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Coulomb analogy for nonhermitian degeneracies near quantum phase transitions
Degeneracies near the real axis in a complex-extended parameter space of a
hermitian Hamiltonian are studied. We present a method to measure distributions
of such degeneracies on the Riemann sheet of a selected level and apply it in
classification of quantum phase transitions. The degeneracies are shown to
behave similarly as complex zeros of a partition function.Comment: 4 page
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How organized is deep convection over Germany?
Deep moist convection shows a tendency to organize into mesoscale structures. To be able to understand the potential effect of convective organization on the climate, one needs first to characterize organization. In this study, we systematically characterize the organizational state of convection over Germany based on two years of cloud-top observations derived from the Meteosat Second Generation satellite and of precipitation cores detected by the German C-band radar network. The organizational state of convection is characterized by commonly employed organization indices, which are mostly based on the object numbers, sizes and nearest-neighbour distances. According to the organization index Iorg, cloud tops and precipitation cores are found to be in an organized state for 69% and 92% of the time, respectively. There is an increase in rainfall when the number of objects and their sizes increase, independently of the organizational state. Case-studies of specific days suggest that convectively organized states correspond to either local multi-cell clusters, with less numerous, larger objects close to each other, or to scattered clusters, with more numerous, smaller organized objects spread out over the domain. For those days, simulations are performed with the large-eddy model ICON with grid spacings of 625, 312 and 156?m. Although the model underestimates rainfall and shows a too large cold cloud coverage, the organizational state is reasonably well represented without significant differences between the grid spacings
Different Methods to Define Utility Functions Yield Similar Results but Engage Different Neural Processes
Although the concept of utility is fundamental to many economic theories, up to now a generally accepted method determining a subject's utility function is not available. We investigated two methods that are used in economic sciences for describing utility functions by using response-locked event-related potentials in order to assess their neural underpinnings. For determining the certainty equivalent, we used a lottery game with probabilities to win p = 0.5, for identifying the subjects’ utility functions directly a standard bisection task was applied. Although the lottery tasks’ payoffs were only hypothetical, a pronounced negativity was observed resembling the error related negativity (ERN) previously described in action monitoring research, but this occurred only for choices far away from the indifference point between money and lottery. By contrast, the bisection task failed to evoke an remarkable ERN irrespective of the responses’ correctness. Based on these findings we are reasoning that only decisions made in the lottery task achieved a level of subjective relevance that activates cognitive-emotional monitoring. In terms of economic sciences, our findings support the view that the bisection method is unaffected by any kind of probability valuation or other parameters related to risk and in combination with the lottery task can, therefore, be used to differentiate between payoff and probability valuation
Not all subhaloes are created equal: modelling the diversity of subhalo density profiles in TNG50
In this work, we analyse the density profiles of subhaloes with masses Msh ≥ 1.4 × 108 M in the TNG50 simulation, with the aim of including baryonic effects. We evaluate the performance of frequently used models, such as the standard Navarro–Frenk–White (NFW), the Einasto, and a smoothly truncated version of the NFW profile. We find that these models do not perform well for the majority of subhaloes, with the NFW profile giving the worst fit in most cases. This is primarily due to mismatches in the inner and outer logarithmic slopes, which are significantly steeper for a large number of subhaloes in the presence of baryons. To address this issue, we propose new three-parameter models and show that they significantly improve the goodness of fit independently of the subhalo’s specific properties. Our best-performing model is a modified version of the NFW profile with an inner log-slope of −2 and a variable truncation that is sharper and steeper than the slope transition in the standard NFW profile. Additionally, we investigate how both the parameter values of the best density profile model and the average density profiles vary with subhalo mass, Vmax, distance from the host halo centre, baryon content, and infall time, and we also present explicit scaling relations for the mean parameters of the individual profiles. The newly proposed fit and the scaling relations are useful to predict the properties of realistic subhaloes in the mass range 108 M ≤Msh ≤ 1013 M that can be influenced by the presence of baryons
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