8,388 research outputs found
Quantum-Mechanical Dualities on the Torus
On classical phase spaces admitting just one complex-differentiable
structure, there is no indeterminacy in the choice of the creation operators
that create quanta out of a given vacuum. In these cases the notion of a
quantum is universal, i.e., independent of the observer on classical phase
space. Such is the case in all standard applications of quantum mechanics.
However, recent developments suggest that the notion of a quantum may not be
universal. Transformations between observers that do not agree on the notion of
an elementary quantum are called dualities. Classical phase spaces admitting
more than one complex-differentiable structure thus provide a natural framework
to study dualities in quantum mechanics. As an example we quantise a classical
mechanics whose phase space is a torus and prove explicitly that it exhibits
dualities.Comment: New examples added, some precisions mad
Spanning tree generating functions and Mahler measures
We define the notion of a spanning tree generating function (STGF) , which gives the spanning tree constant when evaluated at and gives
the lattice Green function (LGF) when differentiated. By making use of known
results for logarithmic Mahler measures of certain Laurent polynomials, and
proving new results, we express the STGFs as hypergeometric functions for all
regular two and three dimensional lattices (and one higher-dimensional
lattice). This gives closed form expressions for the spanning tree constants
for all such lattices, which were previously largely unknown in all but one
three-dimensional case. We show for all lattices that these can also be
represented as Dirichlet -series. Making the connection between spanning
tree generating functions and lattice Green functions produces integral
identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday.
This version has additional references, additional calculations, and minor
correction
Evolution of InAs branches in InAs/GaAs nanowire heterostructures
Branched nanowireheterostructures of InAs∕GaAs were observed during Au-assisted growth of InAs on GaAsnanowires. The evolution of these branches has been determined through detailed electron microscopy characterization with the following sequence: (1) in the initial stage of InAsgrowth, the Au droplet is observed to slide down the side of the GaAsnanowire, (2) the downward movement of Aunanoparticle later terminates when the nanoparticle encounters InAsgrowing radially on the GaAsnanowire sidewalls, and (3) with further supply of In and As vapor reactants, the Aunanoparticles assist the formation of InAs branches with a well-defined orientation relationship with GaAs∕InAs core/shell stems. We anticipate that these observations advance the understanding of the kink formation in axial nanowireheterostructures.The Australian Research Council is acknowledged for
the financial support of this project. One of the authors
M.P. acknowledges the support of an International Postgraduate
Research Scholarship
A combinatorial approach to knot recognition
This is a report on our ongoing research on a combinatorial approach to knot
recognition, using coloring of knots by certain algebraic objects called
quandles. The aim of the paper is to summarize the mathematical theory of knot
coloring in a compact, accessible manner, and to show how to use it for
computational purposes. In particular, we address how to determine colorability
of a knot, and propose to use SAT solving to search for colorings. The
computational complexity of the problem, both in theory and in our
implementation, is discussed. In the last part, we explain how coloring can be
utilized in knot recognition
Absence of spontaneous magnetic order at non-zero temperature in one- and two-dimensional Heisenberg and XY systems with long-range interactions
The Mermin-Wagner theorem is strengthened so as to rule out magnetic
long-range order at T>0 in one- or two-dimensional Heisenberg and XY systems
with long-range interactions decreasing as R^{-alpha} with a sufficiently large
exponent alpha. For oscillatory interactions, ferromagnetic long-range order at
T>0 is ruled out if alpha >= 1 (D=1) or alpha > 5/2 (D=2). For systems with
monotonically decreasing interactions ferro- or antiferromagnetic long-range
order at T>0 is ruled out if alpha >= 2D.Comment: RevTeX, 4 pages. Further (p)reprints available from
http://www.mpi-halle.de/~theory ; v2: revised versio
Characterizing temporary hydrological regimes at a European scale
Monthly duration curves have been constructed from climate data across Europe to help address the relative frequency of ecologically critical low flow stages in temporary rivers, when flow persists only in disconnected pools in the river bed. The hydrological model is 5 based on a partitioning of precipitation to estimate water available for evapotranspiration and plant growth and for residual runoff. The duration curve for monthly flows has then been analysed to give an estimate of bankfull flow based on recurrence interval. The corresponding frequency for pools is then based on the ratio of bank full discharge to pool flow, arguing from observed ratios of cross-sectional areas at flood 10 and low flows to estimate pool flow as 0.1% of bankfull flow, and so estimate the frequency of the pool conditions that constrain survival of river-dwelling arthropods and fish. The methodology has been applied across Europe at 15 km resolution, and can equally be applied under future climatic scenarios
Low-temperature coherence in the periodic Anderson model: Predictions for photoemission of heavy Fermions
We present numerically exact predictions of the periodic and single-impurity
Anderson models to address photoemission experiments on heavy Fermion systems.
Unlike the single impurity model the lattice model is able to account for the
enhanced intensity, dispersion, and apparent weak temperature dependence of the
Kondo resonant peak seen in recent controversial photoemission experiments. We
present a consistent interpretation of these results as a crossover from the
impurity regime to an effective Hubbard model regime described by Nozieres.Comment: 4 pages, 3 figure
Surgery and the Spectrum of the Dirac Operator
We show that for generic Riemannian metrics on a simply-connected closed spin
manifold of dimension at least 5 the dimension of the space of harmonic spinors
is no larger than it must be by the index theorem. The same result holds for
periodic fundamental groups of odd order.
The proof is based on a surgery theorem for the Dirac spectrum which says
that if one performs surgery of codimension at least 3 on a closed Riemannian
spin manifold, then the Dirac spectrum changes arbitrarily little provided the
metric on the manifold after surgery is chosen properly.Comment: 23 pages, 4 figures, to appear in J. Reine Angew. Mat
Optimal interlayer hopping and high temperature Bose–Einstein condensation of local pairs in quasi 2D superconductors
Both FeSe and cuprate superconductors are quasi 2D materials with high transition temperatures and local fermion pairs. Motivated by such systems, we investigate real space pairing of fermions in an anisotropic lattice model with intersite attraction, V, and strong local Coulomb repulsion, U, leading to a determination of the optimal conditions for superconductivity from Bose–Einstein condensation. Our aim is to gain insight as to why high temperature superconductors tend to be quasi 2D. We make both analytically and numerically exact solutions for two body local pairing applicable to intermediate and strong V. We find that the Bose–Einstein condensation temperature of such local pairs pairs is maximal when hopping between layers is intermediate relative to in-plane hopping, indicating that the quasi 2D nature of unconventional superconductors has an important contribution to their high transition temperatures
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