Quantum diffusion of the random Schrödinger evolution in the scaling limit
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Publication:943040
DOI10.1007/s11511-008-0027-2zbMath1155.82015arXivmath-ph/0512014OpenAlexW2096837264MaRDI QIDQ943040
László Erdős, Manfred Salmhofer, Horng-Tzer Yau
Publication date: 8 September 2008
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math-ph/0512014
Brownian motion (60J65) Feynman diagrams (81T18) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bounds on completely convergent Euclidean Feynman graphs
- On the essential selfadjointness of stochastic Schrödinger operators
- Transfer matrices, hyperbolic geometry and absolutely continuous spectrum for some discrete Schrödinger operators on graphs
- Diffusion in a weakly random Hamiltonian flow
- Grad \(\phi\) perturbations of massless Gaussian fields
- Absolutely continuous spectra of quantum tree graphs with weak disorder
- Kinetic limit for wave propagation in a random medium
- Absence of diffusion in the Anderson tight binding model for large disorder or low energy
- On the Boltzmann equation for the Lorentz gas
- A renormalizable field theory: The massive Gross-Neveu model in two dimensions
- Asymptotic motion of a classical particle in a random potential in two dimensions: Landau model
- A limit theorem for stochastic acceleration
- A mechanical model of Brownian motion
- Statistical properties of Lorentz gas with periodic configuration of scatterers
- A pure point spectrum of the stochastic one-dimensional Schrödinger operator
- The Lorentz process converges to a random flight process
- A representation for fermionic correlation functions
- Localization at large disorder and at extreme energies: an elementary derivation
- Frequency concentration and location lengths for the Anderson model at small disorders
- Positivity and convergence in fermionic quantum field theory
- Perturbation theory around nonnested Fermi surfaces. I: Keeping the Fermi surface fixed.
- Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field
- Convergence of perturbation expansions in fermionic models. II: Overlapping loops
- Absolutely continuous spectrum in the Anderson model on the Bethe lattice
- The short distance behavior of \((\Phi^ 4_ 3)\)
- Quantum diffusion for the Anderson model in the scaling limit
- Quantum diffusion of the random Schrödinger evolution in the scaling limit. II: The recollision diagrams
- Localization lengths and Boltzmann limit for the Anderson model at small disorders in dimension 3
- Regularity of interacting nonspherical Fermi surfaces: The full self-energy
- ON THE WEAK COUPLING LIMIT FOR A FERMI GAS IN A RANDOM POTENTIAL
- Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
- Towards the Quantum Brownian Motion
- Derivation of the transport equation for electrons moving through random impurities
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