Showing papers by "Mehran Kardar published in 2017"

Nonequilibrium Fluctuational Quantum Electrodynamics: Heat Radiation, Heat Transfer, and Force

Abstract: Quantum and thermal fluctuations of electromagnetic waves are the cornerstone of quantum and statistical physics, and inherent to such phenomena as thermal radiation and van der Waals forces. While the basic principles are the material of elementary texts, recent experimental and technological advances have made it necessary to come to terms with counterintuitive consequences of electromagnetic fluctuations at short scales -- in the so called {\it near-field} regime. We focus on three manifestations of such behavior: {\bf (i)} The Stefan--Boltzmann law describes thermal radiation from macroscopic bodies, but fails to account for magnitude, polarization and coherence of radiation from small objects (say compared to the skin depth). {\bf (ii)} The heat transfer between two bodies at similar close proximity is dominated by evanescent waves, and can be several orders of magnitude larger than the classical contribution due to propagating waves. {\bf (iii)} Casimir/van der Waals interactions are a dominant force between objects at sub-micron separation; the non-equilibrium analogs of this force (for objects at different temperatures) have not been sufficiently explored (at least experimentally). To explore these phenomena we introduce the tool of fluctuational quantum electrodynamics (QED) originally introduced by Rytov in the 1950s. Combined with a scattering formalism, this enables studies of heat radiation and transfer, equilibrium and non-equilibrium forces for objects of different material properties, shapes, separations and arrangements.

A Population Dynamics Model for Clonal Diversity in a Germinal Center.

Abstract: Germinal centers (GCs) are micro-domains where B cells mature to develop high affinity antibodies. Inside a GC, B cells compete for antigen and T cell help, and the successful ones continue to evolve. New experimental results suggest that, under identical conditions, a wide spectrum of clonal diversity is observed in different GCs, and high affinity B cells are not always the ones selected. We use a birth, death and mutation model to study clonal competition in a GC over time. We find that, like all evolutionary processes, diversity loss is inherently stochastic. We study two selection mechanisms, birth-limited and death limited selection. While death limited selection maintains diversity and allows for slow clonal homogenization as affinity increases, birth limited selection results in more rapid takeover of successful clones. Finally, we qualitatively compare our model to experimental observations of clonal selection in mice.

Transient Casimir Forces from Quenches in Thermal and Active Matter

Abstract: We compute fluctuation-induced (Casimir) forces for classical systems after a temperature quench. Using a generic coarse-grained model for fluctuations of a conserved density, we find that transient forces arise even if the initial and final states are force free. In setups reminiscent of Casimir (planar walls) and van der Waals (small inclusions) interactions, we find comparable exact universal expressions for the force. Dynamical details only scale the time axis of transient force curves. We propose that such quenches can be achieved, for instance, in experiments on active matter, employing tunable activity or interaction protocols.

Attractive and repulsive polymer-mediated forces between scale-free surfaces.

Abstract: We consider forces acting on objects immersed in, or attached to, long fluctuating polymers. The confinement of the polymer by the obstacles results in polymer-mediated forces that can be repulsive (due to loss of entropy) or attractive (if some or all surfaces are covered by adsorbing layers). The strength and sign of the force in general depends on the detailed shape and adsorption properties of the obstacles but assumes simple universal forms if characteristic length scales associated with the objects are large. This occurs for scale-free shapes (such as a flat plate, straight wire, or cone) when the polymer is repelled by the obstacles or is marginally attracted to it (close to the depinning transition where the absorption length is infinite). In such cases, the separation h between obstacles is the only relevant macroscopic length scale, and the polymer-mediated force equals Ak_{B}T/h, where T is temperature. The amplitude A is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of A, which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find A=0 for ideal polymers at the adsorption transition point, irrespective of shapes of the obstacles, i.e., at this special point there is no polymer-mediated force between obstacles (scale free or not).

Pinning and unbinding of ideal polymers from a wedge corner

Abstract: A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a repulsive wedge. The well-known mapping between the statistical mechanics of an ideal polymer and the quantum problem of a particle in a potential is then used to analyze the singular behavior of the unbinding transition of the polymer. The divergence of the localization length is found to be governed by an exponent that varies continuously with the angle (when reflex). Numerical treatment of the discrete (lattice) version of such an adsorption problem confirms this behavior.

Publisher’s Note: Transient Casimir Forces from Quenches in Thermal and Active Matter [Phys. Rev. Lett. 118 , 015702 (2017)]

Abstract: This corrects the article DOI: 10.1103/PhysRevLett.118.015702.

Pinning and unbinding of ideal polymers from a wedge corner.

Abstract: A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a repulsive wedge. The well-known mapping between the statistical mechanics of an ideal polymer and the quantum problem of a particle in a potential is then used to analyze the singular behavior of the unbinding transition of the polymer. The divergence of the localization length is found to be governed by an exponent that varies continuously with the angle (when reflex). Numerical treatment of the discrete (lattice) version of such an adsorption problem confirms this behavior.

Optimal paths on the road network as directed polymers.

Abstract: We analyze the statistics of the shortest and fastest paths on the road network between randomly sampled end points We find that, to a good approximation, the optimal paths can be described as directed polymers in a disordered medium, which belong to the Kardar-Parisi-Zhang universality class of interface roughening Comparing the scaling behavior of our data with simulations of directed polymers and previous theoretical results, we are able to point out the few characteristics of the road network that are relevant to the large-scale statistics of optimal paths Indeed, we show that the local structure is akin to a disordered environment with a power-law distribution which become less important at large scales where long-ranged correlations in the network control the scaling behavior of the optimal paths

Spectroscopic Probe of the van der Waals Interaction between Polar Molecules and a Curved Surface

Abstract: We study the shift of rotational levels of a diatomic polar molecule due to its van der Waals interaction with a gently curved dielectric surface at temperature $T$, and submicron separations. The molecule is assumed to be in its electronic and vibrational ground state, and the rotational degrees are described by a rigid rotor model. We show that under these conditions retardation effects and surface dispersion can be neglected. The level shifts are found to be independent of $T$, and given by the quantum state averaged classical electrostatic interaction of the dipole with its image on the surface. We use a derivative expansion for the static Green's function to express the shifts in terms of surface curvature. We argue that the curvature induced line splitting is experimentally observable, and not obscured by natural linewidths and thermal broadening.

Pinning of Diffusional Instabilities by Non-Uniform Curvature

Abstract: Turing patterns emerge from a spatially uniform state following a linear instability driven by diffusion. Features of the eventual pattern (stabilized by non-linearities) are already present in the initial unstable modes. On a uniform flat surface or perfect sphere, the unstable modes and final patterns are degenerate, reflecting translational/rotational symmetry. This symmetry can be broken, e.g. by a bump on a flat substrate or by deforming a sphere. As the diffusion operator on a two dimensional manifold depends on the underlying curvature, the degeneracy of the initial unstable mode is similarly reduced. Different shapes can pin different modes. We adapt methods of conformal mapping and perturbation theory to analytically examine how bumps and ripples entrain modes of the diffusion operator on cylinders and spheres. We confirm these results numerically, and provide closed form expressions that describe how non-uniformities in curvature pin diffusion-driven instabilities and the resulting patterns.