Quantum Buckling

We study the mechanical buckling of a two dimensional membrane coated with a thin layer of superfluid. It is seen that a singularity (vortex or anti-vortex defect) in the phase of the quantum order parameter, distorts the membrane metric into a negative conical singularity surface, irrespective of the defect sign. The defect-curvature coupling and the observed instability is in striking contrast with classical elasticity where, the in-plane strain induced by positive (negative) disclinations is screened by a corresponding positive (negative) conical singularity surface. Defining a dimensionless ratio between superfluid stiffness and membrane bending modulus, we derive conditions under which the quantum buckling instability occurs. An ansatz for the resulting shape of the buckled membrane is analytically and numerically confirmed

Soliton attenuation and emergent hydrodynamics in fragile matter

Disordered packings of soft grains are fragile mechanical systems that loose rigidity upon lowering the external pressure towards zero. At zero pressure, we find that any infinitesimal strain-impulse propagates initially as a non-linear solitary wave progressively attenuated by disorder. We demonstrate that the particle fluctuations generated by the solitary-wave decay, can be viewed as a granular analogue of temperature. Their presence is manifested by two emergent macroscopic properties absent in the unperturbed granular packing: a finite pressure that scales with the injected energy (akin to a granular temperature) and an anomalous viscosity that arises even when the microscopic mechanisms of energy dissipation are negligible. Consistent with the interpretation of this state as a fluid-like thermalized state, the shear modulus remains zero. Further, we follow in detail the attenuation of the initial solitary wave identifying two distinct regimes : an initial exponential decay, followed by a longer power law decay and suggest simple models to explain these two regimes.Comment: 8 pages, 3 Figure

Extrema statistics in the dynamics of a non-Gaussian random field

When the equations that govern the dynamics of a random field are nonlinear, the field can develop with time non-Gaussian statistics even if its initial condition is Gaussian. Here, we provide a general framework for calculating the effect of the underlying nonlinear dynamics on the relative densities of maxima and minima of the field. Using this simple geometrical probe, we can identify the size of the non-Gaussian contributions in the random field, or alternatively the magnitude of the nonlinear terms in the underlying equations of motion. We demonstrate our approach by applying it to an initially Gaussian field that evolves according to the deterministic KPZ equation, which models surface growth and shock dynamics.Comment: 9 pages, 3 figure

The physics of forgetting: Landauer's erasure principle and information theory

This article discusses the concept of information and its intimate relationship with physics. After an introduction of all the necessary quantum mechanical and information theoretical concepts we analyze Landauer's principle that states that the erasure of information is inevitably accompanied by the generation of heat. We employ this principle to rederive a number of results in classical and quantum information theory whose rigorous mathematical derivations are difficult. This demonstrates the usefulness of Landauer's principle and provides an introduction to the physical theory of information.Comment: 36 pages, 13 figures, Very basic introductory article for Contemporary Physic

Crystallography on Curved Surfaces

We study static and dynamical properties that distinguish two dimensional crystals constrained to lie on a curved substrate from their flat space counterparts. A generic mechanism of dislocation unbinding in the presence of varying Gaussian curvature is presented in the context of a model surface amenable to full analytical treatment. We find that glide diffusion of isolated dislocations is suppressed by a binding potential of purely geometrical origin. Finally, the energetics and biased diffusion dynamics of point defects such as vacancies and interstitials is explained in terms of their geometric potential.Comment: 12 Pages, 8 Figure

Stochastic geometry and topology of non-Gaussian fields

Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter and cosmology to biomedical imaging. The standard test of non-Gaussianity is to measure higher order correlation functions. In the present work, we take a different route. We show how geometric and topological properties of Gaussian fields, such as the statistics of extrema, are modified by the presence of a non-Gaussian perturbation. The resulting discrepancies give an independent way to detect and quantify non-Gaussianities. In our treatment, we consider both local and nonlocal mechanisms that generate non-Gaussian fields, both statically and dynamically through nonlinear diffusion.Comment: 8 pages, 4 figure