Browsing Mathematical Physics (MP) by Title
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Macroscopic conductivity of free fermions in disordered media
(Reviews in Mathematical Physics, 20141231)We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic ... 
Measurevalued weak solutions to some kinetic equations with singular kernels for quantum particles
(20181219)In this thesis, we present a mathematical study of three problems arising in the kinetic theory of quantum gases. In the first part, we consider a Boltzmann equation that is used to describe the time evolution of the ... 
Microscopic conductivity of lattice fermions at equilibrium. I. Noninteracting particles
(Journal of Mathematical Physics, 20151231)We consider free lattice fermions subjected to a static bounded potential and a timeand spacedependent electric field. For any bounded convex region R âŠ‚ â„ (d (d â‰¥ 1) of space, electric fields Îµ within R drive currents. ... 
Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles
(Letters in Mathematical Physics, 20160101)We apply Liebâ€“Robinson bounds for multicommutators we recently derived (Bru and de Siqueira Pedra, Liebâ€“Robinson bounds for multicommutators and applications to response theory, 2015) to study the (possibly nonlinear) ... 
Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles
(Letters in Mathematical Physics, 20151231)We apply Lieb–Robinson bounds for multicommutators we recently derived (Bru and de Siqueira Pedra, Lieb–Robinson bounds for multicommutators and applications to response theory, 2015) to study the (possibly nonlinear) ... 
Mixed têteàtête twists as monodromies associated with holomorphic function germs
(20180401)Têteàtête graphs were introduced by N. A’Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed têteàtête graphs provide a generalization which define mixed têteàtête twists, which ... 
Modeling anomalous heat diffusion: Comparing fractional derivative and nonlinear diffusivity treatments
(International Journal of Thermal Sciences, 201811)In the Fourier heat conduction equation, when the flux definition is expressed as the product of a constant diffusivity and the temperature gradient, the characteristic length scale evolves as the square root of time. ... 
Modeling nonstationarities in highfrequency financial time series
(Physica A: Statistical Mechanics and its Applications, 201901)We study tickbytick financial returns for the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We confirm previously detected nonstationarities. Scaling properties reported before for other highfrequency ... 
Modeling of birthdeath and diffusion processes in biological complex environments
(20180420)This thesis is centered on the theory of stochastic processes and their applications in biological systems characterized by a complex environment. Three case studies have been modeled by the use of the three fundamental ... 
Modelling and simulation of wildland fire in the framework of the level set method
(Ricerche di Matematica, 20160101)Among the modelling approaches that have been proposed for the simulation of wildfire propagation, two have gained considerable attention in recent years: the one based on a reactiondiffusion equation, and the one based ... 
Modelling wildland fire propagation by tracking random fronts
(Natural Hazards and Earth System Sciences, 20141231)Abstract. Wildland fire propagation is studied in the liter ature by two alternative approaches, namely the reaction– diffusion equation and the levelset method. These two ap proaches are considered alternatives to each ... 
Moderately Discontinuous Algebraic Topology for Metric Subanalytic Germs
(20191031)We have developed both a homology theory and a homotopy theory in the context of metric subanalytic germs (see Definition 2.1). The former is called MD homology and is covered in Chapter 2, which contains a paper that is ... 
Monodromies as têteàtête graphs
(20180508) 
Multiplicity and degree as bi‐Lipschitz invariants for complex sets
(Journal of Topology, 20180829)We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer biLipschitz transformations (outer biLipschitz homeomorphims of germs in the first case and outer biLipschitz ... 
Multiplicity of singularities is not a biLipschitz invariant
(Mathematische Annalen, 20200117)It was conjectured that multiplicity of a singularity is biLipschitz invariant. We disprove this conjecture constructing examples of biLipschitz equivalent complex algebraic singularities with different values of multiplicity. 
Multiplicity, regularity and blowspherical equivalence of complex analytic sets
(The Asian Journal of Mathematics, 20200129)This paper is devoted to study multiplicity and regularity of complex analytic sets. We present an equivalence for complex analytical sets, named blowspherical equivalence and we obtain several applications with this new ... 
The Nash Problem from a Geometric and Topological Perspective
(20180417)We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the au thors influenced it. Later we summarize the main ideas in the higher dimen ... 
The Nash Problem from Geometric and Topological Perspective
(WORLD SCIENTIFIC (EUROPE), 20200301)We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later, we summarize the main ideas in the higher dimensional ... 
Neron models of intermediate Jacobians associated to moduli spaces
(Revista Matemática Complutense, 20191201)Let $\pi_1:\mathcal{X} \to \Delta$ be a flat family of smooth, projective curves of genus $g \ge 2$, degenerating to an irreducible nodal curve $X_0$ with exactly one node. Fix an invertible sheaf $\mathcal{L}$ on $\mathcal{X}$ ... 
Némethi’s division algorithm for zetafunctions of plumbed 3manifolds
(Bulletin of the London Mathematical Society, 20180827)A polynomial counterpart of the SeibergWitten invariant associated with a negative definite plumbing 3manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zetafunction ...