narrow (Gaussian) distribution with a mean winding angle of the order of $\sqrt{\ln t}$.

cond-mat.stat-mech↗

arXiv1996

A Model for Growth of Binary Alloys with Fast Surface Equilibration

We study a simple growth model for (d+1)-dimensional films of binary alloys in which atoms are allowed to interact and equilibrate at the surface, but are frozen in the bulk. The resulting crystal is highly anisotropic: Correlations perpendicular to the growth direction are identical to a d-dimensional two-layer system in equilibrium, while parallel correlations generally reflect the (Glauber) dynamics of such a system. For stronger in-plane interactions, the correlation volumes change from oblate to highly prolate shapes near a critical demixing or ordering transition. In d=1, the critical exponent z relating the scaling of the two correlation lengths varies continuously with the chemical interactions.

cond-mat.stat-mech↗

arXiv1996

Freezing Transition of Compact Polyampholytes

Polyampholytes (PAs) are heteropolymers with long range Coulomb interactions. Unlike polymers with short range forces, PA energy levels have non-vanishing correlations and are thus very different from the Random Energy Model (REM). Nevertheless, if charges in the PA globule are screened as in a regular plasma, PAs freeze in REM fashion. Our results shed light on the potential role of Coulomb interactions in folding and evolution of {\it proteins}, which are weakly charged PAs, in particular making connection with the finding that sequences of charged amino acids in proteins are not random.

cond-mat↗

arXiv1996

Fluctuation-Induced Interactions between Rods on a Membrane

We consider the interaction between two rods embedded in a fluctuating surface. The modification of fluctuations by the rods leads to an attractive long-range interaction between them. We consider fluctuations governed by either surface tension (films) or bending rigidity (membranes). In both cases the interaction falls off with the separation of the rods as $1/R^4$. The orientational part of the interaction is proportional to $\cos^2\left[ θ_1+θ_2 \right]$ in the former case, and to $\cos^2\left[ 2\left(θ_1+θ_2\right) \right]$ in the latter, where $θ_1$ and $θ_2$ are angles between the rods and the line joining them. These interactions are somewhat reminiscent of dipolar forces and will tend to align collections of such rods into chains.

cond-mat↗

arXiv1996

Conformations of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M< (N/M)^(nu). The number of links needed to collapse a polymer in three dimensions thus scales as N^(phi), with (phi) > 0.43.

cond-mat↗

arXiv1996

Collapse of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N. This result is inconsistent with results obtained from free energy considerations by Brygelson and Thirumalai (PRL76, 542 (1996)).

cond-mat↗

arXiv1996

Winding Angle Distributions for Random Walks and Flux Lines

We study analytically and numerically the winding of a flux line around a columnar defect. Reflecting and absorbing boundary conditions apply to marginal or repulsive defects, respectively. In both cases, the winding angle distribution decays exponentially for large angles, with a decay constant depending only on the boundary condition, but not on microscopic features. New {\it non-universal} distributions are encountered for {\it chiral} defects which preferentially twist the flux line in one direction. The resulting asymmetric distributions have decay constants that depend on the degree of chirality. In particular, strong chirality encourages entanglements and leads to broad distributions. We also examine the windings of flux lines in the presence of point impurities (random bonds). Our results suggest that pinning to impurities reduces entanglements, leading to a narrow (Gaussian) distribution.

cond-mat↗