Quantum diffusion via an approximate semigroup property

Perturbation theories for operators and differential equations in quantum theory (81Q15) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44) Transport equations (35Q49)

Cites Work

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Weakly nonlinear Schrödinger equation with random initial data
Asymptotics of resolvent integrals: The suppression of crossings for analytic lattice dispersion relations
Convergence in higher mean of a random Schrödinger to a linear Boltzmann evolution
Quantum diffusion of the random Schrödinger evolution in the scaling limit
On the Boltzmann equation for the Lorentz gas
Asymptotic motion of a classical particle in a random potential in two dimensions: Landau model
Self-averaging of Wigner transforms in random media
Random walk on the randomly-oriented Manhattan lattice
The weak coupling limit for the random Schrödinger equation: the average wave function
Invariance principle for the random Lorentz gas -- beyond the Boltzmann-Grad limit
Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation
Deterministic walks in random environment
On the quantum Boltzmann equation
Kinetic limits for waves in a random medium
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
Diffusion in the Lorentz Gas
Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation
A new spectral analysis of stationary random Schrödinger operators
On the derivation of the wave kinetic equation for NLS
Statistical Physics of Non Equilibrium Quantum Phenomena
On the kinetic wave turbulence description for NLS
HOMOGENIZATION OF THE SCHRÖDINGER EQUATION WITH LARGE, RANDOM POTENTIAL
The weakly nonlinear large-box limit of the 2D cubic nonlinear Schrödinger equation
Derivation of the transport equation for electrons moving through random impurities

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