1,067 research outputs found
Self-referential Monte Carlo method for calculating the free energy of crystalline solids
A self-referential Monte Carlo method is described for calculating the free energy of crystalline solids. All Monte Carlo methods for the free energy of classical crystalline solids calculate the free-energy difference between a state whose free energy can be calculated relatively easily and the state of interest. Previously published methods employ either a simple model crystal, such as the Einstein crystal, or a fluid as the reference state. The self-referential method employs a radically different reference state; it is the crystalline solid of interest but with a different number of unit cells. So it calculates the free-energy difference between two crystals, differing only in their size. The aim of this work is to demonstrate this approach by application to some simple systems, namely, the face centered cubic hard sphere and Lennard-Jones crystals. However, it can potentially be applied to arbitrary crystals in both bulk and confined environments, and ultimately it could also be very efficient
Monopoles and Solitons in Fuzzy Physics
Monopoles and solitons have important topological aspects like quantized
fluxes, winding numbers and curved target spaces. Naive discretizations which
substitute a lattice of points for the underlying manifolds are incapable of
retaining these features in a precise way. We study these problems of discrete
physics and matrix models and discuss mathematically coherent discretizations
of monopoles and solitons using fuzzy physics and noncommutative geometry. A
fuzzy sigma-model action for the two-sphere fulfilling a fuzzy Belavin-Polyakov
bound is also put forth.Comment: 17 pages, Latex. Uses amstex, amssymb.Spelling of the name of one
Author corrected. To appear in Commun.Math.Phy
An Invitation to Higher Gauge Theory
In this easy introduction to higher gauge theory, we describe parallel
transport for particles and strings in terms of 2-connections on 2-bundles.
Just as ordinary gauge theory involves a gauge group, this generalization
involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie
group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes,
which play an important role in string theory and multisymplectic geometry.
Second, every group representation gives a Lie 2-group; the representation of
the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which
leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint
representation of any Lie group on its own Lie algebra gives a 'tangent
2-group', which serves as a gauge 2-group in 4d BF theory, which has
topological gravity as a special case. Fourth, every Lie group has an 'inner
automorphism 2-group', which serves as the gauge group in 4d BF theory with
cosmological constant term. Fifth, every Lie group has an 'automorphism
2-group', which plays an important role in the theory of nonabelian gerbes. And
sixth, every compact simple Lie group gives a 'string 2-group'. We also touch
upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra
that governs 11-dimensional supergravity.Comment: 60 pages, based on lectures at the 2nd School and Workshop on Quantum
Gravity and Quantum Geometry at the 2009 Corfu Summer Institut
Properties of Quantum Hall Skyrmions from Anomalies
It is well known that the Fractional Quantum Hall Effect (FQHE) may be
effectively represented by a Chern-Simons theory. In order to incorporate QH
Skyrmions, we couple this theory to the topological spin current, and include
the Hopf term. The cancellation of anomalies for chiral edge states, and the
proviso that Skyrmions may be created and destroyed at the edge, fixes the
coefficients of these new terms. Consequently, the charge and the spin of the
Skyrmion are uniquely determined. For those two quantities we find the values
and , respectively, where is electron charge,
is the filling fraction and is the Skyrmion winding number. We
also add terms to the action so that the classical spin fluctuations in the
bulk satisfy the standard equations of a ferromagnet, with spin waves that
propagate with the classical drift velocity of the electron.Comment: 8 pages, LaTeX file; Some remarks are included to clarify the
physical results obtained, and the role of the Landau-Lifshitz equation is
emphasized. Some references adde
Quantum Picturalism
The quantum mechanical formalism doesn't support our intuition, nor does it
elucidate the key concepts that govern the behaviour of the entities that are
subject to the laws of quantum physics. The arrays of complex numbers are kin
to the arrays of 0s and 1s of the early days of computer programming practice.
In this review we present steps towards a diagrammatic `high-level' alternative
for the Hilbert space formalism, one which appeals to our intuition. It allows
for intuitive reasoning about interacting quantum systems, and trivialises many
otherwise involved and tedious computations. It clearly exposes limitations
such as the no-cloning theorem, and phenomena such as quantum teleportation. As
a logic, it supports `automation'. It allows for a wider variety of underlying
theories, and can be easily modified, having the potential to provide the
required step-stone towards a deeper conceptual understanding of quantum
theory, as well as its unification with other physical theories. Specific
applications discussed here are purely diagrammatic proofs of several quantum
computational schemes, as well as an analysis of the structural origin of
quantum non-locality. The underlying mathematical foundation of this high-level
diagrammatic formalism relies on so-called monoidal categories, a product of a
fairly recent development in mathematics. These monoidal categories do not only
provide a natural foundation for physical theories, but also for proof theory,
logic, programming languages, biology, cooking, ... The challenge is to
discover the necessary additional pieces of structure that allow us to predict
genuine quantum phenomena.Comment: Commissioned paper for Contemporary Physics, 31 pages, 84 pictures,
some colo
Benefits of Cover Cropping Systems in Walnut Orchards as Sustainable Agricultural Practice
In recent years walnut orchards implemented cover crops in between rows to improve soil’s quality, lessen soil’s erosion, increase organic matter, manage nutrient movement and availability, enhance water retention, and expand microbe, insect, and flora diversity. Commonly selected cover crops in California are from families Poaceae, Brassicaceae, and Fabaceae. Considerations should be made when choosing a particular cover crop mixture to enhance multiple benefits and improve sustainable practices in orchard settings. An experiment was conducted in a walnut orchard to compare functionality and benefits of three systems multi-crop, monocrop, and no vegetation cover crop system. The following components were evaluated: cover crop and weed biomass, cover crop species field distribution, and ability to provide better coverage and weed suppression properties. Brassica mixture, clover and grasses showed highest presence in field conditions and excellent weed competition attributes, while peas and faba beans had low presence and did not compete well growing in a mixture with other cover crops. Multi-crop treatment demonstrated the highest dry and wet biomass as well as the greatest weed suppression. Recommendations are to carefully consider current practices in walnut orchards, to seasonally include vegetation cover rather than bare soil, and to choose multi-crop cover rather than monocrop. Implementation of multi-crop species as a sustainable practice would increase soil’s quality, improve biological management through rise of natural beneficial predators and enhance integrated pest management methods
Mocarts: a lightweight radiation transport simulator for easy handling of complex sensing geometries
In functional neuroimaging (fNIRS), elaborated sensing geometries pairing multiple light sources and detectors arranged over the tissue surface are needed. A variety of software tools for probing forward models of radiation transport in tissue exist, but their handling of sensing geometries and specification of complex tissue architectures is, most times, cumbersome. In this work, we introduce a lightweight simulator, Monte Carlo Radiation Transport Simulator (MOCARTS) that attends these demands for simplifying specification of tissue architectures and complex sensing geometries. An object-oriented architecture facilitates such goal. The simulator core is evolved from the Monte Carlo Multi-Layer (mcml) tool but extended to support multi-channel simulations. Verification against mcml yields negligible error (RMSE~4-10e-9) over a photon trajectory. Full simulations show concurrent validity of the proposed tool. Finally, the ability of the new software to simulate multi-channel sensing geometries and to define biological tissue models in an intuitive nested-hierarchy way are exemplified
Spin Foam Models of Riemannian Quantum Gravity
Using numerical calculations, we compare three versions of the Barrett-Crane
model of 4-dimensional Riemannian quantum gravity. In the version with face and
edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we
show the partition function diverges very rapidly for many triangulated
4-manifolds. In the version with modified face and edge amplitudes due to Perez
and Rovelli, we show the partition function converges so rapidly that the sum
is dominated by spin foams where all the spins labelling faces are zero except
for small, widely separated islands of higher spin. We also describe a new
version which appears to have a convergent partition function without drastic
spin-zero dominance. Finally, after a general discussion of how to extract
physics from spin foam models, we discuss the implications of convergence or
divergence of the partition function for other aspects of a spin foam model.Comment: 23 pages LaTeX; this version to appear in Classical and Quantum
Gravit
Quantum Theory of Gravity I: Area Operators
A new functional calculus, developed recently for a fully non-perturbative
treatment of quantum gravity, is used to begin a systematic construction of a
quantum theory of geometry. Regulated operators corresponding to areas of
2-surfaces are introduced and shown to be self-adjoint on the underlying
(kinematical) Hilbert space of states. It is shown that their spectra are {\it
purely} discrete indicating that the underlying quantum geometry is far from
what the continuum picture might suggest. Indeed, the fundamental excitations
of quantum geometry are 1-dimensional, rather like polymers, and the
3-dimensional continuum geometry emerges only on coarse graining. The full
Hilbert space admits an orthonormal decomposition into finite dimensional
sub-spaces which can be interpreted as the spaces of states of spin systems.
Using this property, the complete spectrum of the area operators is evaluated.
The general framework constructed here will be used in a subsequent paper to
discuss 3-dimensional geometric operators, e.g., the ones corresponding to
volumes of regions.Comment: 33 pages, ReVTeX, Section 4 Revised: New results on the effect of
topology of a surface on the eigenvalues and eigenfunctions of its area
operator included. The proof of the bound on the level spacing of eigenvalues
(for large areas) simplified and its ramification to the Bekenstein-Mukhanov
analysis of black-hole evaporation made more explicit. To appear in CQ
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