236 research outputs found
Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
A single-particle mobility edge (SPME) marks a critical energy separating
extended from localized states in a quantum system. In one-dimensional systems
with uncorrelated disorder, a SPME cannot exist, since all single-particle
states localize for arbitrarily weak disorder strengths. However, if
correlations are present in the disorder potential, the localization transition
can occur at a finite disorder strength and SPMEs become possible. In this
work, we find experimental evidence for the existence of such a SPME in a
one-dimensional quasi-periodic optical lattice. Specifically, we find a regime
where extended and localized single-particle states coexist, in good agreement
with theoretical simulations, which predict a SPME in this regime
Benchmarking a Novel Efficient Numerical Method for Localized 1D Fermi-Hubbard Systems on a Quantum Simulator
Quantum simulators have made a remarkable progress towards exploring the
dynamics of many-body systems, many of which offer a formidable challenge to
both theoretical and numerical methods. While state-of-the-art quantum
simulators are in principle able to simulate quantum dynamics well outside the
domain of classical computers, they are noisy and limited in the variability of
the initial state of the dynamics and the observables that can be measured.
Despite these limitations, here we show that such a quantum simulator can be
used to in-effect solve for the dynamics of a many-body system. We develop an
efficient numerical technique that facilitates classical simulations in regimes
not accessible to exact calculations or other established numerical techniques.
The method is based on approximations that are well suited to describe
localized one-dimensional Fermi-Hubbard systems. Since this new method does not
have an error estimate and the approximations do not hold in general, we use a
neutral-atom Fermi-Hubbard quantum simulator with
lattice sites to benchmark its performance in terms of accuracy and convergence
for evolution times up to tunnelling times. We then use these
approximations in order to derive a simple prediction of the behaviour of
interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems, which
we show to be in quantitative agreement with experimental results. Finally, we
demonstrate that the convergence of our method is the slowest when the
entanglement depth developed in the many-body system we consider is neither too
small nor too large. This represents a promising regime for near-term
applications of quantum simulators.Comment: 24 pages, 10 figure
Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
The thermalization of isolated quantum many-body systems is deeply related to
fundamental questions of quantum information theory. While integrable or
many-body localized systems display non-ergodic behavior due to extensively
many conserved quantities, recent theoretical studies have identified a rich
variety of more exotic phenomena in between these two extreme limits. The
tilted one-dimensional Fermi-Hubbard model, which is readily accessible in
experiments with ultracold atoms, emerged as an intriguing playground to study
non-ergodic behavior in a clean disorder-free system. While non-ergodic
behavior was established theoretically in certain limiting cases, there is no
complete understanding of the complex thermalization properties of this model.
In this work, we experimentally study the relaxation of an initial
charge-density wave and find a remarkably long-lived initial-state memory over
a wide range of parameters. Our observations are well reproduced by numerical
simulations of a clean system. Using analytical calculations we further provide
a detailed microscopic understanding of this behavior, which can be attributed
to emergent kinetic constraints.Comment: accepted in Nature Communication
The Unique Determination of Neuronal Currents in the Brain via Magnetoencephalography
The problem of determining the neuronal current inside the brain from
measurements of the induced magnetic field outside the head is discussed under
the assumption that the space occupied by the brain is approximately spherical.
By inverting the Geselowitz equation, the part of the current which can be
reconstructed from the measurements is precisely determined. This actually
consists of only certain moments of one of the two functions specifying the
tangential part of the current. The other function specifying the tangential
part of the current as well as the radial part of the current are completely
arbitrary. However, it is also shown that with the assumption of energy
minimization, the current can be reconstructed uniquely. A numerical
implementation of this unique reconstruction is also presented
Non-Equilibrium Mass Transport in the 1D Fermi-Hubbard Model
We experimentally and numerically investigate the sudden expansion of
fermions in a homogeneous one-dimensional optical lattice. For initial states
with an appreciable amount of doublons, we observe a dynamical phase separation
between rapidly expanding singlons and slow doublons remaining in the trap
center, realizing the key aspect of fermionic quantum distillation in the
strongly-interacting limit. For initial states without doublons, we find a
reduced interaction dependence of the asymptotic expansion speed compared to
bosons, which is explained by the interaction energy produced in the quench
Fast Optimal Transport Averaging of Neuroimaging Data
Knowing how the Human brain is anatomically and functionally organized at the
level of a group of healthy individuals or patients is the primary goal of
neuroimaging research. Yet computing an average of brain imaging data defined
over a voxel grid or a triangulation remains a challenge. Data are large, the
geometry of the brain is complex and the between subjects variability leads to
spatially or temporally non-overlapping effects of interest. To address the
problem of variability, data are commonly smoothed before group linear
averaging. In this work we build on ideas originally introduced by Kantorovich
to propose a new algorithm that can average efficiently non-normalized data
defined over arbitrary discrete domains using transportation metrics. We show
how Kantorovich means can be linked to Wasserstein barycenters in order to take
advantage of an entropic smoothing approach. It leads to a smooth convex
optimization problem and an algorithm with strong convergence guarantees. We
illustrate the versatility of this tool and its empirical behavior on
functional neuroimaging data, functional MRI and magnetoencephalography (MEG)
source estimates, defined on voxel grids and triangulations of the folded
cortical surface.Comment: Information Processing in Medical Imaging (IPMI), Jun 2015, Isle of
Skye, United Kingdom. Springer, 201
Nonequilibrium Mass Transport in the 1D Fermi-Hubbard Model.
We experimentally and numerically investigate the sudden expansion of fermions in a homogeneous one-dimensional optical lattice. For initial states with an appreciable amount of doublons, we observe a dynamical phase separation between rapidly expanding singlons and slow doublons remaining in the trap center, realizing the key aspect of fermionic quantum distillation in the strongly interacting limit. For initial states without doublons, we find a reduced interaction dependence of the asymptotic expansion speed compared to bosons, which is explained by the interaction energy produced in the quench
Open Database of Epileptic EEG with MRI and Postoperational Assessment of Foci—a Real World Verification for the EEG Inverse Solutions
This paper introduces a freely accessible database http://eeg.pl/epi, containing 23 datasets from patients diagnosed with and operated on for drug-resistant epilepsy. This was collected as part of the clinical routine at the Warsaw Memorial Child Hospital. Each record contains (1) pre-surgical electroencephalography (EEG) recording (10–20 system) with inter-ictal discharges marked separately by an expert, (2) a full set of magnetic resonance imaging (MRI) scans for calculations of the realistic forward models, (3) structural placement of the epileptogenic zone, recognized by electrocorticography (ECoG) and post-surgical results, plotted on pre-surgical MRI scans in transverse, sagittal and coronal projections, (4) brief clinical description of each case. The main goal of this project is evaluation of possible improvements of localization of epileptic foci from the surface EEG recordings. These datasets offer a unique possibility for evaluating different EEG inverse solutions. We present preliminary results from a subset of these cases, including comparison of different schemes for the EEG inverse solution and preprocessing. We report also a finding which relates to the selective parametrization of single waveforms by multivariate matching pursuit, which is used in the preprocessing for the inverse solutions. It seems to offer a possibility of tracing the spatial evolution of seizures in time
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