Cluster Dynamical Mean-Field Theory of the density-driven Mott transition in the one-dimensional Hubbard model

The one-dimensional Hubbard model is investigated by means of two different cluster schemes suited to introduce short-range spatial correlations beyond the single-site Dynamical Mean-Field Theory, namely the Cluster-Dynamical Mean-Field Theory and its periodized version. It is shown that both cluster schemes are able to describe with extreme accuracy the evolution of the density as a function of the chemical potential from the Mott insulator to the metallic state. Using exact diagonalization to solve the cluster impurity model, we discuss the role of the truncation of the Hilbert space of the bath, and propose an algorithm that gives higher weights to the low frequency hybridization matrix elements and improves the speed of the convergence of the algorithm.Comment: 6 pages, 4 figures, minor corrections in v

Pseudogap induced by short-range spin correlations in a doped Mott insulator

We study the evolution of a Mott-Hubbard insulator into a correlated metal upon doping in the two-dimensional Hubbard model using the Cellular Dynamical Mean Field Theory. Short-range spin correlations create two additional bands apart from the familiar Hubbard bands in the spectral function. Even a tiny doping into this insulator causes a jump of the Fermi energy to one of these additional bands and an immediate momentum dependent suppression of the spectral weight at this Fermi energy. The pseudogap is closely tied to the existence of these bands. This suggests a strong-coupling mechanism that arises from short-range spin correlations and large scattering rates for the pseudogap phenomenon seen in several cuprates.Comment: 6 pages, 6 figure

Sequence-Selection-Based Constellation Shaping for Nonlinear Channels

Probabilistic shaping is, nowadays, a pragmatic and popular approach to improve the performance of coherent optical fiber communication systems. In the linear regime, the potential of probabilistic shaping in terms of shaping gain and rate granularity is well known, and its practical implementation has been mostly mastered. In the nonlinear regime, the advantages offered by probabilistic shaping remain not only valid, but might also increase thanks to the appealing opportunity to use the same technique to mitigate nonlinear effects and obtain an additional nonlinear shaping gain. Unfortunately, despite the recent research efforts, the optimization of conventional shaping techniques, such as probabilistic amplitude shaping (PAS), yields a relevant nonlinear shaping gain only in particular scenarios of limited practical interest, e.g., in the absence of carrier phase recovery. Recently, a more theoretical approach, referred to as sequence selection, has been proposed to understand the performance and limitation of nonlinear constellation shaping. Sequence selection shapes the distribution of the transmitted symbols by selecting or discarding the sequences generated by a certain source according to a metric that measures their quality. In this manuscript, after a brief review of conventional probabilistic shaping, we use sequence selection to investigate through simulations the potential, opportunities, and challenges offered by probabilistic shaping for nonlinear channels. First, we show that ideal sequence selection is able to provide up to 0.13 b/s/Hz additional gain with respect to PAS with an optimized blocklength. However, this additional gain is obtained only if the selection metric accounts for the signs of the symbols, ruling out the possibility of using one of the simple recently proposed sign-independent metrics. We also show that, while the signs must be known to compute the selection metric, there is no need to shape them, since nearly the same gain can be obtained by properly selecting the amplitudes (with a sign-dependent metric) and leaving the signs uniform i.i.d. Furthermore, we show that the selection depends in a non-critical way on the symbol rate and link length: the sequences selected for a certain scenario still provide a relevant gain if the link length or baud rate are modified (within a reasonable range). Then, we analyze and compare several practical implementations of sequence selection by taking into account interaction with forward error correction (FEC), information loss due to selection, and complexity. Overall, we conclude that the single block and the multi block FEC-independent bit scrambling are the best options for the practical implementation of sequence selection, with a gain up to 0.08 b/s/Hz. The main challenge and limitation to their practical implementation remains the evaluation of the metric, whose complexity is currently too high. Finally, we show that the nonlinear shaping gain provided by sequence selection persists when carrier phase recovery is included, in contrast to the nonlinear shaping gain offered by optimizing the blocklength of conventional PAS techniques

On the Nonlinear Shaping Gain with Probabilistic Shaping and Carrier Phase Recovery

The performance of different probabilistic amplitude shaping (PAS)techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques—namely, sphere shaping, shell mapping with different number of shells, and constant composition DM—and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations ($1\times 180$ km, $15\times 80$ km, and $27\times 80$ km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm

Unconventional high-energy-state contribution to the Cooper pairing in under-doped copper-oxide superconductor HgBa2_2Ca2_2Cu3_3O8+δ_{8+\delta}

We study the temperature-dependent electronic B1g Raman response of a slightly under-doped single crystal HgBa$_2$Ca$_2$Cu$_3$O$_{8+\delta}$ with a superconducting critical temperature Tc=122 K. Our main finding is that the superconducting pair-breaking peak is associated with a dip on its higher-energy side, disappearing together at Tc. This result hints at an unconventional pairing mechanism, whereas spectral weight lost in the dip is transferred to the pair-breaking peak at lower energies. This conclusion is supported by cellular dynamical mean-field theory on the Hubbard model, which is able to reproduce all the main features of the B1g Raman response and explain the peak-dip behavior in terms of a nontrivial relationship between the superconducting and the pseudo gaps.Comment: 7 pages 4 figure

Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators

Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step towards a quantitative theory of the competition between antiferromagnetism (AFM) and d-wave superconductivity (SC) in the cuprates, we use Cellular Dynamical Mean Field Theory to compute zero temperature properties of the two-dimensional square lattice Hubbard model. The d-wave order parameter is found to scale like the superexchange coupling J for on-site interaction U comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second-neighbor hopping t', the zero temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third-neighbor hopping t'' improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs T_{c}/T_{c}^{max} phase diagram of the cuprates is universal. The calculated ARPES spectrum displays the observed electron-hole asymmetry. Our calculations reproduce important features of d-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard BCS approach.Comment: 13 pages, 7 figure

Polarization-multiplexed nonlinear inverse synthesis with standard and reduced-complexity NFT processing

In this work, we study the performance of polarization division multiplexing nonlinear inverse synthesis transmission schemes for fiber-optic communications, expected to have reduced nonlinearity impact. Our technique exploits the integrability of the Manakov equation—the master model for dual-polarization signal propagation in a single mode fiber—and employs nonlinear Fourier transform (NFT) based signal processing. First, we generalize some algorithms for the NFT computation to the two- and multicomponent case. Then, we demonstrate that modulating information on both polarizations doubles the channel information rate with a negligible performance degradation. Moreover, we introduce a novel dual-polarization transmission scheme with reduced complexity which separately processes each polarization component and can also provide a performance improvement in some practical scenarios

Sericin-based resins from silk degumming wastewater for the removal of heavy metal ions from water

Chromium (VI) is a water pollutant categorized as \u2018likely to be a carcinogen to humans\u2019 compound when orally ingested with estimated cancer potency 0.5 mg/kg/day. The European Directive 2001/59/EC poses a 5 \ub5g/L threshold concentration for Cr(VI) in groundwaters. In this work, a chemical process was devised to obtain heavy metal ion absorbing resins by the polyaddition of bisacrylamides and 1,2-diaminoethane with sericin using as reaction solvent raw waste-water from silk degumming processes. Silk sericin (SS) is a natural globural protein deriving from silk worm Bombyx mori with molecular weight ranging from 10000 to 300000. Following the alkaline degumming process, sericin is degraded to peptides with molecular weight 20000. These peptides contain lysine-deriving residues that participate in the polyaddition leaving to a resin. This resin is a hybrid one in which a substantial portion is constituted by sericin peptides. The rationale of this approach is that the guanidinum ion has the ability to strongly bind oxoanions, due to its geometrical Y-shaped, planar orientation, optimizing charge distribution and hydrogen bonds [1]. SS resins were evaluated for the removal of both positively charged (Cu2+, Co2+, Ni2+, Mn2+) and negatively charged heavy metals oxoanions (CrO42-) from water. Different resins were obtained containing different amounts of sericin. These resins were characterized by elemental analysis and their structure confirmed by FT-IR/ATR spectroscopy. The swelling capacity of the new absorbents in different media and their thermal stability by DSC and TGA techniques were evaluated. The removal properties of resins towards Cu2+, Co2+, Ni2+, Mn2+ and CrO42- ions in aqueous single metal dilute and concentrate solutions were performed in batch absorption experiments and evaluated by EDTA titration in the case of Cu2+, Co2+, Ni2+, Mn2+, and by the UV-VIS spectroscopy in the case of CrO42-. The products showed different absorption capacities depending on the SS content in the resin. Treatment with 0.1 M HCl showed excellent regeneration with maintenance of the resins absorption capacity for 20 regeneration cycles. In conclusion, sericin-based resins, besides being biocompatible, were endowed with environmental friendly preparation process; biodegradability; moderate cost; ability to fast and quantitatively absorb from aqueous solutions even at low pollutant concentration; full reversibility of the absorption process making it economically convenient both for regeneration and metal recovery

Urotensin II Modulates Rapid Eye Movement Sleep Through Activation of Brainstem Cholinergic Neurons

Urotensin II (UII) is a cyclic neuropeptide with strong vasoconstrictive activity in the peripheral vasculature. UII receptor mRNA is also expressed in the CNS, in particular in cholinergic neurons located in the mesopontine tegmental area, including the pedunculopontine tegmental (PPT) and lateral dorsal tegmental nuclei. This distribution suggests that the UII system is involved in functions regulated by acetylcholine, such as the sleep-wake cycle. Here, we tested the hypothesis that UII influences cholinergic PPT neuron activity and alters rapid eye movement (REM) sleep patterns in rats. Local administration of UII into the PPT nucleus increases REM sleep without inducing changes in the cortical blood flow. Intracerebroventricular injection of UII enhances both REM sleep and wakefulness and reduces slow-wave sleep 2. Intracerebroventricular, but not local, administration of UII increases cortical blood flow. Moreover, whole-cell recordings from rat-brain slices show that UII selectively excites cholinergic PPT neurons via an inward current and membrane depolarization that were accompanied by membrane conductance decreases. This effect does not depend on action potential generation or fast synaptic transmission because it persisted in the presence of TTX and antagonists of ionotropic glutamate, GABA, and glycine receptors. Collectively, these results suggest that UII plays a role in the regulation of REM sleep independently of its cerebrovascular actions by directly activating cholinergic brainstem neurons