More about chiral symmetry restoration at finite temperature in the planar limit

In the planar limit, in the deconfined phase, the Euclidean Dirac operator has a spectral gap around zero. We show that functions of eigenvalues close to the spectral edge, which are independent of common rescalings and shifts gauge configuration by gauge configuration, have distributions described by a Gaussian Hermitian matrix model. However, combinations of eigenvalues that are scale and shift invariant only on the average, do not match this matrix model.     

Exact solution of the XXX Gaudin model with generic open boundaries

The XXX Gaudin model with generic integrable open boundaries specified by the most general non-diagonal reflecting matrices is studied. Besides the inhomogeneous parameters, the associated Gaudin operators have six free parameters which break the U(1)$U\left(1\right)$-symmetry. With the help of the off-diagonal Bethe ansatz, we successfully obtained the eigenvalues of these Gaudin operators and the corresponding Bethe ansatz equations.     

The Ising model on random lattices in arbitrary dimensions

We study analytically the Ising model coupled to random lattices in dimension three and higher. The family of random lattices we use is generated by the large N limit of a colored tensor model generalizing the two-matrix model for Ising spins on random surfaces. We show that, in the continuum limit, the spin system does not exhibit a phase transition at finite temperature, in agreement with numerical investigations. Furthermore we outline a general method to study critical behavior in colored tensor models.     

Compact complex surfaces with geometric structures related to split quaternions

We study the problem of existence of geometric structures on compact complex surfaces that are related to split quaternions. These structures, called para-hypercomplex, para-hyperhermitian and para-hyperkähler, are analogs of the hypercomplex, hyperhermitian and hyperkähler structures in the definite case. We show that a compact 4-manifold carries a para-hyperkähler structure iff it has a metric of split signature together with two parallel, null, orthogonal, pointwise linearly independent vector fields. Every compact complex surface admitting a para-hyperhermitian structure has vanishing first Chern class and we show that, unlike the definite case, many of these surfaces carry infinite-dimensional families of such structures. We provide also compact examples of complex surfaces with para-hyperhermitian structures which are not locally conformally para-hyperkähler. Finally, we discuss the problem of non-existence of para-hyperhermitian structures on Inoue surfaces of type S⁰$S^0$ and provide a list of compact complex surfaces which could carry para-hypercomplex structures.     

Superconnections and index theory

We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate η$\eta$-invariants and prove an APS theorem, and construct a geometric determinant line bundle for families of such operators, computing its curvature and holonomy in terms of familiar index theoretic quantities.     

Maximum entropy production principle in physics,chemistry and biology

The tendency of the entropy to a maximum as an isolated system is relaxed to the equilibrium (the second law of thermodynamics) has been known since the mid-19th century. However, independent theoretical and applied studies, which suggested the maximization of the entropy production during nonequilibrium processes (the so-called maximum entropy production principle, MEPP), appeared in the 20th century. Publications on this topic were fragmented and different research teams, which were concerned with this principle, were unaware of studies performed by other scientists. As a result, the recognition and the use of MEPP by a wider circle of researchers were considerably delayed. The objectives of the present review consist in summation and analysis of studies dealing with MEPP. The first part of the review is concerned with the thermodynamic and statistical basis of the principle (including the relationship of MEPP with the second law of thermodynamics and Prigogine's principle). Various existing applications of the principle to analysis of nonequilibrium systems will be discussed in the second part.     

Anisotropy and magnetization process in soft magnets: Principles,experiments, applications

Understanding and controlling the anisotropy energy and its effects has proved vital to the development of soft magnetic materials and their applications. Indeed, acting on composition and structure and working out specific annealing treatments, a large variety of anisotropy-governed behaviors under DC and AC excitation can be obtained. These are discussed in the present paper, together with special problems arising in the characterization of anisotropic soft magnets and a few significant applications. It is stressed how features like J$J$–H$H$ loop shape, energy losses, and magnetoresistance effects can be controlled, in crystalline and amorphous materials, by the methods of induced anisotropy. The high-frequency behavior of these materials can be strongly affected by the anisotropy field via resonant absorption of energy. This calls for tradeoff between the values of permeability and resonance frequency.     

A centrality measure for communication ability in weighted network

This paper proposes a new node centrality measurement in a weighted network, the communication centrality, which is inspired by Hirsch’s h$h$-index. We investigated the properties of the communication centrality, and proved that the distribution of the communication centrality has the power-law upper tail in weighted scale-free networks. Relevant measures for node and network are discussed as extensions. A case study of a scientific collaboration network indicates that the communication centrality is different from other common centrality measures and other h$h$-type indexes. Communication centrality displays moderate correlation with other indexes, and contains a well-balanced mix of other centrality measures and cannot be replaced by any of them.     

The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders

Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N$1/N$ expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D  -ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N$1/N$. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.     

Commuting conformal and dual conformal symmetries in the Regge limit

In this paper we continue our study of the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry of the BFKL equation, analogous to the dual conformal symmetry of N=4$N=4$ super-Yang–Mills. We find that the ordinary and dual SL(2,C)$\mathit{SL}(2,C)$ symmetries do not generate a Yangian, in contrast to the ordinary and dual conformal symmetries in the four-dimensional gauge theory. The algebraic structure is still reminiscent of that of N=4$N=4$ SYM, however, and one can extract a generator from the dual SL(2,C)$\mathit{SL}(2,C)$ close to the bi-local form associated with Yangian algebras. We also discuss the issue of whether the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry, which in its original form is broken by IR effects, is broken in a controlled way, similar to the way the dual conformal symmetry of N=4$N=4$ satisfies an anomalous Ward identity. At least for the lowest orders it seems possible to recover the dual SL(2,C)$\mathit{SL}(2,C)$ by deforming its representation, keeping open the possibility that it is an exact symmetry of BFKL. Independently of a possible relation to N=4$N=4$ scattering amplitudes, this opens an avenue for explaining the integrability of BFKL in terms of two finite-dimensional subalgebras.     

Qubits and chirotopes

We show that qubit and chirotope concepts are closely related. In fact, we prove that the qubit concept leads to a generalization of the chirotope concept, which we call qubitope. Moreover, we argue that a possible qubitope theory may suggest interesting applications of oriented matroid theory in at least three physical contexts, in which qubits make their appearance, namely string theory, black holes and quantum information.     

Kinetic theory of Onsager’s vortices in two-dimensional hydrodynamics

Starting from the Liouville equation and using a BBGKY-like hierarchy, we derive a kinetic equation for the point vortex gas in two-dimensional (2D) hydrodynamics, taking two-body correlations and collective effects into account. This equation is valid at the order 1/N$1/N$ where N?1$N?1$ is the number of point vortices in the system (we assume that their individual circulation scales like γ∼1/N$\gamma \sim 1/N$). It gives the first correction, due to graininess and correlation effects, to the 2D Euler equation that is obtained for N→+∞$N\to +\infty$. For axisymmetric distributions, this kinetic equation does not   relax towards the Boltzmann distribution of statistical equilibrium. This implies either that (i) the “collisional” (correlational) relaxation time is larger than N_tD$N{t}_D$, where _tD$t_D$ is the dynamical time, so that three-body, four-body… correlations must be taken into account in the kinetic theory, or (ii) that the point vortex gas is non-ergodic (or does not mix well) and will never attain statistical equilibrium. Non-axisymmetric distributions may relax towards the Boltzmann distribution on a timescale of the order N_tD$N{t}_D$ due to the existence of additional resonances, but this is hard to prove from the kinetic theory. On the other hand, 2D Euler unstable vortex distributions can experience a process of “collisionless” (correlationless) violent relaxation towards a non-Boltzmannian quasistationary state (QSS) on a very short timescale of the order of a few dynamical times. This QSS is possibly described by the Miller–Robert–Sommeria (MRS) statistical theory which is the counterpart, in the context of two-dimensional hydrodynamics, of the Lynden-Bell statistical theory of violent relaxation in stellar dynamics.     

The periodic Anderson model: Symmetry-based results and some exact solutions

The topic “magnetic impurities in metals” is certainly one of the most studied problems of the solid-state physics in the last years. The interest toward this argument relies on the fact that the interaction between the magnetic moment of the impurities and the conduction electrons of the host metal, is responsible for a large variety of physical phenomena.     

Fitting the flow curve of a plastically deformed silicon steel for the prediction of magnetic properties

We report measurements and modelling of magnetic effects due to plastic deformation in 2.2% Si steel, emphasizing new tensile deformation data. The modelling approach is to take the Ludwik law for the strain-hardening stress and use it to compute the dislocation density, which is then used in the computation of magnetic hysteresis. A nonlinear extrapolation is used across the discontinuous yield region to obtain the value of stress at the yield point that is used in fitting Ludwik's law to the mechanical data. The computed magnetic hysteresis exhibits sharp shearing of the loops at small deformation, in agreement with experimental behavior. Magnetic hysteresis loss is shown to follow a Ludwik-like dependence on the residual strain, but with a smaller Ludwik exponent than applies for the mechanical behavior.     

Connection between microstructure and magnetic properties of soft magnetic materials

The magnetic behavior of soft magnetic materials is discussed with some emphasis on the connection between macroscopic properties and underlying micromagnetic energy aspects. It is shown that important conceptual gaps still exist in the interpretation of macroscopic magnetic properties in terms of the micromagnetic formulation. Different aspects of hysteresis modeling, power loss prediction and magnetic non-destructive evaluation are discussed in this perspective.