Many-spin effects in inelastic neutron scattering and electron paramagnetic resonance of molecular nanomagnets

Many molecular magnetic clusters, such as single-molecule magnets, are characterized by spin ground states with defined total spin S exhibiting zero-field-splittings. In this work, the spectroscopic intensities of the transitions within the ground-state multiplet are analyzed. In particular, the effects of a mixing with higher-lying spin multiplets, which is produced by anisotropic interactions and is neglected in the standard single-spin description, are investigated systematically for the two experimental techniques of inelastic neutron scattering (INS) and electron paramagnetic resonance (EPR), with emphasis on the former technique. The spectroscopic transition intensities are calculated analytically by constructing corresponding effective spin operators perturbationally up to second order and consequently using irreducible tensor operator techniques. Three main effects of spin mixing are observed. Firstly, a pronounced dependence of the INS intensities on the momentum transfer Q, with a typical oscillatory behavior, emerges in first order, signaling the many-spin nature of the wave functions in exchange-coupled clusters. Secondly, as compared to the results of a first-order calculation, the intensities of the transitions within the spin multiplet are affected differently by spin mixing. This allows one, thirdly, to differentiate the higher-order contributions to the cluster magnetic anisotropy which come from the single-ion ligand-field terms and spin mixing, respectively. The analytical results are illustrated by means of the three examples of an antiferromagnetic heteronuclear dimer, the Mn-[3 x 3] grid molecule, and the single-molecule magnet Mn12.Comment: 18 pages, 3 figures, REVTEX4, to appear in PR

Homotopy colimits and global observables in Abelian gauge theory

We study chain complexes of field configurations and observables for Abelian gauge theory on contractible manifolds, and show that they can be extended to non-contractible manifolds by using techniques from homotopy theory. The extension prescription yields functors from a category of manifolds to suitable categories of chain complexes. The extended functors properly describe the global field and observable content of Abelian gauge theory, while the original gauge field configurations and observables on contractible manifolds are recovered up to a natural weak equivalence

Thermal Transient Measurements of an Ultra-Low-Power MOX Sensor

This paper describes a system for the simultaneous dynamic control and thermal characterization of the heating of an Ultra Low Power (ULP) micromachined sensor. A Pulse Width Modulated (PWM) powering system has been realized using a microcontroller to characterize the thermal behavior of a device. Objectives of the research were to analyze the relation between the time period and duty cycle of the PWM signal and the operating temperature of such ULP micromachined systems, to observe the thermal time constants of the device during the heating phase and to measure the total thermal conductance. Constant target heater resistance experiments highlighted that an approximately constant heater temperature at regime can only be obtained if the time period of the heating signal is smaller than 50 s. Constant power experiments show quantitatively a thermal time constant that decreases during heating in a range from 2.3 ms to 2 ms as a function of an increasing temperature rise between the ambient and the operating temperature. Moreover, we calculated the total thermal conductance. Finally, repeatability of experimental results was assessed by guaranteeing the standard deviation of the controlled temperature which was within C in worst case conditions

The Geometric Phase and Ray Space Isometries

We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner's proof is best viewed as an use of the Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.Comment: 17 pages, Latex file, no figures, To appear in Pramana J. Phy

Spin dynamics in molecular ring nanomagnets: Significant effect of acoustic phonons and magnetic anisotropies

The nuclear spin-lattice relaxation rate 1/T_1_ is calculated for magnetic ring clusters by fully diagonalizing their microscopic spin Hamiltonians. Whether the nearest-neighbor exchange interaction J is ferromagnetic or antiferromagnetic, 1/T_1_ versus temperature T in ring nanomagnets may be peaked at around k_B_T=|J| provided the lifetime broadening of discrete energy levels is in proportion to T^3^. Experimental findings for ferromagnetic and antiferromagnetic Cu^II^ rings are reproduced with crucial contributions of magnetic anisotropies as well as acoustic phonons.Comment: 5 pages with 5 figures embedded, to be published in J. Phys. Soc. Jpn. 75, No. 10 (2006

Geometrization of Quantum Mechanics

We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.Comment: 16 pages. To appear in Theor. Math. Phys. Some typos corrected. Definition 2 in page 5 rewritte

Subclinical liver fibrosis in patients with idiopathic 1 pulmonary fibrosis.

Background - Data on the presence of subclinical fibrosis across multiple organs in patients with idiopathic lung fibrosis (IPF) are lacking. Our study aimed at investigating through hepatic transient elastography (HTE) the prevalence and clinical impact of subclinical liver fibrosis in a cohort of patients with IPF. Methods - Patients referred to the Centre for Rare Lung Disease of the University Hospital of Modena (Italy) from March 2012 to February 2013with established diagnosis of IPF and without a documented history of liver diseases were consecutively enrolled and underwent HTE. Based on hepatic stiffness status as assessed through METAVIR score patients were categorized as \u201c with liver fibrosis \u201d (corresponding to a METAVIR score of F1-F4) and \u201c without liver fibrosis\u201d (METAVIR F0). Potential predictors of liver fibrosis were investigated through logistic regression model among clinical and serological variables. The overall survival (OS) was assessed according to liver fibrosis and multivariate Cox regression analysis was used to identify independent predictors. Results - In 13 out of 37 patients (35%) with IPF a certain degree of liver fibrosis was documented.No correlation was found between liver stiffness and clinical-functional parameters. OS was lower in patients \u2018 with liver fibrosis\u2019 than in patients \u2018 without liver fibrosis\u2019 (median months 33[23-55] vs. 63[26-94], p=0.038). Patients \u2018 with liver fibrosis\u2019 presented a higher risk of death at seven years as compared to patients \u2018without liver fibrosis\u2019 (HR=2.6, 95%CI[1.003\u20136.7],p= 0.049). Higher level of AST to platelet ratio Index (APRI)was an independent predictor of survival (HR=4.52 95%CI[1.3\u201315.6], p=0.02). Conclusions - In our cohort, more than one third of IPF patients had concomitant subclinical liver fibrosis that negatively affected OS. These preliminary claims further investigation aimed at clarifying the mechanisms beyond multiorgan fibrosis and its clinical implication in patients with IPF

Geometric Quantum Mechanics

The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given quantum system can be represented by specific geometrical features that are selected and preferentially identified in this complex manifold. Here we construct a number of examples of such geometrical features as they arise in the state spaces for spin-1/2, spin-1, and spin-3/2 systems, and for pairs of spin-1/2 systems. A study is undertaken on the geometry of entangled states, and a natural measure is assigned to the degree of entanglement of a given state for a general multi-particle system. The properties of this measure are analysed for the entangled states of a pair of spin-1/2 particles. With the specification of a quantum Hamiltonian, the resulting Schrodinger trajectory induces a Killing field, which is quasiergodic on a toroidal subspace of the energy surface. When the dynamical trajectory is lifted orthogonally to Hilbert space, it induces a geometric phase shift on the wave function. The uncertainty of an observable in a given state is the length of the gradient vector of the level surface of the expectation of the observable in that state, a fact that allows us to calculate higher order corrections to the Heisenberg relations. A general mixed state is determined by a probability density function on the state space, for which the associated first moment is the density matrix. The advantage of a general state is in its applicability in various attempts to go beyond the standard quantum theory.Comment: 27 pages. Extended with additional materia

Trend of incidence, subsite distribution and staging of colorectal neoplasms in the 15-year experience of a specialised cancer registry

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Dirac's Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge

We define the {\it rest-frame instant form} of tetrad gravity restricted to Christodoulou-Klainermann spacetimes. After a study of the Hamiltonian group of gauge transformations generated by the 14 first class constraints of the theory, we define and solve the multitemporal equations associated with the rotation and space diffeomorphism constraints, finding how the cotriads and their momenta depend on the corresponding gauge variables. This allows to find quasi-Shanmugadhasan canonical transformation to the class of 3-orthogonal gauges and to find the Dirac observables for superspace in these gauges. The construction of the explicit form of the transformation and of the solution of the rotation and supermomentum constraints is reduced to solve a system of elliptic linear and quasi-linear partial differential equations. We then show that the superhamiltonian constraint becomes the Lichnerowicz equation for the conformal factor of the 3-metric and that the last gauge variable is the momentum conjugated to the conformal factor. The gauge transformations generated by the superhamiltonian constraint perform the transitions among the allowed foliations of spacetime, so that the theory is independent from its 3+1 splittings. In the special 3-orthogonal gauge defined by the vanishing of the conformal factor momentum we determine the final Dirac observables for the gravitational field even if we are not able to solve the Lichnerowicz equation. The final Hamiltonian is the weak ADM energy restricted to this completely fixed gauge.Comment: RevTeX file, 141 page