43 research outputs found
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 -color Potts model. We also
provide analogous results for the limit that corresponds to
percolation where the observable has a logarithmic singularity. Our conjectures
are tested against Monte Carlo simulations showing excellent agreement for
.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 and .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 term 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