The Hubbard model on a complete graph: Exact Analytical results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.Comment: Email:[email protected]

Landau-Zener Tunneling of Bose-Einstein Condensates in an Optical Lattice

A theory of the non-symmetric Landau-Zener tunneling of Bose-Einstein condensates in deep optical lattices is presented. It is shown that periodic exchange of matter between the bands is described by a set of linearly coupled nonlinear Schr\"{o}dinger equations. The key role of the modulational instability in rendering the inter-band transitions irreversible is highlighted.Comment: 4 pages, 3 figure

Synthesis of Curcumin Derivatives and Analysis of Their Antitumor Effects in Triple Negative Breast Cancer (TNBC) Cell Lines

We analyzed antitumor effects of a series of curcumin analogues. Some of them were obtained by reaction of substitution involving the two phenolic OH groups of curcumin while the analogues with a substituent at C-4 was prepared following an original procedure that regards the condensation of benzenesulfenic acid onto the nucleophilic central carbon of the curcumin skeleton. We analyzed cytotoxic effects of such derivatives on two TNBC (triple negative breast cancer) cell lines, SUM 149 and MDA-MB-231, but only three of them showed an IC50 in a lower micromolar range with respect to curcumin. We also focused on these three derivatives that in both cell lines exhibited a higher or at least equivalent pro-apoptotic effect than curcumin. The analysis of molecular mechanisms of action of the curcumin derivatives under study has highlighted that they decreased NF-κB transcriptional factor activity, and consequently the expression of some NF-κB targets. Our data confirmed once again that curcumin may represent a very good lead compound to design analogues with higher antitumor capacities and able to overcome drug resistance with respect to conventional ones, even in tumors difficult to treat as TNBC

Hierarchy of boundary driven phase transitions in multi-species particle systems

Interacting systems with $K$ driven particle species on a open chain or chains which are coupled at the ends to boundary reservoirs with fixed particle densities are considered. We classify discontinuous and continuous phase transitions which are driven by adiabatic change of boundary conditions. We build minimal paths along which any given boundary driven phase transition (BDPT) is observed and reveal kinetic mechanisms governing these transitions. Combining minimal paths, we can drive the system from a stationary state with all positive characteristic speeds to a state with all negative characteristic speeds, by means of adiabatic changes of the boundary conditions. We show that along such composite paths one generically encounters $Z$ discontinuous and $2(K-Z)$ continuous BDPTs with $Z$ taking values $0\leq Z\leq K$ depending on the path. As model examples we consider solvable exclusion processes with product measure states and $K=1,2,3$ particle species and a non-solvable two-way traffic model. Our findings are confirmed by numerical integration of hydrodynamic limit equations and by Monte Carlo simulations. Results extend straightforwardly to a wide class of driven diffusive systems with several conserved particle species.Comment: 12 pages, 11 figure

Soliton ratchets induced by ac forces with harmonic mixing

The ratchet dynamics of a kink (topological soliton) of a dissipative sine-Gordon equation in the presence of ac forces with harmonic mixing (at least bi-harmonic) of zero mean is studied. The dependence of the kink mean velocity on system parameters is investigated numerically and the results are compared with a perturbation analysis based on a point particle representation of the soliton. We find that first order perturbative calculations lead to incomplete descriptions, due to the important role played by the soliton-phonon interaction in establishing the phenomenon. The role played by the temporal symmetry of the system in establishing soliton ratchets is also emphasized. In particular, we show the existence of an asymmetric internal mode on the kink profile which couples to the kink translational mode through the damping in the system. Effective soliton transport is achieved when the internal mode and the external force get phase locked. We find that for kinks driven by bi-harmonic drivers consisting of the superposition of a fundamental driver with its first odd harmonic, the transport arises only due to this {\it internal mode} mechanism, while for bi-harmonic drivers with even harmonic superposition, also a point-particle contribution to the drift velocity is present. The phenomenon is robust enough to survive the presence of thermal noise in the system and can lead to several interesting physical applications.Comment: 9 pages, 13 figure

Compactons in Nonlinear Schr\"odinger Lattices with Strong Nonlinearity Management

The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the resulting effective inter-well tunneling depends on modulation parameters {\it and} on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multi-site stable discrete compactons in nonlinear optical waveguide and BEC arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.Comment: 4 pages, 4 figure

Ratchet-like dynamics of fluxons in annular Josephson junctions driven by bi-harmonic microwave fields

Experimental observation of the unidirectional motion of a topological soliton driven by a bi-harmonic ac force of zero mean is reported. The observation is made by measuring the current-voltage characteristics for a fluxon trapped in an annular Josephson junction that was placed into a microwave field. The measured dependence of the fluxon mean velocity (rectified voltage) at zero dc bias versus the phase shift between the first and second harmonic of the driving force is in qualitative agreement with theoretical expectations.Comment: 6 figure

Discrete soliton ratchets driven by biharmonic fields

Directed motion of topological solitons (kinks or antikinks) in the damped and AC-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform unidirectional motion. The phenomenon resembles the well known effects of ratchet transport and nonlinear harmonic mixing. Direction of the motion and its velocity depends on the shape of the AC drive. Necessary conditions for the occurrence of the effect are formulated. In comparison with the previously studied continuum case, the discrete case shows a number of new features: non-zero depinning threshold for the driving amplitude, locking to the rational fractions of the driving frequency, and diffusive ratchet motion in the case of weak intersite coupling.Comment: 13 pages, 13 figure

The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions

We propose a method by which the quantization of the Hall conductance can be directly measured in the transport of a one-dimensional atomic gas. Our approach builds on two main ingredients: (1) a constriction optical potential, which generates a mesoscopic channel connected to two reservoirs, and (2) a time-periodic modulation of the channel, specifically designed to generate motion along an additional synthetic dimension. This fictitious dimension is spanned by the harmonic-oscillator modes associated with the tightly-confined channel, and hence, the corresponding "lattice sites" are intimately related to the energy of the system. We analyze the quantum transport properties of this hybrid two-dimensional system, highlighting the appealing features offered by the synthetic dimension. In particular, we demonstrate how the energetic nature of the synthetic dimension, combined with the quasi-energy spectrum of the periodically-driven channel, allows for the direct and unambiguous observation of the quantized Hall effect in a two-reservoir geometry. Our work illustrates how topological properties of matter can be accessed in a minimal one-dimensional setup, with direct and practical experimental consequences.

Separaxion anxiety in pediatric migraine without aura: A pilot study

Background: Separation anxiety (SA) can be defined as the fear reaction and protest manifested by children when the main caregivers move away from him/her or in front of unfamiliar person. SA near eight months may be considered as an important and normal phase of the correct and typical social neurodevelopment. Aims of the present pilot study is assessing the prevalence of separation anxiety in a population of patients with migraine without aura (MwA). Materials and methods: 119 children (69 males) suffering from MwA (mean age 1.78 ± 7:59) were consecutively recruited. The control population consisted of 231 (114 males) healthy subjects similar for age (7.64 ± 1:34; p = 0.768) and gender (p=0.987) The Screen for child anxiety related emotional disorders (SCARED) test was used to assess the prevalence of separation anxiety among MwA children. Results: Healthy individuals are on average less affected (mean 4.72 ± 0:32) of the Separation Anxiety Disorder respect of MwA children (mean 6.83 ± 0.97; p < 0.001) (Figure 1). Conclusion. MwA presents many psychiatric comorbidities and among ones separation anxiety may be considered in the clinical and therapeutic management of pediatric primary headache