Search results for " mathematical physics"
showing 10 items of 396 documents
A Diffusive Strategic Dynamics for Social Systems
2010
We propose a model for the dynamics of a social system, which includes diffusive effects and a biased rule for spin-flips, reproducing the effect of strategic choices. This model is able to mimic some phenomena taking place during marketing or political campaigns. Using a cost function based on the Ising model defined on the typical quenched interaction environments for social systems (Erdos-Renyi graph, small-world and scale-free networks), we find, by numerical simulations, that a stable stationary state is reached, and we compare the final state to the one obtained with standard dynamics, by means of total magnetization and magnetic susceptibility. Our results show that the diffusive str…
Quantum waveguides with magnetic fields
2019
International audience; We study generalised quantum waveguides in the presence of moderate and strong external magnetic fields. Applying recent results on the adiabatic limit of the connection Laplacian we show how to construct and compute effective Hamiltonians that allow, in particular, for a detailed spectral analysis of magnetic waveguide Hamiltonians. We apply our general construction to a number of explicit examples, most of which are not covered by previous results.
The Functional Renormalization Group
2018
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The Vlasov Limit for a System of Particles which Interact with a Wave Field
2008
In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.
Coupling of heat flux and vortex polarization in superfluid helium
2020
We consider a macroscopic description of the mutual influence between heat flux and vortex polarization in superfluid helium, in which the vortices produce a lateral deviation of the heat flux, and the heat flux produces a lateral drift of vortices. This coupling is a consequence of a microscopic Magnus force and mutual friction force between the vortices and the flow of excitations carrying the heat. We keep track of these effects with simplified macroscopic equations, and we apply them to second sound propagation between rotating concentric cylinders and to spatial distribution of polarization across a rectangular channel with vortices polarized orthogonally to the channel in the presence…
A star-product approach to noncompact Quantum Groups
1995
Using duality and topological theory of well behaved Hopf algebras (as defined in [2]) we construct star-product models of non compact quantum groups from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras of simple Lie algebras. Our star-products act not only on coefficient functions of finite-dimensional representations, but actually on all $C^\infty$ functions, and they exist even for non linear (semi-simple) Lie groups.
A Remark on an Overdetermined Problem in Riemannian Geometry
2016
Let (M, g) be a Riemannian manifold with a distinguished point O and assume that the geodesic distance d from O is an isoparametric function. Let \(\varOmega \subset M\) be a bounded domain, with \(O \in \varOmega \), and consider the problem \(\varDelta _p u = -1\ \mathrm{in}\ \varOmega \) with \(u=0\ \mathrm{on}\ \partial \varOmega \), where \(\varDelta _p\) is the p-Laplacian of g. We prove that if the normal derivative \(\partial _{\nu }u\) of u along the boundary of \(\varOmega \) is a function of d satisfying suitable conditions, then \(\varOmega \) must be a geodesic ball. In particular, our result applies to open balls of \(\mathbb {R}^n\) equipped with a rotationally symmetric metr…
A note on the Pais-Uhlenbeck model and its coherent states
2011
In some recent papers many quantum aspects of the Pais-Uhlenbeck model were discussed. In particular, several inequivalent hamiltonians have been proposed, with different features, giving rise, at a quantum level, to the fourth-order differential equation of the model. Here we propose two new possible hamiltonians which also produce the same differential equation. In particular our first hamiltonian is self-adjoint and positive. Our second proposal is written in terms of pseudo-bosonic operators. We discuss in details the ground states of these hamiltonians and the (bi-)coherent states of the models.
Nilpotence of orbits under monodromy and the length of Melnikov functions
2021
Abstract Let F ∈ ℂ [ x , y ] be a polynomial, γ ( z ) ∈ π 1 ( F − 1 ( z ) ) a non-trivial cycle in a generic fiber of F and let ω be a polynomial 1-form, thus defining a polynomial deformation d F + e ω = 0 of the integrable foliation given by F . We study different invariants: the orbit depth k , the nilpotence class n , the derivative length d associated with the couple ( F , γ ) . These invariants bind the length l of the first nonzero Melnikov function of the deformation d F + e ω along γ . We analyze the variation of the aforementioned invariants in a simple but informative example, in which the polynomial F is defined by a product of four lines. We study as well the relation of this b…
A calorimeter for the precise determination of the activity of the 144Ce-144Pr anti-neutrino source in the SOX experiment
2018
We describe the design and the performance of a high precision thermal calorimeter, whose purpose was the measurement of the total activity of the 144Ce-144Pr anti-neutrino source of the SOX (Short distance neutrino Oscillation with BoreXino) experiment. SOX aimed at the search for eV-scale sterile neutrinos by means of the Borexino detector at the Laboratori Nazionali del Gran Sasso in Italy and of a very powerful artificial anti-neutrino source located at 8.51 m from the detector center. In order to obtain the required sensitivity, the activity of the source (approximately 150 kCi) had to be known at 1% precision. In this work we report the design of the experimental apparatus and the res…