Comparative study of semiclassical approaches to quantum dynamics

Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to their numerical implementation. As test cases, we consider the time evolution of Gaussian wave packets in different one-dimensional geometries, whereby tunneling, resonance and anharmonicity effects are taken into account. The results and methods are benchmarked against an exact quantum mechanical treatment of the system, which is based on a highly efficient Chebyshev expansion technique of the time evolution operator.Comment: 32 pages, 8 figures, corrected typos and added references; version as publishe

Response of electrically coupled spiking neurons: a cellular automaton approach

Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by $n$-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is $\alpha=1$, while for deterministic spike propagation we obtain $\alpha=1/2$, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.Comment: 11 pages, 8 figures, to appear in the Phys. Rev.

The influence of marketing on the sports betting attitudes and consumption behaviours of young men: Implications for harm reduction and prevention strategies

Background: Gambling can cause significant health and social harms for individuals, their families, and communities. While many studies have explored the individual factors that may lead to and minimise harmful gambling, there is still limited knowledge about the broader range of factors that may contribute to gambling harm. There are significant regulations to prevent the marketing of some forms of gambling but comparatively limited regulations relating to the marketing of newer forms of online gambling such as sports betting. There is a need for better information about how marketing strategies may be shaping betting attitudes and behaviours and the range of policy and regulatory responses that may help to prevent the risky or harmful consumption of these products. Methods: We conducted qualitative, semi-structured interviews with 50 Australian men (aged 20-37 years) who gambled on sports. We explored their attitudes and opinions regarding sports betting marketing, the embedding of marketing within sports and other non-gambling community environments, and the implications this had for the normalisation of betting. Results: Our findings indicate that most of the environments in which participants reported seeing or hearing betting advertisements were not in environments specifically designed for betting. Participants described that the saturation of marketing for betting products, including through sports-based commentary and sports programming, normalised betting. Participants described that the inducements offered by the industry were effective marketing strategies in getting themselves and other young men to bet on sports. Inducements were also linked with feelings of greater control over betting outcomes and stimulated some individuals to sign up with more than one betting provider. Conclusions: This research suggests that marketing plays a strong role in the normalisation of gambling in sports. This has the potential to increase the risks and subsequent harms associated with these products. Legislators must begin to consider the cultural lag between an evolving gambling landscape, which supports sophisticated marketing strategies, and effective policies and practices which aim to reduce and prevent gambling harm. © 2017 The Author(s)

Minimax estimation of the Wigner function in quantum homodyne tomography with ideal detectors

We estimate the quantum state of a light beam from results of quantum homodyne measurements performed on identically prepared pulses. The state is represented through the Wigner function, a ``quasi-probability density'' on $\mathbb{R}^{2}$ which may take negative values and must respect intrinsic positivity constraints imposed by quantum physics. The data consists of $n$ i.i.d. observations from a probability density equal to the Radon transform of the Wigner function. We construct an estimator for the Wigner function, and prove that it is minimax efficient for the pointwise risk over a class of infinitely differentiable functions. A similar result was previously derived by Cavalier in the context of positron emission tomography. Our work extends this result to the space of smooth Wigner functions, which is the relevant parameter space for quantum homodyne tomography.Comment: 15 page

Phase-space-region operators and the Wigner function: Geometric constructions and tomography

Quasiprobability measures on a canonical phase space give rise through the action of Weyl's quantization map to operator-valued measures and, in particular, to region operators. Spectral properties, transformations, and general construction methods of such operators are investigated. Geometric trace-increasing maps of density operators are introduced for the construction of region operators associated with one-dimensional domains, as well as with two-dimensional shapes (segments, canonical polygons, lattices, etc.). Operational methods are developed that implement such maps in terms of unitary operations by introducing extensions of the original quantum system with ancillary spaces (qubits). Tomographic methods of reconstruction of the Wigner function based on the radon transform technique are derived by the construction methods for region operators. A Hamiltonian realization of the region operator associated with the radon transform is provided, together with physical interpretations

Strange Decays of Nonstrange Baryons

The strong decays of excited nonstrange baryons into the final states Lambda K, Sigma K, and for the first time into Lambda(1405) K, Lambda(1520) K, Sigma(1385) K, Lambda K*, and Sigma K*, are examined in a relativized quark pair creation model. The wave functions and parameters of the model are fixed by previous calculations of N pi and N pi pi, etc., decays. Our results show that it should be possible to discover several new negative parity excited baryons and confirm the discovery of several others by analyzing these final states in kaon production experiments. We also establish clear predictions for the relative strengths of certain states to decay to Lambda(1405) K and Lambda(1520) K, which can be tested to determine if a three-quark model of the Lambda(1405) K is valid. Our results compare favorably with the results of partial wave analyses of the limited existing data for the Lambda K and Sigma K channels. We do not find large Sigma K decay amplitudes for a substantial group of predicted and weakly established negative-parity states, in contrast to the only previous work to consider decays of these states into the strange final states Lambda K and Sigma K.Comment: 25 pages, 8 figures, RevTe

The visible effect of a very heavy magnetic monopole at colliders

If a heavy Dirac monopole exists, the light-to-light scattering below the monopole production threshold is enhanced due to strong coupling of monopoles to photons. At the next Linear Collider with electron beam energy 250 GeV this photon pair production could be observable at monopole masses less than 2.5-6.4 TeV in the $e^+e^-$ mode or 3.7-10 TeV in the $\gamma\gamma$ mode, depending on the monopole spin. At the upgraded Tevatron such an effect is expected to be visible at monopole masses below 1-2.5 TeV. The strong dependence on the initial photon polarizations allows to find the monopole spin in experiments at $e^+e^-$ and $\gamma\gamma$ colliders. We consider the $Z\gamma$ production and the $3\gamma$ production at $e^+e^-$ and $pp$ or $p\bar{p}$ colliders via the same monopole loop. The possibility to discover these processes is significantly lower than that of the $\gamma\gamma$ case.Comment: 18 pages, 2 figures, RevTe

Variation in dermcidin expression in a range of primary human tumours and in hypoxic/oxidatively stressed human cell lines.

Dermcidin acts as a survival factor in a variety of cancer cell lines under hypoxia or oxidative stress. The aim of this study was to evaluate dermcidin expression in cell lines following simulation of tumour microenvironmental conditions and in a range of primary tumours. Tumour tissues were collected from patients with oesophageal (28 samples), gastric (20), pancreatic (five), bile duct (one) and prostatic (52) carcinomas as well as 30 benign tissue samples, for assessment of dermcidin mRNA levels using real-time PCR. Dermcidin expression was assessed in prostatic and pancreatic cancer cell lines, with and without induction of hypoxia or oxidative stress. Dermcidin mRNA expression was very low or absent in both unstressed and stressed prostate cell lines. None of the primary prostate tissue, benign or malignant, expressed dermcidin mRNA. Only two (4%) of the gastro-oesophageal cancer samples expressed moderate quantities of dermcidin mRNA. However, three (60%) of the pancreatic cancer samples and the single cholangiocarcinoma specimen had moderate/high levels of dermcidin expression. Of the two pancreatic cancer cell lines, one expressed dermcidin moderately but neither showed a response to hypoxia or oxidative stress. Expression of dermcidin in human primary tumours appears highly variable and is not induced substantially by hypoxia/oxidative stress in cell line model systems. The relationship of these findings to dermcidin protein levels and cell survival remains to be determined