SU(N) Matrix Difference Equations and a Nested Bethe Ansatz

A system of SU(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz, also called "off shell" Bethe Ansatz. The highest weight property of the solutions is proved. (Part I of a series of articles on the generalized nested Bethe Ansatz and difference equations.)Comment: 18 pages, LaTe

Dynamical generation of synthetic electric fields for photons in the quantum regime

Optomechanics offers a natural way to implement synthetic dynamical gauge fields, leading to synthetic electric fields for phonons and, as a consequence, to unidirectional light transport. Here we investigate the quantum dynamics of synthetic gauge fields in the minimal setup of two optical modes coupled by phonon-assisted tunneling where the phonon mode is undergoing self-oscillations. We use the quantum van-der-Pol oscillator as the simplest dynamical model for a mechanical self-oscillator that allows us to perform quantum master equation simulations. We identify a single parameter, which controls the strength of quantum fluctuations, enabling us to investigate the classical-to-quantum crossover. We show that the generation of synthetic electric fields is robust against noise and that it leads to unidirectional transport of photons also in the quantum regime, albeit with a reduced isolation ratio. Our study opens the path for studying dynamical gauge fields in the quantum regime based on optomechanical arrays

Adding many Baumgartner clubs

I define a homogeneous ℵ2–c.c. proper product forcing for adding many clubs of ω1 with finite conditions. I use this forcing to build models of b(ω1)=ℵ2, together with d(ω1) and 2ℵ0 large and with very strong failures of club guessing at ω1

Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases

The analysis of noisy quantum states prepared on current quantum computers is getting beyond the capabilities of classical computing. Quantum neural networks based on parametrized quantum circuits, measurements and feed-forward can process large amounts of quantum data to reduce measurement and computational costs of detecting non-local quantum correlations. The tolerance of errors due to decoherence and gate infidelities is a key requirement for the application of quantum neural networks on near-term quantum computers. Here we construct quantum convolutional neural networks (QCNNs) that can, in the presence of incoherent errors, recognize different symmetry-protected topological phases of generalized cluster-Ising Hamiltonians from one another as well as from topologically trivial phases. Using matrix product state simulations, we show that the QCNN output is robust against symmetry-breaking errors below a threshold error probability and against all symmetry-preserving errors provided the error channel is invertible. This is in contrast to string order parameters and the output of previously designed QCNNs, which vanish in the presence of any symmetry-breaking errors. To facilitate the implementation of the QCNNs on near-term quantum computers, the QCNN circuits can be shortened from logarithmic to constant depth in system size by performing a large part of the computation in classical post-processing. These constant-depth QCNNs reduce sample complexity exponentially with system size in comparison to the direct sampling using local Pauli measurements.Comment: 24 pages, 12 figure

Reference values for spirometry and their use in test interpretation: A Position Statement from the Australian and New Zealand Society of Respiratory Science

Traditionally, spirometry testing tended to be confined to the realm of hospital-based laboratories but is now performed in a variety of health care settings. Regardless of the setting in which the test is conducted, the fundamental basis of spirometry is that the test is both performed and interpreted according to the international standards. The purpose of this Australian and New Zealand Society of Respiratory Science (ANZSRS) statement is to provide the background and recommendations for the interpretation of spirometry results in clinical practice. This includes the benchmarking of an individual's results to population reference data, as well as providing the platform for a statistically and conceptually based approach to the interpretation of spirometry results. Given the many limitations of older reference equations, it is imperative that the most up-to-date and relevant reference equations are used for test interpretation. Given this, the ANZSRS recommends the adoption of the Global Lung Function Initiative (GLI) 2012 spirometry reference values throughout Australia and New Zealand. The ANZSRS also recommends that interpretation of spirometry results is based on the lower limit of normal from the reference values and the use of Z-scores where available

Difference Equations and Highest Weight Modules of U_q[sl(n)]

The quantized version of a discrete Knizhnik-Zamolodchikov system is solved by an extension of the generalized Bethe Ansatz. The solutions are constructed to be of highest weight which means they fully reflect the internal quantum group symmetry.Comment: 9 pages, LaTeX, no figure

The nested SU(N) off-shell Bethe ansatz and exact form factors

The form factor equations are solved for an SU(N) invariant S-matrix under the assumption that the anti-particle is identified with the bound state of N-1 particles. The solution is obtained explicitly in terms of the nested off-shell Bethe ansatz where the contribution from each level is written in terms of multiple contour integrals.Comment: This work is dedicated to the 75th anniversary of H. Bethe's foundational work on the Heisenberg chai

Highest Weight Uq[sl(n)]U_q[sl(n)] Modules and Invariant Integrable n-State Models with Periodic Boundary Conditions"

The weights are computed for the Bethe vectors of an RSOS type model with periodic boundary conditions obeying $U_q[sl(n)]$ ($q=\exp(i\pi/r)$) invariance. They are shown to be highest weight vectors. The q-dimensions of the corresponding irreducible representations are obtained.Comment: 5 pages, LaTeX, SFB 288 preprin

Matrix difference equations for the supersymmetric Lie algebra sl(2,1) and the `off-shell' Bethe ansatz

Based on the rational R-matrix of the supersymmetric sl(2,1) matrix difference equations are solved by means of a generalization of the nested algebraic Bethe ansatz. These solutions are shown to be of highest-weight with respect to the underlying graded Lie algebra structure.Comment: 10 pages, LaTex, references and acknowledgements added, spl(2,1) now called sl(2,1