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

Intramyocardial hemorrhage: An enigma for cardiac MRI?

Cardiovascular magnetic resonance (CMR) is a useful noninvasive technique for determining the presence of microvascular obstruction (MVO) and intramyocardial hemorrhage (IMH), frequently occurring in patients after reperfused myocardial infarction (MI). MVO, or the so-called no-reflow phenomenon, is associated with adverse ventricular remodeling and a poor prognosis during follow-up. Similarly, IMH is considered a severe damage after revascularization by percutaneous primary coronary intervention (PPCI) or fibrinolysis, which represents a worse prognosis. However, the pathophysiology of IMH is not fully understood and imaging modalities might help to better understand that phenomenon. While, during the past decade, several studies examined the distribution patterns of late gadolinium enhancement with different CMR sequences, the standardized CMR protocol for assessment of IMH is not yet well established. The aim of this review is to evaluate the available literature on this issue, with particular regard to CMR sequences. New techniques, such as positron emission tomography/magnetic resonance imaging (PET/MRI), could be useful tools to explore molecular mechanisms of the myocardial infarction healing process

The rare case of positive FDG-positron emission tomography for giant cavernous hemangioma of the liver

Hemangioma is the most common benign liver tumor and the second most common liver tumor after metastases. Large hemangiomas are often heterogeneous. When they exceed 4 cm in diameter, they are termed giant hemangiomas. These giant hemangiomas often present heterogeneous patterns. These heterogeneous appearances are shown because of intratumoral changes due to several degenerative phenomena. PET/CT is reported to be useful for the differentiation of benign from malignant liver lesions. We report the case of a large hepatic hemangioma characterized by high FDG uptake

Supernova Neutrino Energy Spectra and the MSW Effect

The distortions in the thermal energy spectra for neutrinos produced in a supernova when a resonant oscillation, MSW effect, occurs are determined. In order to show this effect for some relevant and representative examples of unified gauge models, we have chosen $SO(10)$, and $SU(5)_{SUSY}$, $SO(10)_{SUSY}$ with a particular scheme for fermion masses (DHR model). The analysis has been performed for two choices of neutrinos parameters, predicted by the above models, and capable to explain the solar neutrino problem. In both cases one observes a strong distortion in the electron neutrino energy spectrum. This effect, computed for a wide range of $SO(10)_{SUSY}$ models has produced the same results of the previous supersymmetric ones.Comment: 14 pages, plain LaTeX, 6 figures, revised version to be published in Z. Phys.

The Pacific Decadal Oscillation modulates tropical cyclone days on the interannual timescale in the North Pacific Ocean

The North Pacific Ocean is the most active region on our planet in terms of tropical cyclone (TC) activity. These storms are responsible for numerous fatalities and economic damages, affecting the livelihood of those living in the impacted areas. Historically the examination of TCs in the North Pacific Ocean has been performed separately for its two main sub-basins: the West North Pacific and the East North Pacific. Here, we consider the TC activity in the North Pacific as a single basin and examine the climate processes responsible for its number of TC days. We show that the Pacific Decadal Oscillation modulates the number of TC days in the North Pacific Ocean through its connection to the sea surface temperature. The insights from this work will advance the understanding of the climate processes responsible for these storms, and will provide valuable information toward our preparation and adaptation efforts on long timescales

Crosstalk Cascades for Frame-rate Pedestrian Detection

Cascades help make sliding window object detection fast, nevertheless, computational demands remain prohibitive for numerous applications. Currently, evaluation of adjacent windows proceeds independently; this is suboptimal as detector responses at nearby locations and scales are correlated. We propose to exploit these correlations by tightly coupling detector evaluation of nearby windows. We introduce two opposing mechanisms: detector excitation of promising neighbors and inhibition of inferior neighbors. By enabling neighboring detectors to communicate, crosstalk cascades achieve major gains (4-30x speedup) over cascades evaluated independently at each image location. Combined with recent advances in fast multi-scale feature computation, for which we provide an optimized implementation, our approach runs at 35-65 fps on 640 x 480 images while attaining state-of-the-art accuracy

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

On the physical nudging equations

In this work we show how it is possible to derive a new set of nudging equations, a tool still used in many data assimilation problems, starting from statistical physics considerations and availing ourselves of stochastic parameterizations that take into account unresolved interactions. The fluctuations used are thought of as Gaussian white noise with zero mean. The derivation is based on the conditioned Langevin dynamics technique. Exploiting the relation between the Fokker-Planck and the Langevin equations, the nudging equations are derived for a maximally observed system that converges towards the observations in finite time. The new nudging term found is the analog of the so called quantum potential of the Bohmian mechanics. In order to make the new nudging equations feasible for practical computations, two approximations are developed and used as bases from which extending this tool to non-perfectly observed systems. By means of a physical framework, in the zero noise limit, all the physical nudging parameters are fixed by the model under study and there is no need to tune other free ad-hoc variables. The limit of zero noise shows that also for the classical nudging equations it is necessary to use dynamical information to correct the typical relaxation term. A comparison of these approximations with a 3DVar scheme, that use a conjugate gradient minimization, is then shown in a series of four twin experiments that exploit low order chaotic models