9,176 research outputs found
Observation of many-body localization of interacting fermions in a quasi-random optical lattice
We experimentally observe many-body localization of interacting fermions in a
one-dimensional quasi-random optical lattice. We identify the many-body
localization transition through the relaxation dynamics of an
initially-prepared charge density wave. For sufficiently weak disorder the time
evolution appears ergodic and thermalizing, erasing all remnants of the initial
order. In contrast, above a critical disorder strength a significant portion of
the initial ordering persists, thereby serving as an effective order parameter
for localization. The stationary density wave order and the critical disorder
value show a distinctive dependence on the interaction strength, in agreement
with numerical simulations. We connect this dependence to the ubiquitous
logarithmic growth of entanglement entropy characterizing the generic many-body
localized phase.Comment: 6 pages, 6 figures + supplementary informatio
Combined population dynamics and entropy modelling supports patient stratification in chronic myeloid leukemia
Modelling the parameters of multistep carcinogenesis is key for a better understanding of cancer
progression, biomarker identification and the design of individualized therapies. Using chronic
myeloid leukemia (CML) as a paradigm for hierarchical disease evolution we show that combined
population dynamic modelling and CML patient biopsy genomic analysis enables patient stratification
at unprecedented resolution. Linking CD34+ similarity as a disease progression marker to patientderived
gene expression entropy separated established CML progression stages and uncovered
additional heterogeneity within disease stages. Importantly, our patient data informed model enables
quantitative approximation of individual patients’ disease history within chronic phase (CP) and
significantly separates “early” from “late” CP. Our findings provide a novel rationale for personalized
and genome-informed disease progression risk assessment that is independent and complementary to
conventional measures of CML disease burden and prognosis
Phase field modeling of partially saturated deformable porous media
A poromechanical model of partially saturated deformable porous media is
proposed based on a phase field approach at modeling the behavior of the
mixture of liquid water and wet air, which saturates the pore space, the phase
field being the saturation (ratio). While the standard retention curve is
expected still to provide the intrinsic retention properties of the porous
skeleton, depending on the porous texture, an enhanced description of surface
tension between the wetting (liquid water) and the non-wetting (wet air) fluid,
occupying the pore space, is stated considering a regularization of the phase
field model based on an additional contribution to the overall free energy
depending on the saturation gradient. The aim is to provide a more refined
description of surface tension interactions.
An enhanced constitutive relation for the capillary pressure is established
together with a suitable generalization of Darcy's law, in which the gradient
of the capillary pressure is replaced by the gradient of the so-called
generalized chemical potential, which also accounts for the \lq\lq
force\rq\rq\, associated to the local free energy of the phase field model. A
micro-scale heuristic interpretation of the novel constitutive law of capillary
pressure is proposed, in order to compare the envisaged model with that one
endowed with the concept of average interfacial area.
The considered poromechanical model is formulated within the framework of
strain gradient theory in order to account for possible effects, at laboratory
scale, of the micro-scale hydro-mechanical couplings between highly-localized
flows (fingering) and localized deformations of the skeleton (fracturing)
Exact Maps in Density Functional Theory for Lattice Models
In the present work, we employ exact diagonalization for model systems on a
real-space lattice to explicitly construct the exact density-to-potential and
for the first time the exact density-to-wavefunction map that underly the
Hohenberg-Kohn theorem in density functional theory. Having the explicit
wavefunction-to- density map at hand, we are able to construct arbitrary
observables as functionals of the ground-state density. We analyze the
density-to-potential map as the distance between the fragments of a system
increases and the correlation in the system grows. We observe a feature that
gradually develops in the density-to-potential map as well as in the
density-to-wavefunction map. This feature is inherited by arbitrary expectation
values as functional of the ground-state density. We explicitly show the
excited-state energies, the excited-state densities, and the correlation
entropy as functionals of the ground-state density. All of them show this exact
feature that sharpens as the coupling of the fragments decreases and the
correlation grows. We denominate this feature as intra-system steepening. We
show that for fully decoupled subsystems the intra-system steepening transforms
into the well-known inter-system derivative discontinuity. An important
conclusion is that for e.g. charge transfer processes between localized
fragments within the same system it is not the usual inter-system derivative
discontinuity that is missing in common ground-state functionals, but rather
the differentiable intra-system steepening that we illustrate in the present
work
Holographic Relaxation of Finite Size Isolated Quantum Systems
We study holographically the out of equilibrium dynamics of a finite size
closed quantum system in 2+1 dimensions, modelled by the collapse of a shell of
a massless scalar field in AdS4. In global coordinates there exists a variety
of evolutions towards final black hole formation which we relate with different
patterns of relaxation in the dual field theory. For large scalar initial data
rapid thermalization is achieved as a priori expected. Interesting phenomena
appear for small enough amplitudes. Such shells do not generate a black hole by
direct collapse, but quite generically an apparent horizon emerges after enough
bounces off the AdS boundary. We relate this bulk evolution with relaxation
processes at strong coupling which delay in reaching an ergodic stage. Besides
the dynamics of bulk fields, we monitor the entanglement entropy, finding that
it oscillates quasi-periodically before final equilibration. The radial
position of the traveling shell is brought into correspondence with the
evolution of the entanglement pattern in the dual field theory. The
entanglement entropy is not only able to portrait the streaming of entangled
excitations, but it is also a useful probe of interaction effects.Comment: 37 pages, 27 figure
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