arXiv subjects

M. Kardar

Publications and source records attributed to M. Kardar.

22 records · Page 2Linked to original sources

arXiv2006

Casimir interaction between a plate and a cylinder

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate--sphere, where it is known at large separations. The force has an unexpectedly weak decay \sim L/(H^3 \ln(H/R)) at large plate--cylinder separations H (L and R are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures.

cond-mat.stat-mech↗

arXiv1995

Fluctuation-Induced Interactions between Rods on Membranes and Interfaces

We consider the interaction between two rods embedded in a fluctuating surface which is governed by either surface tension or rigidity. The modification of fluctuations by the rods leads to an attractive long-range interaction that falls off as $1/R^4$ with their separation. The orientational dependence of the resulting interaction is non-trivial and may lead to interesting patterns of rod-like objects on such surfaces.

cond-mat↗

arXiv1995

Matrix generalizations of some dynamic field theories

We introduce matrix generalizations of the Navier--Stokes (NS) equation for fluid flow, and the Kardar--Parisi--Zhang (KPZ) equation for interface growth. The underlying field, velocity for the NS equation, or the height in the case of KPZ, is promoted to a matrix that transforms as the adjoint representation of $SU(N)$. Perturbative expansions simplify in the $N\to\infty$ limit, dominated by planar graphs. We provide the results of a one--loop analysis, but have not succeeded in finding the full solution of the theory in this limit.

cond-mat↗

arXiv1994

Driven Depinning in Anisotropic Media

We show that the critical behavior of a driven interface, depinned from quenched random impurities, depends on the isotropy of the medium. In anisotropic media the interface is pinned by a bounding (conducting) surface characteristic of a model of mixed diodes and resistors. Different universality classes describe depinning along a hard and a generic direction. The exponents in the latter (tilted) case are highly anisotropic, and obtained exactly by a mapping to growing surfaces. Various scaling relations are proposed in the former case which explain a number of recent numerical observations.

cond-mat↗