Zobrazeno 1 - 10
of 58
pro vyhledávání: '"Tourigny, Yves"'
Publikováno v:
Phys. Rev. E 105, 064210 (2022)
We consider the one-dimensional Schr\"odinger equation with a random potential and study the cumulant generating function of the logarithm of the wave function $\psi(x)$, known in the literature as the "generalized Lyapunov exponent"; this is tantamo
Externí odkaz:
http://arxiv.org/abs/2110.01522
The statistical behaviour of a product of independent, identically distributed random matrices in $\text{SL}(2,{\mathbb R})$ is encoded in the generalised Lyapunov exponent $\Lambda$; this is a function whose value at the complex number $2 \ell$ is t
Externí odkaz:
http://arxiv.org/abs/1911.00117
Autor:
Comtet, Alain, Tourigny, Yves
This is an introduction to the theory of one-dimensional disordered systems and products of random matrices, confined to the 2 by 2 case. The notion of impurity model--- that is, a system in which the interactions are highly localised--- links the tw
Externí odkaz:
http://arxiv.org/abs/1601.01822
Autor:
Comtet, Alain, Tourigny, Yves
We consider two aspects of Marc Yor's work that have had an impact in statistical physics: firstly, his results on the windings of planar Brownian motion and their implications for the study of polymers; secondly, his theory of exponential functional
Externí odkaz:
http://arxiv.org/abs/1409.3777
Publikováno v:
J. Stat. Phys. 155(2), 237-276 (2014)
We study the one-dimensional Schr\"odinger equation with a disordered potential of the form $V (x) = \phi(x)^2+\phi'(x) + \kappa(x) $ where $\phi(x)$ is a Gaussian white noise with mean $\mu g$ and variance $g$, and $\kappa(x)$ is a random superposit
Externí odkaz:
http://arxiv.org/abs/1310.6519
Publikováno v:
J. Phys. A: Math. Theor. 46, 254003 (2013)
The concept of Lyapunov exponent has long occupied a central place in the theory of Anderson localisation; its interest in this particular context is that it provides a reasonable measure of the localisation length. The Lyapunov exponent also feature
Externí odkaz:
http://arxiv.org/abs/1207.0725
Publikováno v:
Journal of Statistical Physics vol: 145 , Issue: 5 , Pages: 1291 - 1323, 2011
We consider the Schroedinger equation with a supersymmetric random potential, where the superpotential is a Levy noise. We focus on the problem of computing the so-called complex Lyapunov exponent, whose real and imaginary parts are, respectively, th
Externí odkaz:
http://arxiv.org/abs/1105.5506
Autor:
Tourigny, Yves
The spectral data of a vibrating string are encoded in its so-called characteristic function. We consider the problem of recovering the distribution of mass along the string from its characteristic function. It is well-known that Stieltjes' continued
Externí odkaz:
http://arxiv.org/abs/1101.2989
Publikováno v:
J. Stat. Phys. 140(3), 427-466 (2010)
To every product of $2\times2$ matrices, there corresponds a one-dimensional Schr\"{o}dinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and their posi
Externí odkaz:
http://arxiv.org/abs/1004.2415
Autor:
Comtet, Alain, Tourigny, Yves
It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of
Externí odkaz:
http://arxiv.org/abs/0906.4651