Phase separation and interface structure in two dimensions from field theory

We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly takes into account the topological nature of the elementary excitations. The result known for the Ising model from its lattice solution is recovered as a particular case. In the asymptotic infrared limit the interface behaves as a simple curve characterized by a gaussian passage probability density. The leading deviation, due to branching, from this behavior is also derived and its coefficient is determined for the Potts model. As a byproduct, for random percolation we obtain the asymptotic density profile of a spanning cluster conditioned to touch only the left half of the boundary.Comment: 12 pages, 3 figures; published version, references adde

Four-point boundary connectivities in critical two-dimensional percolation from conformal invariance

We conjecture an exact form for an universal ratio of four-point cluster connectivities in the critical two-dimensional $Q$-color Potts model. We also provide analogous results for the limit $Q\rightarrow 1$ that corresponds to percolation where the observable has a logarithmic singularity. Our conjectures are tested against Monte Carlo simulations showing excellent agreement for $Q=1,2,3$.Comment: 29 pages, 9 Figures. Published version: improved discussion, additional numerical tests and reference

Local logarithmic correlators as limits of Coulomb gas integrals

We will describe how logarithmic singularities arise as limits of Coulomb Gas integrals. Our approach will combine analytic properties of the time-like Liouville structure constants, together with the recursive formula of the Virasoro conformal blocks. Although the Coulomb Gas formalism forces a diagonal coupling between the chiral and antichiral sectors of the Conformal Field Theory (CFT), we present new results for the multi-screening integrals which are potentially interesting for applications to critical statistical systems described by Logarithmic CFTs. In particular our findings extend and complement previous results, derived with Coulomb Gas methods, at $c=0$ and $c=-2$.Comment: 38 pages, 12 figure

Chiral entanglement in massive quantum field theories in 1+1 dimensions

We determine both analytically and numerically the entanglement between chiral degrees of freedom in the ground state of massive perturbations of 1+1 dimensional conformal field theories quantised on a cylinder. Analytic predictions are obtained from a variational Ansatz for the ground state in terms of smeared conformal boundary states recently proposed by J. Cardy, which is validated by numerical results from the Truncated Conformal Space Approach. We also extend the scope of the Ansatz by resolving ground state degeneracies exploiting the operator product expansion. The chiral entanglement entropy is computed both analytically and numerically as a function of the volume. The excellent agreement between the analytic and numerical results provides further validation for Cardy's Ansatz. The chiral entanglement entropy contains a universal $O(1)$ term $\gamma$ for which an exact analytic result is obtained, and which can distinguish energetically degenerate ground states of gapped systems in 1+1 dimensions.Comment: version 2, references added, minor changes, 31 pages, 12 figures, 6 table

High Framerate Imaging of Ultrasound Contrast Agents

Ultrasound contrast agents (UCAs) consists of a suspension of tiny gas bubbles that is injected into a patient's bloodstream to enhance the visualization of blood in ultrasound images. As UCAs respond differently to ultrasound pulses compared to the surrounding soft tissues and blood, it is possible to employ specialized techniques to identify and isolate UCAs in an ultrasound image. This is commonly referred to as Ultrasound Contrast Imaging. This PhD thesis evaluates several traditional ultrasound contrast imaging strategies, based on scanning images through linear arrays; furthermore, innovative high frame rate strategies are explored, which are shown to be suited for high sensitivity tracking of even a single microbubble

Inhomogeneous quenches in a fermionic chain: exact results

We consider the non-equilibrium physics induced by joining together two tight binding fermionic chains to form a single chain. Before being joined, each chain is in a many-fermion ground state. The fillings (densities) in the two chains might be the same or different. We present a number of exact results for the correlation functions in the non-interacting case. We present a short-time expansion, which can sometimes be fully resummed, and which reproduces the so-called `light cone' effect or wavefront behavior of the correlators. For large times, we show how all interesting physical regimes may be obtained by stationary phase approximation techniques. In particular, we derive semiclassical formulas in the case when both time and positions are large, and show that these are exact in the thermodynamic limit. We present subleading corrections to the large-time behavior, including the corrections near the edges of the wavefront. We also provide results for the return probability or Loschmidt echo. In the maximally inhomogeneous limit, we prove that it is exactly gaussian at all times. The effects of interactions on the Loschmidt echo are also discussed.Comment: 5 pages+14 pages supplementary material+9 figure