Condensed Matter Theory

Abstract:

Random quantum circuits yield minimally structured models for chaotic quantum dynamics, which are able to capture, for example, universal properties of entanglement growth. We provide exact results and coarse-grained models for the spreading of operators by quantum circuits made of Haar-random unitaries. We study both 1+1D and higher dimensions and argue that the coarse-grained pictures carry over to operator spreading in generic many-body systems. In 1+1D, we demonstrate that the out-of-time-order correlator (OTOC) satisfies a biased diffusion equation, which gives exact results for the spatial profile of the OTOC and determines the butterfly speed vB. We find that in 1+1D, the “front” of the OTOC broadens diffusively, with a width scaling in time as t1/2. We address fluctuations in the OTOC between different realizations of the random circuit, arguing that they are negligible in comparison to the broadening of the front within a realization. Turning to higher dimensions, we show that the averaged OTOC can be understood exactly via a remarkable correspondence with a purely classical droplet growth problem. This implies that the width of the front of the averaged OTOC scales as t1/3 in 2+1D and as t0.240 in 3+1D (exponents of the Kardar-Parisi-Zhang universality class). We support our analytic argument with simulations in 2+1D. We point out that, in two or higher spatial dimensions, the shape of the spreading operator at late times is affected by underlying lattice symmetries and, in general, is not spherical. However, when full spatial rotational symmetry is present in 2+1D, our mapping implies an exact asymptotic form for the OTOC, in terms of the Tracy-Widom distribution. For an alternative perspective on the OTOC in 1+1D, we map it to the partition function of an Ising-like statistical mechanics model. As a result of special structure arising from unitarity, this partition function reduces to a random walk calculation which can be performed exactly. We also use this mapping to give exact results for entanglement growth in 1+1D circuits.

Abstract:

Inspired by recent successes using single-stranded DNA tiles to produce complex structures, we develop a two-step coarse-graining approach that uses detailed thermodynamic calculations with oxDNA, a nucleotide-based model of DNA, to parametrize a coarser kinetic model that can reach the time and length scales needed to study the assembly mechanisms of these structures. We test the model by performing a detailed study of the assembly pathways for a two-dimensional target structure made up of 334 unique strands each of which are 42 nucleotides long. Without adjustable parameters, the model reproduces a critical temperature for the formation of the assembly that is close to the temperature at which assembly first occurs in experiments. Furthermore, the model allows us to investigate in detail the nucleation barriers and the distribution of critical nucleus shapes for the assembly of a single target structure. The assembly intermediates are compact and highly connected (although not maximally so), and classical nucleation theory provides a good fit to the height and shape of the nucleation barrier at temperatures close to where assembly first occurs.

Abstract:

We analyze the inner products of edge state wave functions in the fractional quantum Hall effect, specifically for the Laughlin and Moore-Read states. We use an effective description for these inner products given by a large-N expansion ansatz proposed in a recent work by J. Dubail, N. Read, and E. Rezayi [Phys. Rev. B 86, 245310 (2012)]. As noted by these authors, the terms in this ansatz can be constrained using symmetry, a procedure we perform to high orders. We then check this conjecture by calculating the overlaps exactly for small system sizes and compare the numerics with our high-order expansion. We find the effective description to be very accurate.

Abstract:

The frequency-dependent spectrum of current fluctuations through nano-scale channels is studied using analytical and computational techniques. Using a stochastic Nernst-Planck description and neglecting the interactions between the ions inside the channel, an expression is derived for the current fluctuations, assuming that the geometry of the channel can be incorporated through the lower limits for various wave-vector modes. Since the resulting expression turns out to be quite complex, a number of further approximations are discussed such that relatively simple expressions can be used for practical purposes. The analytical results are validated using Langevin dynamics simulations.

Abstract:

Using multigenerational, single-cell tracking we explore the earliest events of biofilm formation by Pseudomonas aeruginosa During initial stages of surface engagement (≤20 h), the surface cell population of this microbe comprises overwhelmingly cells that attach poorly (∼95% stay <30 s, well below the ∼1-h division time) with little increase in surface population. If we harvest cells previously exposed to a surface and direct them to a virgin surface, we find that these surface-exposed cells and their descendants attach strongly and then rapidly increase the surface cell population. This "adaptive," time-delayed adhesion requires determinants we showed previously are critical for surface sensing: type IV pili (TFP) and cAMP signaling via the Pil-Chp-TFP system. We show that these surface-adapted cells exhibit damped, coupled out-of-phase oscillations of intracellular cAMP levels and associated TFP activity that persist for multiple generations, whereas surface-naïve cells show uncorrelated cAMP and TFP activity. These correlated cAMP-TFP oscillations, which effectively impart intergenerational memory to cells in a lineage, can be understood in terms of a Turing stochastic model based on the Pil-Chp-TFP framework. Importantly, these cAMP-TFP oscillations create a state characterized by a suppression of TFP motility coordinated across entire lineages and lead to a drastic increase in the number of surface-associated cells with near-zero translational motion. The appearance of this surface-adapted state, which can serve to define the historical classification of "irreversibly attached" cells, correlates with family tree architectures that facilitate exponential increases in surface cell populations necessary for biofilm formation.