arXiv subjects

Mehran Kardar

Publications and source records attributed to Mehran Kardar.

At least 55 records · Page 3Linked to original sources

arXiv2018

Localization of random walks to competing manifolds of distinct dimensions

We consider localization of a random walk (RW) when attracted or repelled by multiple extended manifolds of different dimensionalities. In particular, we focus on $(d-1)$- and $(d-2)$-dimensional manifolds in $d$-dimensional space, where attractive interactions are (fully or marginally) relevant. The RW can then be in one of four phases where it is localized to neither, one, or both manifolds. The four phases merge at a special multi-critical point where (away from the manifolds) the RW spreads diffusively. Extensive numerical analyses on two dimensional RWs confined inside or outside a rectangular wedge confirm general features expected from a continuum theory, but also exhibit unexpected attributes, such as a reentrant localization to the corner while repelled by it.

cond-mat.stat-mech↗

arXiv2018

Non-equilibrium forces following quenches in active and thermal matter

Non-equilibrium systems are known to exhibit long-ranged correlations due to conservation of quantities like density or momentum. This, in turn, leads to long-ranged fluctuation-induced (Casimir) forces, predicted to arise in a variety of non-equilibrium settings. Here, we study such forces, which arise transiently between parallel plates or compact inclusions in a gas of particles, following a change ("quench") in temperature or activity of the medium. Analytical calculations, as well as numerical simulations of passive or active Brownian particles, indicate two distinct forces: (i) The immediate effect of the quench is adsorption or desorption of particles of the medium to the immersed objects, which in turn initiates a front of relaxing (mean) density. This leads to time-dependent {\it density-induced forces}. (ii) A long-term effect of the quench is that density fluctuations are modified, manifested as transient (long-ranged) (pair-)correlations that relax diffusively to their (short-ranged) steady-state limit. As a result, transient {\it fluctuation-induced forces} emerge. We discuss the properties of fluctuation-induced and density-induced forces as regards universality, relaxation as a function of time, and scaling with distance between objects. Their distinct signatures allow us to distinguish the two types of forces in simulation data. Finally, we propose several scenarios for their experimental observation.

cond-mat.stat-mech↗

arXiv2018

How nonuniform contact profiles of T cell receptors modulate thymic selection outcomes

T cell receptors (TCRs) bind foreign or self-peptides attached to major histocompatibility complex (MHC) molecules, and the strength of this interaction determines T cell activation. Optimizing the ability of T cells to recognize a diversity of foreign peptides yet be tolerant of self-peptides is crucial for the adaptive immune system to properly function. This is achieved by selection of T cells in the thymus, where immature T cells expressing unique, stochastically generated TCRs interact with a large number of self-peptide-MHC; if a TCR does not bind strongly enough to any self-peptide-MHC, or too strongly with at least one self-peptide-MHC, the T cell dies. Past theoretical work cast thymic selection as an extreme value problem, and characterized the statistical enrichment or depletion of amino acids in the post-selection TCR repertoire, showing how T cells are selected to be able to specifically recognize peptides derived from diverse pathogens, yet have limited self-reactivity. Here, we investigate how the degree of enrichment is modified by nonuniform contacts that a TCR makes with peptide-MHC. Specifically, we were motivated by recent experiments showing that amino acids at certain positions of a TCR sequence have large effects on thymic selection outcomes, and crystal structure data that reveal a nonuniform contact profile between a TCR and its peptide-MHC ligand. Using a representative TCR contact profile as an illustration, we show via simulations that the degree of enrichment now varies by position according to the contact profile, and, importantly, it depends on the implementation of nonuniform contacts during thymic selection. We explain these nontrivial results analytically. Our study has implications for understanding the selection forces that shape the functionality of the post-selection TCR repertoire.

q-bio.PE↗

arXiv2017

Pinning and unbinding of (ideal) polymers from a wedge corner

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.

cond-mat.stat-mech↗

arXiv2017

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

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 ${\cal A} \, k_{B}T/h$, where $T$ is temperature. The amplitude ${\cal A}$ is akin to a critical exponent, depending only on geometry and universality of the polymer system. The value of ${\cal A}$, which we compute for simple geometries and ideal polymers, can be positive or negative. Remarkably, we find ${\cal A}=0$ 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).

cond-mat.stat-mech↗

arXiv2016

Transient Casimir forces from quenches in thermal and active matter

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.

cond-mat.stat-mech↗

arXiv2016

Active particles with soft and curved walls: Equation of state, ratchets, and instabilities

We study, from first principles, the pressure exerted by an active fluid of spherical particles on general boundaries in two dimensions. We show that, despite the non-uniform pressure along curved walls, an equation of state is recovered upon a proper spatial averaging. This holds even in the presence of pairwise interactions between particles or when asymmetric walls induce ratchet currents, which are accompanied by spontaneous shear stresses on the walls. For flexible obstacles, the pressure inhomogeneities lead to a modulational instability as well as to the spontaneous motion of short semi-flexible filaments. Finally, we relate the force exerted on objects immersed in active baths to the particle flux they generate around them.

cond-mat.stat-mech↗

arXiv2016

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

We study the shift of rotational levels of a diatomic polar molecule due to its van der Waals (vdW) 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 line widths and thermal broadening.

quant-ph↗

arXiv2016

Probability distributions for directed polymers in random media with correlated noise

The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in $d=1+1$ dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified in the presence of spatially correlated noise. The width of the distribution scales as the DPRM length to an exponent $β$, in good (but not full) agreement with previous renormalization group and numerical results. The scaled probability is well described by the Tracy-Widom form for uncorrelated noise, but becomes symmetric with increasing correlation exponent. We thus find a class of distributions that continuously interpolates between Tracy-Widom and Gaussian forms.

cond-mat.stat-mech↗

arXiv2016

Flight of a heavy particle nonlinearly coupled to a quantum bath

Fluctuation and dissipation are by-products of coupling to the `environment.' The Caldeira-Leggett model, a successful paradigm of quantum Brownian motion, views the environment as a collection of harmonic oscillators linearly coupled to the system. However, symmetry considerations may forbid a linear coupling, e.g. for a neutral particle in quantum electrodynamics. We argue that nonlinear couplings can lead to a fundamentally different behavior. Specifically, we consider a heavy particle quadratically coupled to quantum fluctuations of the bath. In one dimension the particle undergoes anomalous diffusion, unfolding as a power-law distribution in space, reminiscent of Lévy flights. We suggest condensed matter analogs where similar effects may arise.

quant-ph↗

arXiv2015

Coalescence Model for Crumpled Globules Formed in Polymer Collapse

The rapid collapse of a polymer, due to external forces or changes in solvent, yields a long-lived `crumpled globule.' The conjectured fractal structure shaped by hierarchical collapse dynamics has proved difficult to establish, even with large simulations. To unravel this puzzle, we study a coarse-grained model of in-falling spherical blobs that coalesce upon contact. Distances between pairs of monomers are assigned upon their initial coalescence, and do not `equilibrate' subsequently. Surprisingly, the model reproduces quantitatively the dependence of distance on segment length, suggesting that the slow approach to scaling is related to the wide distribution of blob sizes.

cond-mat.soft↗

arXiv2015

Identification of drug resistance mutations in HIV from constraints on natural evolution

Human immunodeficiency virus (HIV) evolves with extraordinary rapidity. However, its evolution is constrained by interactions between mutations in its fitness landscape. Here we show that an Ising model describing these interactions, inferred from sequence data obtained prior to the use of antiretroviral drugs, can be used to identify clinically significant sites of resistance mutations. Successful predictions of the resistance sites indicate progress in the development of successful models of real viral evolution at the single residue level, and suggest that our approach may be applied to help design new therapies that are less prone to failure even where resistance data is not yet available.

q-bio.PE↗

arXiv2015

Casimir--Polder force between anisotropic nanoparticles and gently curved surfaces

The Casimir--Polder interaction between an anisotropic particle and a surface is orientation dependent. We study novel orientational effects that arise due to curvature of the surface for distances much smaller than the radii of curvature by employing a derivative expansion. For nanoparticles we derive a general short distance expansion of the interaction potential in terms of their dipolar polarizabilities. Explicit results are presented for nano-spheroids made of SiO$_2$ and gold, both at zero and at finite temperatures. The preferred orientation of the particle is strongly dependent on curvature, temperature, as well as material properties.

quant-ph↗

arXiv2015

Fluctuation Induced Forces in Non-equilibrium (Diffusive) Dynamics

Thermal fluctuations in non-equilibrium steady states generically lead to power law decay of correlations for conserved quantities. Embedded bodies which constrain fluctuations in turn experience fluctuation induced forces. We compute these forces for the simple case of parallel slabs in a driven diffusive system. The force falls off with slab separation $d$ as $k_B T/d$ (at temperature $T$, and in all spatial dimensions), but can be attractive or repulsive. Unlike the equilibrium Casimir force, the force amplitude is non-universal and explicitly depends on dynamics. The techniques introduced can be generalized to study pressure and fluctuation induced forces in a broad class of non-equilibrium systems.

cond-mat.stat-mech↗

arXiv2014

Casimir-Polder interaction for gently curved surfaces

We use a derivative expansion for gently curved surfaces to compute the leading and the next-to-leading curvature corrections to the Casimir-Polder interaction between a polarizable small particle and a non-planar surface. While our methods apply to any homogeneous and isotropic surface, explicit results are presented here for perfect conductors. We show that the derivative expansion of the Casimir-Polder potential follows from a resummation of its perturbative series, for small in-plane momenta. We consider the retarded, non-retarded and classical high temperature limits.

quant-ph↗

arXiv2014

Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion

We study the implications of quantum fluctuations of a dispersive medium, under steady rotation, either in or out of thermal equilibrium with its environment. A rotating object exhibits a quantum instability by dissipating its mechanical motion via spontaneous emission of photons, as well as internal heat generation. Universal relations are derived for the radiated energy and angular momentum as trace formulas involving the object's scattering matrix. We also compute the quantum noise by deriving the full statistics of the radiated photons out of thermal and/or dynamic equilibrium. The (entanglement) entropy generation is quantified, and the total entropy is shown to be always increasing. Furthermore, we derive a Fokker-Planck equation governing the stochastic angular motion resulting from the fluctuating back-reaction frictional torque. As a result, we find a quantum limit on the uncertainty of the object's angular velocity in steady rotation. Finally, we show in some detail that a rotating object drags nearby objects, making them spin parallel to its axis of rotation. A scalar toy model is introduced in the first part to simplify the technicalities and ease the conceptual complexities; a detailed discussion of quantum electrodynamics is presented in the second part.

quant-ph↗

arXiv2013

Linear response relations in fluctuational electrodynamics

Near field radiative heat transfer and dynamic Casimir forces are just two instances of topics of technological and fundamental interest studied via the formalism of fluctuational electrodynamics. From the perspective of experiment and simulations, it is hard to precisely control and probe such non-equilibrium situations. Fluctuations in equilibrium are easier to measure, and can typically be related to non-equilibrium response functions by Green-Kubo relations. We consider a collection of arbitrary objects in vacuum, perturbed by changing the temperature or velocity of one object. Developing a method for computation of higher order correlation functions in fluctuational electrodynamics, we explicitly compare linear response and equilibrium fluctuations. We obtain a Green-Kubo relation for the radiative heat transfer, as well as a closed formula for the vacuum friction in arbitrary geometries in the framework of scattering theory. We comment on the signature of the radiative heat conductivity in equilibrium fluctuations.

quant-ph↗

arXiv2013

Quantum Cherenkov Radiation and Non-contact Friction

We present a number of arguments to demonstrate that a quantum analog of Cherenkov effect occurs when two dispersive objects are in relative motion. Specifically we show that two semi-infinite plates experience friction beyond a threshold velocity which, in their center-of-mass frame, is the phase speed of light within their medium. The loss in mechanical energy is radiated away through the plates before getting fully absorbed in the form of heat. By deriving various correlation functions inside and outside the two plates, we explicitly compute the radiation, and discuss its dependence on the reference frame.

quant-ph↗