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Stationary currents in long-range interacting magnetic systems
Springer Science and Business Media LLC - Tập 23 - Trang 1-25 - 2020
Roberto Boccagna
We construct a solution for the 1d integro-differential stationary equation derived from a finite-volume version of the mesoscopic model proposed in Giacomin and Lebowitz (J. Stat. Phys. 87(1), 37–61, 1997). This is the continuous limit of an Ising spin chain interacting at long range through Kac potentials, staying in contact at the two edges with reservoirs of fixed magnetizations. The stationar...... hiện toàn bộ
Supersymmetric Polar Coordinates with Applications to the Lloyd Model
Springer Science and Business Media LLC - Tập 23 Số 1 - Trang 1-21 - 2020
Disertori, Margherita, Lager, Mareike
Spectral properties of random Schrödinger operators are encoded in the average of products of Greens functions. For probability distributions with enough finite moments, the supersymmetric approach offers a useful dual representation. Here we use supersymmetric polar coordinates to derive a dual representation that holds for general distributions. We apply this result to study the density of state...... hiện toàn bộ
On the AC Spectrum of One-dimensional Random Schrödinger Operators with Matrix-valued Potentials
Springer Science and Business Media LLC - Tập 13 - Trang 219-233 - 2010
Richard Froese, David Hasler, Wolfgang Spitzer
We consider discrete one-dimensional random Schrödinger operators with decaying matrix-valued, independent potentials. We show that if the ℓ2-norm of this potential has finite expectation value with respect to the product measure then almost surely the Schrödinger operator has an interval of purely absolutely continuous (ac) spectrum. We apply this result to Schrödinger operators on a strip. This ...... hiện toàn bộ
Height Fluctuations for the Stationary KPZ Equation
Springer Science and Business Media LLC - Tập 18 - Trang 1-95 - 2015
Alexei Borodin, Ivan Corwin, Patrik Ferrari, Bálint Vető
We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data $\mathcal {H}(0,X)=B(X)$ , for B(X) a two-sided standard Brownian motion) and show that as time T goes to infinity, the fluctuations of the height function ...... hiện toàn bộ
A General Framework for Localization of Classical Waves: II. Random Media
Springer Science and Business Media LLC - Tập 7 - Trang 151-185 - 2004
Abel Klein, Andrew Koines
We study localization of classical waves in random media in the general framework introduced in Part I of this work. This framework allows for two random coefficients, encompasses acoustic waves with random position dependent compressibility and mass density, elastic waves with random position dependent Lamé moduli and mass density, electromagnetic waves with random position dependent magnetic per...... hiện toàn bộ
Weyl’s Laws and Connes’ Integration Formulas for Matrix-Valued $$L\!\log \!L$$ -Orlicz Potentials
Springer Science and Business Media LLC - Tập 25 Số 2 - Trang 1-33 - 2022
Ponge, Raphaël
Thanks to the Birman-Schwinger principle, Weyl’s laws for Birman-Schwinger operators yields semiclassical Weyl’s laws for the corresponding Schrödinger operators. In a recent preprint Rozenblum established quite general Weyl’s laws for Birman-Schwinger operators associated with pseudodifferential operators of critical order and potentials that are product of $$L\!\log \!L$$ -Orlicz functions and A...... hiện toàn bộ
An Algebraic Approach to FQHE Variational Wave Functions
Springer Science and Business Media LLC - Tập 22 Số 2 - 2019
S. B. Mulay, John J. Quinn, Mark Shattuck
Well-posedness for Semi-relativistic Hartree Equations of Critical Type
Springer Science and Business Media LLC - Tập 10 - Trang 43-64 - 2007
Enno Lenzmann
We prove local and global well-posedness for semi-relativistic, nonlinear Schrödinger equations $i \partial_t u = \sqrt{-\Delta + m^2} u + F(u)$ with initial data in H s (ℝ3), ...... hiện toàn bộ
Generalized Bessel Functions and Lie Algebra Representation
Springer Science and Business Media LLC - Tập 8 - Trang 299-313 - 2005
Subuhi Khan, Ghazala Yasmin
The generalized Bessel functions (GBF) are framed within the context of the representation Q(ω,m 0) of the three-dimensional Lie algebra $\mathcal{T}_{3}$ . The analysis has been carried out by generalizing the formalism relevant to Bessel functions. New generating relations and identities involving various forms of GBF are obtained. Cer...... hiện toàn bộ
Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere
Springer Science and Business Media LLC - Tập 24 - Trang 1-30 - 2021
Alexander I. Bobenko, Ulrike Bücking
We consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converg...... hiện toàn bộ
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