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M. Kardar

Publications and source records attributed to M. Kardar.

At least 19 recordsLinked to original sources
arXiv2020

Distinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wavefunction amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: phase transitions which are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions which are continuous become governed by new critical exponents. We introduce a more general class of models which encompasses both cases, and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.

cond-mat.stat-mech↗
arXiv2017

Optimal paths on the road network as directed polymers

We analyze the statistics of the shortest and fastest paths on the road network between randomly sampled end points. To a good approximation, these optimal paths are found to be directed in that their lengths (at large scales) are linearly proportional to the absolute distance between them. This motivates comparisons to universal features of directed polymers in random media. There are similarities in scalings of fluctuations in length/time and transverse wanderings, but also important distinctions in the scaling exponents, likely due to long-range correlations in geographic and man-made features. At short scales the optimal paths are not directed due to circuitous excursions governed by a fat-tailed (power-law) probability distribution.

cond-mat.stat-mech↗
arXiv2016

Non-equilibrium Fluctuational Quantum Electrodynamics: Heat Radiation, Heat Transfer, and Force

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.

cond-mat.other↗
arXiv2015

Pressure is not a state function for generic active fluids

Pressure is the mechanical force per unit area that a confined system exerts on its container. In thermal equilibrium, it depends only on bulk properties (density, temperature, etc.) through an equation of state. Here we show that in a wide class of active systems the pressure depends on the precise interactions between the active particles and the confining walls. In general, therefore, active fluids have no equation of state, their mechanical pressures exhibit anomalous properties that defy the familiar thermodynamic reasoning that holds in equilibrium. The pressure remains a function of state, however, in some specific and well-studied active models that tacitly restrict the character of the particle-wall and/or particle-particle interactions.

cond-mat.stat-mech↗
arXiv2015

Pressure and Phase Equilibria in Interacting Active Brownian Spheres

We derive from first principles the mechanical pressure $P$, defined as the force per unit area on a bounding wall, in a system of spherical, overdamped, active Brownian particles at density $ρ$. Our exact result relates $P$, in closed form, to bulk correlators and shows that (i) $P(ρ)$ is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to $P$, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; (iii) $P(ρ)$ is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles, and show that the densities at coexistence do not satisfy a Maxwell construction on $P$.

cond-mat.soft↗
arXiv2014

Reversing the Critical Casimir force by shape deformation

The exact critical Casimir force between periodically deformed boundaries of a 2D semi-infinite strip is obtained for conformally invariant classical systems. Only two parameters (conformal charge and scaling dimension of a boundary changing operator), along withthe solution of an electrostatic problem, determine the Casimir force, rendering the theory practically applicable to any shape and arrangement. The attraction between any two mirror symmetric objects follows directly from our general result. The possibility of purely shape induced reversal of the force, as well as occurrence of stable equilibrium points, is demonstrated for certain conformally invariant models, including the tricritical Ising model.

cond-mat.stat-mech↗
arXiv2013

Conformal Field Theory of Critical Casimir Interactions in 2D

Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two dimensional (2D) conformal field theories (CFT) we derive an exact result for the Casimir interaction between two objects of arbitrary shape, in terms of (1) the free energy of a circular ring whose radii are determined by the mutual capacitance of two conductors with the objects' shape; and (2) a purely geometric energy that is proportional to conformal charge of the CFT, but otherwise super-universal in that it depends only on the shapes and is independent of boundary conditions and other details.

cond-mat.stat-mech↗
arXiv2012

Material dependence of Casimir forces: gradient expansion beyond proximity

A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA). While this approximation is asymptotically exact at vanishing separations, quantifying corrections to PFA has been notoriously difficult. Here we use a derivative expansion to compute the leading curvature correction to PFA for metals (gold) and insulators (SiO$_2$) at room temperature. We derive an explicit expression for the amplitude $\hatθ_1$ of the PFA correction to the force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the Casimir free energy are found to scale logarithmically with distance. For gold, $\hatθ_1$ has an unusually large temperature dependence.

quant-ph↗
arXiv2011

Casimir forces beyond the proximity approximation

The proximity force approximation (PFA) relates the interaction between closely spaced, smoothly curved objects to the force between parallel plates. Precision experiments on Casimir forces necessitate, and spur research on, corrections to the PFA. We use a derivative expansion for gently curved surfaces to derive the leading curvature modifications to the PFA. Our methods apply to any homogeneous and isotropic materials; here we present results for Dirichlet and Neumann boundary conditions and for perfect conductors. A Padé extrapolation constrained by a multipole expansion at large distance and our improved expansion at short distances, provides an accurate expression for the sphere-plate Casimir force at all separations.

quant-ph↗
arXiv2010

Quantitative model for efficient temporal targeting of tumor cells and neovasculature

The combination of cytotoxic therapies and anti-angiogenic agents is emerging as a most promising strategy in the treatment of malignant tumors. However, the timing and sequencing of these treatments seem to play essential roles in achieving a synergic outcome. Using a mathematical modeling approach that is grounded on available experimental data, we investigate the spatial and temporal targeting of tumor cells and neovasculature with a nanoscale delivery system. Our model suggests that the experimental success of the nanoscale delivery system depends crucially on the trapping of chemotherapeutic agents within the tumor tissue. The numerical results also indicate that substantial further improvements in the efficiency of the nanoscale delivery system can be achieved through an adjustment of the temporal targeting mechanism.

q-bio.TO↗
arXiv2008

Casimir manipulations: The orientation dependence of fluctuation-induced forces

The Casimir interaction between two objects, or between an object and a plane, depends on their relative orientations. We make these angular dependences explicit by considering prolate or oblate spheroids. The variation with orientation is calculated exactly at asymptotically large distances for the electromagnetic field, and at arbitrary separations for a scalar field. For a spheroid in front of a mirror, the leading term is orientation independent, and we find the optimal orientation from computations at higher order.

cond-mat.stat-mech↗
arXiv2007

Casimir Forces in a Piston Geometry at Zero and Finite Temperatures

We study Casimir forces on the partition in a closed box (piston) with perfect metallic boundary conditions. Related closed geometries have generated interest as candidates for a repulsive force. By using an optical path expansion we solve exactly the case of a piston with a rectangular cross section, and find that the force always attracts the partition to the nearest base. For arbitrary cross sections, we can use an expansion for the density of states to compute the force in the limit of small height to width ratios. The corrections to the force between parallel plates are found to have interesting dependence on the shape of the cross section. Finally, for temperatures in the range of experimental interest we compute finite temperature corrections to the force (again assuming perfect boundaries).

quant-ph↗
arXiv2007

First passage times and distances along critical curves

We propose a model for anomalous transport in inhomogeneous environments, such as fractured rocks, in which particles move only along pre-existing self-similar curves (cracks). The stochastic Loewner equation is used to efficiently generate such curves with tunable fractal dimension $d_f$. We numerically compute the probability of first passage (in length or time) from one point on the edge of the semi-infinite plane to any point on the semi-circle of radius $R$. The scaled probability distributions have a variance which increases with $d_f$, a non-monotonic skewness, and tails that decay faster than a simple exponential. The latter is in sharp contrast to predictions based on fractional dynamics and provides an experimental signature for our model.

cond-mat.stat-mech↗
arXiv2007

Casimir Forces between Compact Objects: I. The Scalar Case

We have developed an exact, general method to compute Casimir interactions between a finite number of compact objects of arbitrary shape and separation. Here, we present details of the method for a scalar field to illustrate our approach in its most simple form; the generalization to electromagnetic fields is outlined in Ref. [1]. The interaction between the objects is attributed to quantum fluctuations of source distributions on their surfaces, which we decompose in terms of multipoles. A functional integral over the effective action of multipoles gives the resulting interaction. Each object's shape and boundary conditions enter the effective action only through its scattering matrix. Their relative positions enter through universal translation matrices that depend only on field type and spatial dimension. The distinction of our method from the pairwise summation of two-body potentials is elucidated in terms of the scattering processes between three objects. To illustrate the power of the technique, we consider Robin boundary conditions $ϕ-λ\partial_n ϕ=0$, which interpolate between Dirichlet and Neumann cases as $λ$ is varied. We obtain the interaction between two such spheres analytically in a large separation expansion, and numerically for all separations. The cases of unequal radii and unequal $λ$ are studied. We find sign changes in the force as a function of separation in certain ranges of $λ$ and see deviations from the proximity force approximation even at short separations, most notably for Neumann boundary conditions.

cond-mat.stat-mech↗
arXiv2007

Casimir forces between arbitrary compact objects

We develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The energy is obtained as an interaction between multipoles, generated by quantum current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As an example, we obtain this series for two dielectric spheres and the full interaction at all separations for perfectly conducting spheres.

cond-mat.stat-mech↗
arXiv2007

Fractional Laplacian in Bounded Domains

The fractional Laplacian operator, $-(-\triangle)^{\fracα{2}}$, appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalues spectrum are also obtained.

cond-mat.stat-mech↗
arXiv2006

Attractive Casimir Forces in a Closed Geometry

We study the Casimir force acting on a conducting piston with arbitrary cross section. We find the exact solution for a rectangular cross section and the first three terms in the asymptotic expansion for small height to width ratio when the cross section is arbitrary. Though weakened by the presence of the walls, the Casimir force turns out to be always attractive. Claims of repulsive Casimir forces for related configurations, like the cube, are invalidated by cutoff dependence.

quant-ph↗