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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…