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Derivation of the Euler equations from many-body quantum mechanics
Bruno Nachtergaele, Horng-Tzer Yau
The Heisenberg dynamics of the energy, momentum, and particle densities for fermions with short-range pair interactions is shown to converge to the compressible Euler equations in…
Derivation of the Euler Equations from Quantum Dynamics
Bruno Nachtergaele, Horng-Tzer Yau
We derive the Euler equations from quantum dynamics for a class of fermionic many-body systems. We make two types of assumptions. The first type are physical assumptions on the sol…
Classification of Asymptotic Profiles for Nonlinear Schrödinger Equations with Small Initial Data
Tai-Peng Tsai, Horng-Tzer Yau
We consider a nonlinear Schrödinger equation with a bounded local potential in . The linear Hamiltonian is assumed to have two bound states with the eigenvalues satisfying som…
law of the two dimensional asymmetric simple exclusion process
Horng-Tzer Yau
We prove that the diffusion coefficient for the two dimensional asymmetric simple exclusion process diverges as to the leading order. The method applies to nearest…
Superdiffusivity of asymmetric exclusion process in dimensions one and two
C. Landim, J. Quastel, M. Salmhofer +1
We prove that the diffusion coefficient for the asymmetric exclusion process diverges at least as fast as in dimension and in . The method app…