Condensed Matter Theory

Abstract:

We present a number of arguments to demonstrate that a quantum analog of the Cherenkov effect occurs when two nondispersive half spaces are in relative motion. We show that they experience friction beyond a threshold velocity which, in their center-of-mass frame, is the phase speed of light within their medium, and the loss in mechanical energy is radiated through the medium before getting fully absorbed in the form of heat. By deriving various correlation functions inside and outside the two half spaces, we explicitly compute this radiation and discuss its dependence on the reference frame. © 2013 American Physical Society.

Abstract:

Continually moving cilia on the surface of marine organisms provide a natural defense against biofouling. To probe the physical mechanisms underlying this antifouling behavior, we integrate the lattice Boltzmann and immersed boundary methods and undertake the first computational studies of the interactions between actuated, biomimetic cilia and a model swimmer. We find that swimmers are effectively "knocked away" from the ciliated surface through a combination of steric repulsion and locally fluctuating flows. In addition, the net flow generated by the collective motion of the entire ciliary array was important for significantly reducing the times spent by relatively slow swimmers near the surface. The results reveal that active ciliated layers can offer a means to resist a wide range of species with a single surface. © 2013 American Chemical Society.

Abstract:

We consider the statistical mechanics of a class of models involving close-packed loops with fugacity n on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite, and in the other, some loops are infinitely extended. We show that the loop models are discretizations of CPn-1 σ models. The finite and infinite loop phases represent, respectively, disordered and ordered phases of the σ model, and we discuss the relationship between loop properties and σ model correlators. On large scales, loops are Brownian in an ordered phase and have a nontrivial fractal dimension at a critical point. We simulate the models, finding continuous transitions between the two phases for n=1,2,3 and first order transitions for n≥4. We also give a renormalization-group treatment of the CPn-1 model that shows how a continuous transition can survive for values of n larger than (but close to) 2, despite the presence of a cubic invariant in the Landau-Ginzburg description. The results we obtain are of broader relevance to a variety of problems, including SU(n) quantum magnets in (2+1) dimensions, Anderson localization in symmetry class C, and the statistics of random curves in three dimensions. © 2013 American Physical Society.

Abstract:

We consider the statistical mechanics of a class of models involving close-packed loops with fugacity $n$ on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite, and in the other, some loops are infinitely extended. We show that the loop models are discretisations of $CP^{n-1}$ $\sigma$ models. The finite and infinite loop phases represent, respectively, disordered and ordered phases of the $\sigma$ model, and we discuss the relationship between loop properties and $\sigma$ model correlators. On large scales, loops are Brownian in an ordered phase and have a non-trivial fractal dimension at a critical point. We simulate the models, finding continuous transitions between the two phases for $n=1,2,3$ and first order transitions for $n\geq 4$. We also give a renormalisation group treatment of the $CP^{n-1}$ model that shows how a continuous transition can survive for values of $n$ larger than (but close to) two, despite the presence of a cubic invariant in the Landau-Ginzburg description. The results we obtain are of broader relevance to a variety of problems, including SU(n) quantum magnets in (2+1) dimensions, Anderson localisation in symmetry class C, and the statistics of random curves in three dimensions.