Wigner localization in quantum dots from Kohn-Sham density functional theory without symmetry breaking

We address low-density two-dimensional circular quantum dots with spin-restricted Kohn-Sham density functional theory. By using an exchange-correlation functional that encodes the effects of the strongly-correlated regime (and that becomes exact in the limit of infinite correlation), we are able to reproduce characteristic phenomena such as the formation of ring structures in the electronic total density, preserving the fundamental circular symmetry of the system. The observation of this and other well-known effects in Wigner-localized quantum dots such as the flattening of the addition energy spectra, has until now only been within the scope of other, numerically more demanding theoretical approachesComment: 8 pages, 6 figure

Quantum synchronization as a local signature of super- and subradiance

We study the relationship between the collective phenomena of super and subradiance and spontaneous synchronization of quantum systems. To this aim we revisit the case of two detuned qubits interacting through a pure dissipative bosonic environment, which contains the minimal ingredients for our analysis. By using the Liouville formalism, we are able to find analytically the ultimate connection between these phenomena. We find that dynamical synchronization is due to the presence of long standing coherence between the ground state of the system and the subradiant state. We finally show that, under pure dissipation, the emergence of spontaneous synchronization and of subradiant emission occur on the same time scale. This reciprocity is broken in the presence of dephasing noise.Comment: 12 pages, 6 figure

A Satisficing Alternative to Prospect Theory

In this paper, we axiomatize a target-based model of choice that allows decision makers to be both risk averse and risk seeking, depending on the payoff's position relative to a prespecified target. The approach can be viewed as a hybrid model, capturing in spirit two celebrated ideas: first, the satisficing concept of Simon (1955); second, the switch between risk aversion and risk seeking popularized by the prospect theory of Kahneman and Tversky (1979). Our axioms are simple and intuitive; in order to be implemented in practice, our approach requires only the specification of an aspiration level. We show that this approach is dual to a known approach using risk measures, thereby allowing us to connect to existing theory. Though our approach is intended to be normative, we also show that it resolves the classical examples of Allais (1953) and Ellsberg (1961).satisficing; aspiration levels; targets; prospect theory; reflection effect; risk measures; coherent risk measures; convex risk measures; portfolio optimization

Dual representation of choice and aspirational preferences

We consider choice over a set of monetary acts (random variables) and study a general class of preferences. These preferences favor diversification, except perhaps on a subset of sufficiently disliked acts, over which concentration is instead preferred. This structure encompasses a number of known models in this setting. We show that such preferences can be expressed in dual form in terms of a family of measures of risk and a target function. Specifically, the choice function is equivalent to selection of a maximum index level such that the risk of beating the target function at that level is acceptable. This dual representation may help to uncover new models of choice. One that we explore in detail is the special case of a bounded target function. This case corresponds to a type of satisficing and has descriptive relevance. Moreover, the model results in optimization problems that may be efficiently solved in large-scale.

Density functional theory for strongly-correlated bosonic and fermionic ultracold dipolar and ionic gases

We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Due to its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-field theories fail.Comment: 5 pages, 2 figure

Dystonia: sparse synapses for D2 receptors in striatum of a DYT1 knock-out mouse model

Dystonia pathophysiology has been partly linked to downregulation and dysfunction of dopamine D2 receptors in striatum. We aimed to investigate the possible morpho-structural correlates of D2 receptor downregulation in the striatum of a DYT1 Tor1a mouse model. Adult control Tor1a+/+ and mutant Tor1a+/− mice were used. The brains were perfused and free-floating sections of basal ganglia were incubated with polyclonal anti-D2 antibody, followed by secondary immune-fluorescent antibody. Confocal microscopy was used to detect immune-fluorescent signals. The same primary antibody was used to evaluate D2 receptor expression by western blot. The D2 receptor immune-fluorescence appeared circumscribed in small disks (~0.3–0.5 μm diameter), likely representing D2 synapse aggregates, densely distributed in the striatum of Tor1a+/+ mice. In the Tor1a+/− mice the D2 aggregates were significantly smaller (μm2 2.4 ± SE 0.16, compared to μm2 6.73 ± SE 3.41 in Tor1a+/+) and sparse, with ~30% less number per microscopic field, value correspondent to the amount of reduced D2 expression in western blotting analysis. In DYT1 mutant mice the sparse and small D2 synapses in the striatum may be insufficient to “gate” the amount of presynaptic dopamine release diffusing in peri-synaptic space, and this consequently may result in a timing and spatially larger nonselective sphere of influence of dopamine action

Pair densities at contact in the quantum electron gas

The value of the pair distribution function g(r) at contact (r = 0) in a quantum electron gas is determined by the scattering events between pairs of electrons with antiparallel spins. The theoretical results for g(0) as a function of the coupling strength r_s in the paramagnetic electron gas in dimensionality D=2 and 3, that have been obtained from the solution of the two-body scattering problem with a variety of effective scattering potentials embodying many-body effects, are compared with the results of many-body calculations in the ladder approximation and with quantum Monte Carlo data.Comment: 7 pages, 2 figure

Pair-distribution functions of the two-dimensional electron gas

Based on its known exact properties and a new set of extensive fixed-node reptation quantum Monte Carlo simulations (both with and without backflow correlations, which in this case turn out to yield negligible improvements), we propose a new analytical representation of (i) the spin-summed pair-distribution function and (ii) the spin-resolved potential energy of the ideal two-dimensional interacting electron gas for a wide range of electron densities and spin polarization, plus (iii) the spin-resolved pair-distribution function of the unpolarized gas. These formulae provide an accurate reference for quantities previously not available in analytic form, and may be relevant to semiconductor heterostructures, metal-insulator transitions and quantum dots both directly, in terms of phase diagram and spin susceptibility, and indirectly, as key ingredients for the construction of new two-dimensional spin density functionals, beyond the local approximation.Comment: 12 pages, 10 figures; misprints correcte