545 research outputs found
The economic value of wild resources to the Indigenous community of the Wallis Lakes Catchment
There is currently a growing policy interest in the effects of the regulatory environment on the ability of Indigenous people to undertake customary harvesting of wild resources. This Discussion Paper develops and describes a methodology that can be used to estimate the economic benefi ts derived from the use of wild resources. The methodology and the survey instrument that was developed were pilot tested with the Indigenous community of the Wallis Lake catchment. The harvesting of wild resources for consumption makes an important contribution to the livelihoods of Indigenous people living in this area
Non-Commutativity of the Zero Chemical Potential Limit and the Thermodynamic Limit in Finite Density Systems
Monte Carlo simulations of finite density systems are often plagued by the
complex action problem. We point out that there exists certain
non-commutativity in the zero chemical potential limit and the thermodynamic
limit when one tries to study such systems by reweighting techniques. This is
demonstrated by explicit calculations in a Random Matrix Theory, which is
thought to be a simple qualitative model for finite density QCD. The
factorization method allows us to understand how the non-commutativity, which
appears at the intermediate steps, cancels in the end results for physical
observables.Comment: 7 pages, 9 figure
Vacancy-Induced Low-Energy Density of States in the Kitaev Spin Liquid
The Kitaev honeycomb model has attracted significant attention due to its exactly solvable spin-liquid ground state with fractionalized Majorana excitations and its possible materialization in magnetic Mott insulators with strong spin-orbit couplings. Recently, the 5d-electron compound H3LiIr2O6 has shown to be a strong candidate for Kitaev physics considering the absence of any signs of a long-range ordered magnetic state. In this work, we demonstrate that a finite density of random vacancies in the Kitaev model gives rise to a striking pileup of low-energy Majorana eigenmodes and reproduces the apparent power-law upturn in the specific heat measurements of H3LiIr2O6. Physically, the vacancies can originate from various sources such as missing magnetic moments or the presence of nonmagnetic impurities (true vacancies), or from local weak couplings of magnetic moments due to strong but rare bond randomness (quasivacancies). We show numerically that the vacancy effect is readily detectable even at low vacancy concentrations and that it is not very sensitive either to the nature of vacancies or to different flux backgrounds. We also study the response of the site-diluted Kitaev spin liquid to the three-spin interaction term, which breaks time-reversal symmetry and imitates an external magnetic field. We propose a field-induced flux-sector transition where the ground state becomes flux-free for larger fields, resulting in a clear suppression of the low-temperature specific heat. Finally, we discuss the effect of dangling Majorana fermions in the case of true vacancies and show that their coupling to an applied magnetic field via the Zeeman interaction can also account for the scaling behavior in the high-field limit observed in H3LiIr2O6
Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential
In quantum chromodynamics (QCD) at nonzero chemical potential, the
eigenvalues of the Dirac operator are scattered in the complex plane. Can the
fluctuation properties of the Dirac spectrum be described by universal
predictions of non-Hermitian random matrix theory? We introduce an unfolding
procedure for complex eigenvalues and apply it to data from lattice QCD at
finite chemical potential to construct the nearest-neighbor spacing
distribution of adjacent eigenvalues in the complex plane. For intermediate
values of , we find agreement with predictions of the Ginibre ensemble of
random matrix theory, both in the confinement and in the deconfinement phase.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let
The Fractal Geometry of Critical Systems
We investigate the geometry of a critical system undergoing a second order
thermal phase transition. Using a local description for the dynamics
characterizing the system at the critical point T=Tc, we reveal the formation
of clusters with fractal geometry, where the term cluster is used to describe
regions with a nonvanishing value of the order parameter. We show that,
treating the cluster as an open subsystem of the entire system, new
instanton-like configurations dominate the statistical mechanics of the
cluster. We study the dependence of the resulting fractal dimension on the
embedding dimension and the scaling properties (isothermal critical exponent)
of the system. Taking into account the finite size effects we are able to
calculate the size of the critical cluster in terms of the total size of the
system, the critical temperature and the effective coupling of the long
wavelength interaction at the critical point. We also show that the size of the
cluster has to be identified with the correlation length at criticality.
Finally, within the framework of the mean field approximation, we extend our
local considerations to obtain a global description of the system.Comment: 1 LaTeX file, 4 figures in ps-files. Accepted for publication in
Physical Review
On the predictability of supramolecular interactions in molecular cocrystals-the view from the bench
A series of cocrystals involving theophylline and fluorobenzoic acids highlights the difficulty of predicting supramolecular interactions in molecular crystals.MKC and DKB gratefully acknowledge financial support from the UCL Faculty of Mathematical and Physical Sciences. DKB and WJ thank the Royal Society for a Newton International Fellowship and the Isaac Newton Trust (Trinity College, University of Cambridge) for funding. MA thanks the EPSRC for a studentship, while SAS acknowledges funding through the EPSRC CASE scheme with Pfizer. We are grateful for computational support from the UK national high performance computing service, ARCHER, for which access was obtained via the UKCP consortium and funded by EPSRC grant (EP/K013564/1).This is the final version of the article. It first appeared from the Royal Society of Chemistry via https://doi.org//10.1039/C6CE00293
Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
Random Matrix Theory (RMT) is a powerful statistical tool to model spectral
fluctuations. This approach has also found fruitful application in Quantum
Chromodynamics (QCD). Importantly, RMT provides very efficient means to
separate different scales in the spectral fluctuations. We try to identify the
equivalent of a Thouless energy in complete spectra of the QCD Dirac operator
for staggered fermions from SU(2) lattice gauge theory for different lattice
size and gauge couplings. In disordered systems, the Thouless energy sets the
universal scale for which RMT applies. This relates to recent theoretical
studies which suggest a strong analogy between QCD and disordered systems. The
wealth of data allows us to analyze several statistical measures in the bulk of
the spectrum with high quality. We find deviations which allows us to give an
estimate for this universal scale. Other deviations than these are seen whose
possible origin is discussed. Moreover, we work out higher order correlators as
well, in particular three--point correlation functions.Comment: 24 pages, 24 figures, all included except one figure, missing eps
file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised
version, to appear in PRD, minor modifications and corrected typos, Fig.4
revise
Hatano-Nelson model with a periodic potential
We study a generalisation of the Hatano-Nelson Hamiltonian in which a
periodic modulation of the site energies is present in addition to the usual
random distribution. The system can then become localized by disorder or
develop a band gap, and the eigenspectrum shows a wide variety of topologies.
We determine the phase diagram, and perform a finite size scaling analysis of
the localization transition.Comment: 7 pages, 10 figure
Chiral Phase Transition within Effective Models with Constituent Quarks
We investigate the chiral phase transition at nonzero temperature and
baryon-chemical potential within the framework of the linear sigma
model and the Nambu-Jona-Lasinio model. For small bare quark masses we find in
both models a smooth crossover transition for nonzero and and a
first order transition for T=0 and nonzero . We calculate explicitly the
first order phase transition line and spinodal lines in the plane.
As expected they all end in a critical point. We find that, in the linear sigma
model, the sigma mass goes to zero at the critical point. This is in contrast
to the NJL model, where the sigma mass, as defined in the random phase
approximation, does not vanish. We also compute the adiabatic lines in the
plane. Within the models studied here, the critical point does not
serve as a ``focusing'' point in the adiabatic expansion.Comment: 22 pages, 18 figure
Complex Langevin simulations of a finite density matrix model for QCD
We study a random matrix model for QCD at finite density via complex Langevin
dynamics. This model has a phase transition to a phase with nonzero baryon
density. We study the convergence of the algorithm as a function of the quark
mass and the chemical potential and focus on two main observables: the baryon
density and the chiral condensate. For simulations close to the chiral limit,
the algorithm has wrong convergence properties when the quark mass is in the
spectral domain of the Dirac operator. A possible solution of this problem is
discussed.Comment: 10 pages, 9 figures; Contribution to the "12th Quark Confinement and
the Hadron Spectrum" conference, Thessaloniki, 28.08.-04.09.201
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