1,103 research outputs found
Critical holes in undercooled wetting layers
The profile of a critical hole in an undercooled wetting layer is determined
by the saddle-point equation of a standard interface Hamiltonian supported by
convenient boundary conditions. It is shown that this saddle-point equation can
be mapped onto an autonomous dynamical system in a three-dimensional phase
space. The corresponding flux has a polynomial form and in general displays
four fixed points, each with different stability properties. On the basis of
this picture we derive the thermodynamic behaviour of critical holes in three
different nucleation regimes of the phase diagram.Comment: 18 pages, LaTeX, 6 figures Postscript, submitted to J. Phys.
Entanglement subvolume law for 2D frustration-free spin systems
Let be a frustration-free Hamiltonian describing a 2D grid of qudits with
local interactions, a unique ground state, and local spectral gap lower bounded
by a positive constant. For any bipartition defined by a vertical cut of length
running from top to bottom of the grid, we prove that the corresponding
entanglement entropy of the ground state of is upper bounded by
. For the special case of a 1D chain, our result provides a
new area law which improves upon prior work, in terms of the scaling with qudit
dimension and spectral gap. In addition, for any bipartition of the grid into a
rectangular region and its complement, we show that the entanglement
entropy is upper bounded as where
is the boundary of . This represents the first subvolume bound on
entanglement in frustration-free 2D systems. In contrast with previous work,
our bounds depend on the local (rather than global) spectral gap of the
Hamiltonian. We prove our results using a known method which bounds the
entanglement entropy of the ground state in terms of certain properties of an
approximate ground state projector (AGSP). To this end, we construct a new AGSP
which is based on a robust polynomial approximation of the AND function and we
show that it achieves an improved trade-off between approximation error and
entanglement
Nucleation-induced transition to collective motion in active systems
While the existence of polar ordered states in active systems is well
established, the dynamics of the self-assembly processes are still elusive. We
study a lattice gas model of self-propelled elongated particles interacting
through excluded volume and alignment interactions, which shows a phase
transition from an isotropic to a polar ordered state. By analyzing the
ordering process we find that the transition is driven by the formation of a
critical nucleation cluster and a subsequent coarsening process. Moreover, the
time to establish a polar ordered state shows a power-law divergence
Capillary-Wave Model for the Solidification of Dilute Binary Alloys
Starting from a phase-field description of the isothermal solidification of a
dilute binary alloy, we establish a model where capillary waves of the
solidification front interact with the diffusive concentration field of the
solute. The model does not rely on the sharp-interface assumption, and includes
non-equilibrium effects, relevant in the rapid-growth regime. In many
applications it can be evaluated analytically, culminating in the appearance of
an instability which, interfering with the Mullins-Sekerka instability, is
similar to that, found by Cahn in grain-boundary motion.Comment: 17 pages, 12 figure
Translationally Invariant Universal Quantum Hamiltonians in 1D
. Recent work has characterized rigorously what it means for one
quantum system to simulate another and demonstrated the existence of
universal Hamiltonians—simple spin lattice Hamiltonians that can replicate the entire physics of any other quantum many-body system. Previous
universality results have required proofs involving complicated ‘chains’ of
perturbative ‘gadgets.’ In this paper, we derive a significantly simpler
and more powerful method of proving universality of Hamiltonians, directly leveraging the ability to encode quantum computation into ground
states. This provides new insight into the origins of universal models and
suggests a deep connection between universality and complexity. We apply this new approach to show that there are universal models even in
translationally invariant spin chains in 1D. This gives as a corollary a
new Hamiltonian complexity result that the local Hamiltonian problem
for translationally invariant spin chains in one dimension with an exponentially small promise gap is PSPACE-complete. Finally, we use these
new universal models to construct the first known toy model of 2D–1D
holographic duality between local Hamiltonians
Uncomputability of phase diagrams.
The phase diagram of a material is of central importance in describing the properties and behaviour of a condensed matter system. In this work, we prove that the task of determining the phase diagram of a many-body Hamiltonian is in general uncomputable, by explicitly constructing a continuous one-parameter family of Hamiltonians H(φ), where [Formula: see text], for which this is the case. The H(φ) are translationally-invariant, with nearest-neighbour couplings on a 2D spin lattice. As well as implying uncomputablity of phase diagrams, our result also proves that undecidability can hold for a set of positive measure of a Hamiltonian's parameter space, whereas previous results only implied undecidability on a zero measure set. This brings the spectral gap undecidability results a step closer to standard condensed matter problems, where one typically studies phase diagrams of many-body models as a function of one or more continuously varying real parameters, such as magnetic field strength or pressure
On the Efficient Calculation of a Linear Combination of Chi-Square Random Variables with an Application in Counting String Vacua
Linear combinations of chi square random variables occur in a wide range of
fields. Unfortunately, a closed, analytic expression for the pdf is not yet
known. As a first result of this work, an explicit analytic expression for the
density of the sum of two gamma random variables is derived. Then a
computationally efficient algorithm to numerically calculate the linear
combination of chi square random variables is developed. An explicit expression
for the error bound is obtained. The proposed technique is shown to be
computationally efficient, i.e. only polynomial in growth in the number of
terms compared to the exponential growth of most other methods. It provides a
vast improvement in accuracy and shows only logarithmic growth in the required
precision. In addition, it is applicable to a much greater number of terms and
currently the only way of computing the distribution for hundreds of terms. As
an application, the exponential dependence of the eigenvalue fluctuation
probability of a random matrix model for 4d supergravity with N scalar fields
is found to be of the asymptotic form exp(-0.35N).Comment: 21 pages, 19 figures. 3rd versio
Microrheology, stress fluctuations and active behavior of living cells
We report the first measurements of the intrinsic strain fluctuations of
living cells using a recently-developed tracer correlation technique along with
a theoretical framework for interpreting such data in heterogeneous media with
non-thermal driving. The fluctuations' spatial and temporal correlations
indicate that the cytoskeleton can be treated as a course-grained continuum
with power-law rheology, driven by a spatially random stress tensor field.
Combined with recent cell rheology results, our data imply that intracellular
stress fluctuations have a nearly power spectrum, as expected for
a continuum with a slowly evolving internal prestress.Comment: 4 pages, 2 figures, to appear in Phys. Rev. Let
The Story of Their Lives: Understanding Our Students\u27 Literacy Practices and Events
The relationship between teacher and student, teacher and class, and teacher, student and class has been acknowledged as one of the most influential structures in a students\u27 life which can effect their identity, their cognition, and their fundamental humaneness within the societal structure of their culture. The foundation of this paper is to investigate and honor students\u27 shared understanding of literacies both in and out of school, utilizing the knowledge they bring from sociocultural contexts. I believe this vision holds great promise as an avenue of extending the literacy paradigm currently available to children in school
- …