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• 23:44, 4 February 2025 Rosso talk contribs created page File:RMT introduction.pdf (new file without misprints)
• 23:44, 4 February 2025 Rosso talk contribs uploaded File:RMT introduction.pdf (new file without misprints)
• 16:25, 24 March 2024 Rosso talk contribs created page L-9 (Created page with "=Multifractality= In the last lecture we discussed that the eigenstates of the Anderson model can be localized, delocalized or multifractal. The idea is to look at the (generalized) IPR <center><math> IPR(q)=\sum_n |\psi_n|^{2 q} \sim L^{-\tau_q} </math></center> The exponent <math>\tau_q</math> is called <Strong> multifractal exponent </Strong>. Normalization imposes <math>\tau_1 =0 </math> and the fact that the wave fuction is defined everywhere that <math>\tau_0 =-d...")
• 11:52, 16 March 2024 Rosso talk contribs created page L-8 (Created page with "<Strong>Goal:</Strong> we will introduce the Anderson model, discuss the behaviour as a function of the dimension. In 1d localization can be connected to the product of random matrices. = Anderson model (tight bindind model)= We consider a lattice with non-interacting particles hopping between nearest neighbors and feeling on-site disorder. The hamiltonian reads: <center> <math> H= - t \sum_{ <i, j> } (c_i c_j +c_j c_i) \sum_i \epsilon_i c_i c_i </math></center>")
• 18:36, 7 March 2024 Rosso talk contribs created page File:Localization1DB.png
• 18:36, 7 March 2024 Rosso talk contribs uploaded File:Localization1DB.png
• 18:35, 7 March 2024 Rosso talk contribs created page File:Localization1dB.png
• 18:35, 7 March 2024 Rosso talk contribs uploaded File:Localization1dB.png
• 18:31, 7 March 2024 Rosso talk contribs created page L-7 (Created page with "<Strong> Goal </Strong>: This is the first lecture about the localization. Localization is a <Strong> wave phenomenon induced by disorder.</Strong> == The Gaussian packet of free particles: the ballistic behaviour == == The conductance and the diffusive behaviour == Ohm's laws characterize electric transport of (good or bad) conductors: * First law: <center><math> \frac{V}{I}= R, \quad \text{or} \quad \frac{I}{V}= G </math></center> Here <math>R </math> is the res...")
• 23:35, 28 February 2024 Rosso talk contribs created page L-6 (Created page with "= Avalanches and BGW process= = Fully connected model foor the cellular automata (mean field)= Let's study the mean field version of the cellular automata introduced in the previous lecture. * The elastic coupling is with all neighbours <center><math> \sigma_i= h_{CM} - h_i + m^2(w-h_i), \quad </math></center>. * The local random threshold are all equal: <center> <math> \sigma_i^{th}=1, \quad \forall i </math></center>. Instead of following the evoluion...")
• 12:38, 18 February 2024 Rosso talk contribs created page L-5 (Created page with "<Strong> Goal </Strong>: This is the first lecture about the dynamics of a disordered system. We will see that different systems display pinning until a critical threshold. We will revisit Larkin arguments and discuss the spectrum of excitation of the instabilities. =Pinning and depininng of a disordered material= In the first lectures we saw that a disorder system can be trapped in deep energy states and form a glass. Today we will see that disorder systems can be al...")
• 17:48, 3 January 2024 Rosso talk contribs created page L-4 (Created page with "<Strong> Goal 1</Strong>: final lecture on KPZ and directed polymers at finite dimension. We will show that for <math>d>2</math> a "glass transition" takes place. <Strong> Goal 2</Strong>: We will mention some ideas related to glass transition in true glasses. =Part 1: KPZ in finite dimension= * In <math>d=1</math> we found <math>\theta=1/3</math> and a glassy regime present at all temperatures. Moreover, the stationary solution tell us that <math>E_{\min}[x]</math>...")
• 19:22, 1 January 2024 Rosso talk contribs created page File:SketchDPRM.png
• 19:22, 1 January 2024 Rosso talk contribs uploaded File:SketchDPRM.png
• 12:48, 28 December 2023 Rosso talk contribs created page L-3 (Created page with "<strong>Goal: </strong> This lecture is dedicated to a classical model in disordered systems: the directed polymer in random media. It has been introduced to model vortices in superconductur or domain wall in magnetic film. We will focus here on the algorithms that identify the ground state or compute the free energy at temperature T, as well as, on the Cole-Hopf transformation that map this model on the KPZ equation. =Polymers, interfaces and manifolds in random media=")
• 20:32, 26 December 2023 Rosso talk contribs created page L-2 (Created page with "# Interface Growth")