Browsing Mathematical Physics (MP) by Title
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Centreofmass like superposition of OrnsteinUhlenbeck processes: A pathway to nonautonomous stochastic differential equations and to fractional diffusion
(Fractional Calculus and Applied Analysis, 20181025)We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centreofmass ... 
The challenge of brain complexity: A brief discussion about a fractal intermittencybased approach
(PhyCS 2016  Proceedings of the 3rd International Conference on Physiological Computing Systems, 20161030)In the last years, the complexity paradigm is gaining momentum in many research fields where large multidimensional datasets are made available by the advancements in instrumental technology. A complex system is a ... 
Characterization of the QuasiStationary State of an Impurity Driven by Monochromatic Light II: Microscopic Foundations
(Annales Henri Poincare, 20151231)From quantum mechanical first principles only, we rigorously study the timeevolution of a Nlevel atom (impurity) interacting with an external monochromatic light source within an infinite system of free electrons at ... 
Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3manifolds
(201806)Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its SeibergWitten invariant can be computed as the ‘periodic constant’ of the topological multivariable Poincaré series (zeta ... 
Concurent multiscale physical parametrization of firespotting: A study on the role of macro and mesoscale characteristics of the system
(Advances in Forest Fire Research, 2018)The strong impact of wildfires in terms of lives and homes lost and of damage to ecosystems, calls for an urgent improvement in the risk management. The aim of the present research is the improvement of these software ... 
Criterion for logarithmic connections with prescribed residues
(Manucripta Mathematica, 20170401)A theorem of Weil and Atiyah says that a holomorphic vector bundle $E$ on a compact Riemann surface $X$ admits a holomorphic connection if and only if the degree of every direct summand of $E$ is zero. Fix a finite subset ... 
Crossover from anomalous to normal diffusion: truncated powerlaw noise correlations and applications to dynamics in lipid bilayers
(New Journal of Physics, 20181018)The emerging diffusive dynamics in many complex systems shows a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent powerlaws. A prominent example for a ... 
DWave pairing driven by bipolaric modes related to giant electronphonon anomalies in highTc superconductors
(Journal of Statistical Mechanics: Theory and Experiment, 20151231)Taking into account microscopic properties of most usual highTc superconductors, like cuprates, we define a class of microscopic model Hamiltonians for two fermions (electrons or holes) and one boson (bipolaron) on the ... 
DarrieusLandau instabilities in the framework of the Gequation
(Digital proceedings of the 8th European Combustion Meeting, 1821 April 2017, Dubrovnik, Croatia, 201704)We consider a model formulation of the flame front propagation in turbulent premixed combustion based on stochastic fluctuations imposed to the mean flame position. In particular, the mean flame motion is described by ... 
Decay of Complextime Determinantal and Pfaffian\ Correlation Functionals in Lattices
(Commun. Math. Phys., 20180124)We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903931, 2016) for manybody localization of quasifree fermions, by considering the high dimensional case and complextime ... 
Diagonalizing quadratic bosonic operators by nonautonomous flow equations volker bach
(Memoirs of the American Mathematical Society, 20160101)We study a nonautonomous, nonlinear evolution equation on the space of operators on a complex Hilbert space. We specify assumptions that ensure the global existence of its solutions and allow us to derive its asymptotics ... 
The Discretenessdriven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, Ndependence, and the Role of Chaos
(The Astrophysical Journal, 20190110)We investigate the old problem of the fast relaxation of collisionless Nbody systems that are collapsing or perturbed, emphasizing the importance of (noncollisional) discreteness effects. We integrate orbit ensembles in ... 
Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions
(20170428)In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heatsemigroup formalism. Specifically, we combine suitable ... 
Effective selfsimilar expansion for the GrossPitaevskii equation
(Physical Review A, 201804)We consider an effective scaling approach for the free expansion of a onedimensional quantum wave packet, consisting in a selfsimilar evolution to be satisfied on average, i.e., by integrating over the coordinates. A ... 
Equilibrium and Transport Properties of Quantum ManyBody Systems
(20191030)This thesis is a study of equilibrium and dynamical properties of macroscopic quantum manybody problems. An important part of the manuscript concerns the study of heat and charge transport properties of fermions on the ... 
Equisingularity in OneParameter Families of Generically Reduced Curves
(International Mathematics Research Notices, 20160101)We explore some equisingularity criteria in oneparameter families of generically reduced curves. We prove the equivalence between Whitney regularity and Zariski’s discriminant criterion. We prove that topological triviality ... 
Euler reflexion formulas for motivic multiple zeta functions
(Journal of Algebraic Geometry, 20170514)We introduce a new notion of $\boxast$product of two integrable series with coefficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability of and commuting with the limit of rational ... 
Examples of varieties with index one on C1 fields
(Journal of Number Theory, 20190416)Let K be the fraction field of a Henselian discrete valuation ring with algebraically closed residue field k. In this article we give a sufficient criterion for a projective variety over such a field to have index 1. 
Existence of “$d$wave” Pairs and Density Waves in a Class of Microscopic Models for High Transition Temperature Superconductors
(20180321)Hightemperature superconductors have different properties than conventional superconductors, one of these important properties is nonisotropic symmetry of the order parameter. In this work we present a model that shows ... 
Finiteenergy Lévytype motion through heterogeneous ensemble of Brownian particles
(Journal of Physics A: Mathematical and Theoretical, 20190201)Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling $x \sim t^\delta$ with $\delta \neq 1/2$ in the probability density function (PDF). Anomalous diffusion can emerge jointly ...