Characterizing and Quantifying Frustration in Quantum Many-Body Systems

We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.Comment: 8 pages, 1 figur

Entanglement quantification by local unitaries

Invariance under local unitary operations is a fundamental property that must be obeyed by every proper measure of quantum entanglement. However, this is not the only aspect of entanglement theory where local unitaries play a relevant role. In the present work we show that the application of suitable local unitary operations defines a family of bipartite entanglement monotones, collectively referred to as "mirror entanglement". They are constructed by first considering the (squared) Hilbert-Schmidt distance of the state from the set of states obtained by applying to it a given local unitary. To the action of each different local unitary there corresponds a different distance. We then minimize these distances over the sets of local unitaries with different spectra, obtaining an entire family of different entanglement monotones. We show that these mirror entanglement monotones are organized in a hierarchical structure, and we establish the conditions that need to be imposed on the spectrum of a local unitary for the associated mirror entanglement to be faithful, i.e. to vanish on and only on separable pure states. We analyze in detail the properties of one particularly relevant member of the family, the "stellar mirror entanglement" associated to traceless local unitaries with nondegenerate spectrum and equispaced eigenvalues in the complex plane. This particular measure generalizes the original analysis of [Giampaolo and Illuminati, Phys. Rev. A 76, 042301 (2007)], valid for qubits and qutrits. We prove that the stellar entanglement is a faithful bipartite entanglement monotone in any dimension, and that it is bounded from below by a function proportional to the linear entropy and from above by the linear entropy itself, coinciding with it in two- and three-dimensional spaces.Comment: 13 pages, 3 figures. Improved and generalized proof of monotonicity of the mirror and stellar entanglemen

The double-ITCZ syndrome in coupled general circulation models: the role of large-scale vertical circulation regimes

The double-intertropical convergence zone (DI) systematic error, affecting state-of-the-art coupled general circulation models (CGCM) is examined in the multi-model Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) ensemble of simulations of the twentieth-century climate. Aim of this study is to quantify the DI error on precipitation in the tropical Pacific, with a specific focus on the relationship between the DI error and the representation of large-scale vertical circulation regimes in climate models. The DI rainfall signal is analysed using a regime sorting approach for the vertical circulation regimes. Through the use of this compositing technique, precipitation events are regime-sorted based on the large scale vertical motions, as represented by the mid-tropospheric lagrangian pressure tendency omega500 dynamical proxy. This methodology allows the partition of the precipitation signal into deep and shallow convective components. Following the regime-sorting diagnosis, the total DI bias is split into an error affecting the magnitude of precipitation associated with individual convective events and an error affecting the frequency of occurrence of single convective regimes. It is shown that, despite the existing large intra-model differences, CGCMs can be ultimately grouped into a few homegenous clusters, each featuring a well defined rainfall-vertical circulation relationship in the DI region. Three major behavioural clusters are identified within the AR4 models ensemble: two unimodal distributions, featuring maximum precipitation under subsidence and deep convection regimes, respectively, and one bimodal distribution, displaying both components. Extending this analysis to both coupled and uncoupled (atmosphere-only) AR4 simulations reveals that the DI bias in CGCMs is mainly due to the overly frequent occurrence of deep convection regimes, whereas the error on rainfall magnitude associated with individual convective events is overall consistent with errors already present in the corresponding atmosphere stand-alone simulations. A critical parameter controlling the strength of the DI systematic error is identified in the model-dependent sea surface temperature (SST) threshold leading to the onset of deep convection (THR), combined with the average SST in the south-eastern Pacific

Effects of Land-Surface-Vegetation on theboreal summer surface climate of a GCM

A land surface model (LSM) has been included in the ECMWF Hamburg version 4 (ECHAM4) atmospheric general circulation model (AGCM). The LSM is an early version of the Organizing Carbon and Hydrology in Dynamic Ecosystems (ORCHIDEE) and it replaces the simple land surface scheme previously included in ECHAM4. The purpose of this paper is to document how a more exhaustive consideration of the land surface–vegetation processes affects the simulated boreal summer surface climate. To investigate the impacts on the simulated climate, different sets of Atmospheric Model Intercomparison Project (AMIP)-type simulations have been performed with ECHAM4 alone and with the AGCM coupled with ORCHIDEE. Furthermore, to assess the effects of the increase in horizontal resolution the coupling of ECHAM4 with the LSM has been implemented at different horizontal resolutions. The analysis reveals that the LSM has large effects on the simulated boreal summer surface climate of the atmospheric model. Considerable impacts are found in the surface energy balance due to changes in the surface latent heat fluxes over tropical and midlatitude areas covered with vegetation. Rainfall and atmospheric circulation are substantially affected by these changes. In particular, increased precipitation is found over evergreen and summergreen vegetated areas. Because of the socioeconomical relevance, particular attention has been devoted to the Indian summer monsoon (ISM) region. The results of this study indicate that precipitation over the Indian subcontinent is better simulated with the coupled ECHAM4–ORCHIDEE model compared to the atmospheric model alone

The influence of Tropical Indian Ocean SST on the Indian summer monsoon

The Indian Summer Monsoon (ISM) is one of the main components of the Asian summer monsoon. It is well known that one of the starting mechanisms of a summer monsoon is the thermal contrast between land and ocean and that sea surface temperature (SST) and moisture are crucial factors for its evolution and intensity. The Indian Ocean, therefore, may play a very important role in the generation and evolution of the ISM itself. A coupled general circulation model, implemented with a high resolution atmospheric component, appears to be able to simulate the Indian summer monsoon in a realistic way. In particular, the features of the simulated ISM variability are similar to the observations. In this study, the relationships between ISM and Tropical Indian Ocean (TIO) SST anomalies are investigated, as well as the ability of the coupled model to capture those connections. The recent discovery of the Indian Ocean Dipole Mode (IODM) may suggest new perspectives in the relationship between ISM and TIO SST. A new statistical technique, the Coupled Manifold, is used to investigate the TIO SST variability and its relation with the Tropical Pacific Ocean (TPO). The analysis shows that the SST variability in the TIO contains a significant portion that is independent from the TPO variability. The same technique is used to estimate the amount of Indian rainfall variability that can be explained by the Tropical Indian Ocean SST. Indian Ocean SST anomalies are separated in a part remotely forced from the Tropical Pacific Ocean variability and a part independent from that. The relationships between the two SSTA components and the Indian monsoon variability are then investigated in detail

Heatwaves in Europe: areas of homogeneous variability and links with the regional to large-scale atmospheric and SSTs anomalies

This work presents a methodology to study the interannual variability associated with summertime months in which extremely hot temperatures are frequent. Daily time series of maximum and minimum temperature fields (T max and T min, respectively) are used to define indexes of extreme months based on the number of days crossing thresholds. An empirical orthogonal function (EOF) analysis is applied to the monthly indexes. EOF loadings give information about the geographical areas where the number of days per month with extreme temperatures has the largest variability. Correlations between the EOF principal components and the time series of other fields allow plotting maps highlighting the anomalies in the large scale circulation and in the SSTs that are associated with the occurrence of extreme events. The methodology is used to construct the “climatology” of the extremely hot summertime months over Europe. In terms of both interannual and intraseasonal variability, there are three regions in which the frequency of the extremely hot days per month homogeneously varies: north-west Europe, Euro-Mediterranean and Eurasia region. Although extremes over those regions occur during the whole summer (June to August), the anomalous climatic conditions associated with frequent heatwaves present some intraseasonal variability. Extreme climate events over the north-west Europe and Eurasia are typically related to the occurrence of blocking situations. The intraseasonal variability of those patterns is related to the amplitude of the blocking, the relative location of the action centre and the wavetrain of anomalies downstream or upstream of the blocking. During June and July, blocking situations which give extremely hot climate conditions over north-west Europe are also associated with cold conditions over the eastern Mediterranean sector. The Euro-Mediterranean region is a transition area in which extratropical and tropical systems compete, influencing the occurrence of climate events: blockings tend to be related to extremely hot months during June while baroclinic anomalies dominate the variability of the climate events in July and August. We highlight that our method could be easily applied to other regions of the world, to other fields as well as to model outputs to assess, e.g. the potential change of extreme climate events in a warmer climate

Coexistence of supersymmetric and supersymmetry-breaking states in spherical spin-glasses

The structure of states of the perturbed p-spin spherical spin-glass is analyzed. At low enough free energy metastable states have a supersymmetric structure, while at higher free energies the supersymmetry is broken. The transition between the supersymmetric and the supersymmetry-breaking phase is triggered by a change in the stability of states

Changes in Tropical Cyclone Activity due to Global Warming in a General Circulation Model

This study investigates the possible changes that the greenhouse global warming might generate in the characteristics of the tropical cyclones (TCs). The analysis has been performed using scenario climate simulations carried out with a fully coupled high-resolution global general circulation model. The capability of the model to reproduce a reasonably realistic TC climatology has been assessed by comparing the model results from a simulation of the 20th Century with observations. The model appears to be able to simulate tropical cyclone-like vortices with many features similar to the observed TCs. The simulated TC activity exhibits realistic geographical distribution, seasonal modulation and interannual variability, suggesting that the model is able to reproduce the major basic mechanisms that link the TC occurrence with the large scale circulation. The results from the climate scenarios reveal a substantial general reduction of the TC frequency when the atmospheric CO2 concentration is doubled and quadrupled. The reduction appears particularly evident for the tropical North West Pacific (NWP) and North Atlantic (ATL). In the NWP the weaker TC activity seems to be associated with a reduced amount of convective instabilities. In the ATL region the weaker TC activity seems to be due to both the increased stability of the atmosphere and a stronger vertical wind shear. Despite the generally reduced TC activity, there is evidence of increased rainfall associated with the simulated cyclones. Despite the overall warming of the tropical upper ocean and the expansion of warm SSTs to the subtropics and mid-latitudes, the action of the TCs remains well confined to the tropical region and the peak of TC number remains equatorward of 20° latitude in both Hemispheres. An extended version of this work is in available on Journal of Climate (Gualdi et al.,2008 - DOI:10.1175/2008JCLI1921.1

Analysis of the mid-latitude weather regimes in the 200-year control integration of the SINTEX model

Recent results indicate that climate predictions require models which can simulate accurately natural circulation regimes and their associated variability. The main purpose of this study is to investigate whether (and how) a coupled model can simulate the real world weather regimes. A 200-year control integration of a coupled GCM (the «SINTEX model») is considered. The output analysed consists of monthly mean values of Northern Hemisphere extended winter (November to April) 500-hPa geopotential heights. An Empirical Orthogonal Function (EOF) analysis is first applied in order to define a reduced phase space based on the leading modes of variability. Therefore the principal component PDF in the reduced phase space spanned by two leading EOFs is computed. Based on a PDF analysis in the phase space spanned by the leading EOF1 and REOF2, substantial evidence of the nongaussian regime structure of the SINTEX northern winter circulation is found. The model Probability Density Function (PDF) exhibits three maxima. The 500-hPa height geographical patterns of these density maxima are strongly reminiscent of well-documented Northern Hemisphere weather regimes. This result indicates that the SINTEX model can not only simulate the non-gaussian structure of the climatic attractor, but is also able to reproduce the natural modes of variability of the system

Observed shift towards earlier spring discharge in the main Alpine rivers

In this study, we analyse the observed long-term discharge time-series of the Rhine, the Danube, the Rhone and the Po rivers. These rivers are characterised by different seasonal cycles reflecting the diverse climates and morphologies of the Alpine basins. However, despite the intensive and varied water management adopted in the four basins, we found common features in the trend and low-frequency variability of the spring discharge timings. All the discharge time-series display a tendency towards earlier spring peaks of more than two weeks per century. These results can be explained in terms of snowmelt, total precipitation (i.e. the sum of snowfall and rainfall) and rainfall variability. The relative importance of these factors might be different in each basin. However, we show that the change of seasonality of total precipitation plays a major role in the earlier spring runoff over most of the Alps