Letter from Archdeacon RR Davies to Dr GF Story, Hobart 1873

A letter from Archdeacon RR Davies to Dr GF Story, Hobart 1873. The letter discusses a specimen of grass (imperator arundi mareae cyrillo) collected near Kelvedon in 1871. The specimen is enclosed within the letter, and a photograph of it is included in this record. From Cotton Family Papers C7/9

On the Role of Density Matrices in Bohmian Mechanics

It is well known that density matrices can be used in quantum mechanics to represent the information available to an observer about either a system with a random wave function (``statistical mixture'') or a system that is entangled with another system (``reduced density matrix''). We point out another role, previously unnoticed in the literature, that a density matrix can play: it can be the ``conditional density matrix,'' conditional on the configuration of the environment. A precise definition can be given in the context of Bohmian mechanics, whereas orthodox quantum mechanics is too vague to allow a sharp definition, except perhaps in special cases. In contrast to statistical and reduced density matrices, forming the conditional density matrix involves no averaging. In Bohmian mechanics with spin, the conditional density matrix replaces the notion of conditional wave function, as the object with the same dynamical significance as the wave function of a Bohmian system.Comment: 16 pages LaTeX, no figure

Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.Comment: To appear in "Integral Equations and Operator Theory

The Hindered M1 Radiative Decay Υ(2S) → ηb(1S)γ from Lattice NRQCD

We present a calculation of the hindered M$1$ $\Upsilon(2S) \to \eta_b(1S) \gamma$ decay rate using lattice non-relativistic QCD. The calculation includes spin-dependent relativistic corrections to the NRQCD action through $\mathcal{O}(v^6)$ in the quark's relative velocity, relativistic corrections to the leading order current which mediates the transition through the quark's magnetic moment, radiative corrections to the leading spin-magnetic coupling and for the first time a full error budget. We also use gluon field ensembles at multiple lattice spacing values, all of which include $u$, $d$, $s$ and $c$ quark vacuum polarisation. Our result for the branching fraction is $\mathcal{B}(\Upsilon(2S)\to\eta_b(1S)\gamma) = 5.4(1.8)\times 10^{-4}$, which agrees with the current experimental value.This is the author accepted manuscript. The final version is available from APS via http://dx.doi.org/10.1103/PhysRevD.92.09450

Bell-Type Quantum Field Theories

In [Phys. Rep. 137, 49 (1986)] John S. Bell proposed how to associate particle trajectories with a lattice quantum field theory, yielding what can be regarded as a |Psi|^2-distributed Markov process on the appropriate configuration space. A similar process can be defined in the continuum, for more or less any regularized quantum field theory; such processes we call Bell-type quantum field theories. We describe methods for explicitly constructing these processes. These concern, in addition to the definition of the Markov processes, the efficient calculation of jump rates, how to obtain the process from the processes corresponding to the free and interaction Hamiltonian alone, and how to obtain the free process from the free Hamiltonian or, alternatively, from the one-particle process by a construction analogous to "second quantization." As an example, we consider the process for a second quantized Dirac field in an external electromagnetic field.Comment: 53 pages LaTeX, no figure

Improving the kinetic couplings in lattice nonrelativistic QCD

We improve the non-relativistic QCD (NRQCD) action by comparing the dispersion relation to that of the continuum through $\mathcal{O}(p^6)$ in perturbation theory. The one-loop matching coefficients of the $\mathcal{O}(p^4)$ kinetic operators are determined, as well as the scale at which to evaluate $\alpha_s$ in the $V$-scheme for each quantity. We utilise automated lattice perturbation theory using twisted boundary conditions as an infrared regulator. The one-loop radiative corrections to the mass renormalisation, zero-point energy and overall energy-shift of an NRQCD $b$-quark are also found. We also explore how a Fat$3$-smeared NRQCD action and changes of the stability parameter $n$ affect the coefficients. Finally, we use gluon field ensembles at multiple lattice spacing values, all of which include $u$, $d$, $s$ and $c$ quark vacuum polarisation, to test how the improvements affect the non-perturbatively determined $\Upsilon(1S)$ and $\eta_b(1S)$ kinetic masses, and the tuning of the $b$ quark mass

Obituary: Professor Patrick Gerard Quilty AM

Patrick Quilty had a long and distinguished career in Earth Science and Antarctic exploration. His many contributions to The Royal Society of Tasmania have been very significant and highly regarded by members and Council

B, Bs, K and pi weak matrix elements with physical light quarks

Calculations of pseudoscalar decay constants of B, Bs, K and pi mesons with physical light quarks are presented. We use HISQ ensembles that include u,d,s and c sea quarks at three lattice spacings. HISQ is used for the valence light quarks and a radiatively improved NRQCD action for the heavy quarks. The key results are f_{B^+}=0.184(4)$ GeV, f_{B_s}=0.224(4) GeV, f_{B_s}/f_{B^+}=1.217(8), f_{K^+}/f_{pi^+}=1.1916(21), f_{K^+}=155.37(34) MeV, giving a significant improvement over previous results that required chiral extrapolation. We also calculate the Wilson flow scale w_0, finding w_0=0.1715(9) fm

Neutral B-meson mixing from full lattice QCD at the physical point

We calculate the bag parameters for neutral $B$-meson mixing in and beyond the Standard Model, in full four-flavour lattice QCD for the first time. We work on gluon field configurations that include the effect of $u$, $d$, $s$ and $c$ sea quarks with the Highly Improved Staggered Quark (HISQ) action at three values of the lattice spacing and with three $u/d$ quark masses going down to the physical value. The valence $b$ quarks use the improved NRQCD action and the valence light quarks, the HISQ action. Our analysis was blinded. Our results for the bag parameters for all five operators are the most accurate to date. For the Standard Model operator between $B_s$ and $B_d$ mesons we find: $\hat{B}_{B_s}=1.232(53)$, $\hat{B}_{B_d}=1.222(61)$. Combining our results with lattice QCD calculations of the decay constants using HISQ quarks from the Fermilab/MILC collaboration and with experimental values for $B_s$ and $B_d$ oscillation frequencies allows determination of the CKM elements $V_{ts}$ and $V_{td}$. We find $V_{ts} = 0.04189(93)$, $V_{td} = 0.00867(23)$ and $V_{ts}/V_{td} = 0.2071(27)$. Our results agree well (within $2\sigma$) with values determined from CKM unitarity constraints based on tree-level processes (only). Using a ratio to $\Delta M$ in which CKM elements cancel in the Standard Model, we determine the branching fractions ${\text{Br}}(B_s\rightarrow \mu^+\mu^-) = 3.81(18) \times 10^{-9}$ and ${\text{Br}}(B_d\rightarrow \mu^+\mu^-) = 1.031(54) \times 10^{-10}$. We also give results for matrix elements of the operators $R_0$, $R_1$ and $\tilde{R}_1$ that contribute to neutral $B$-meson width differences.This work was funded by STFC, the Royal Society, the Wolfson Foundation and the US DOE and National Science Foundation

Two-neutron knockout from neutron-deficient 34^{34}Ar, 30^{30}S, and 26^{26}Si

Two-neutron knockout reactions from nuclei in the proximity of the proton dripline have been studied using intermediate-energy beams of neutron-deficient $^{34}$Ar, $^{30}$S, and $^{26}$Si. The inclusive cross sections, and also the partial cross sections for the population of individual bound final states of the $^{32}$Ar, $^{28}$S and $^{24}$Si knockout residues, have been determined using the combination of particle and $\gamma$-ray spectroscopy. Similar to the two-proton knockout mechanism on the neutron-rich side of the nuclear chart, these two-neutron removal reactions from already neutron-deficient nuclei are also shown to be consistent with a direct reaction mechanism.Comment: Phys. Rev. C, rapid communication, in pres