TY - CONF
AB - We outline the status of rigorous derivations of certain classical evolution equations as limits of Schrödinger dynamics. We explain two recent results jointly with H.T. Yau in more details. The first one is the derivation of the linear Boltzmann equation as the long time limit of the one-body Schrödinger equation with a random potential. The second one is the mean field limit of high density bosons with Coulomb interaction that leads to the nonlinear Hartree equation.
AU - László Erdös
ID - 2694
TI - Scaling limits of Schrödinger quantum mechanics
VL - 597
ER -
TY - CONF
AU - László Erdös
ID - 2708
TI - Two dimensional Pauli operator via scalar potential
VL - 307
ER -
TY - JOUR
AB - We derive the time-dependent Schrödinger–Poisson equation as the weak coupling limit of the N-body linear Schrödinger equation with Coulomb potential.
AU - Bardos, Claude
AU - László Erdös
AU - Golse, François
AU - Mauser, Norbert J
AU - Yau, Horng-Tzer
ID - 2737
IS - 6
JF - Comptes Rendus Mathematique
TI - Derivation of the Schrödinger-Poisson equation from the quantum N-body problem
VL - 334
ER -
TY - JOUR
AB - We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear Boltzmann equation globally in time. The collision kernel is identified as the sum of an emission and an absorption term that depend on the equilibrium distribution of the free phonon modes.
AU - László Erdös
ID - 2738
IS - 5-6
JF - Journal of Statistical Physics
TI - Linear Boltzmann equation as the long time dynamics of an electron weakly coupled to a phonon field
VL - 107
ER -
TY - JOUR
AB - We define the two dimensional Pauli operator and identify its core for magnetic fields that are regular Borel measures. The magnetic field is generated by a scalar potential hence we bypass the usual A L 2loc condition on the vector potential, which does not allow to consider such singular fields. We extend the Aharonov-Casher theorem for magnetic fields that are measures with finite total variation and we present a counterexample in case of infinite total variation. One of the key technical tools is a weighted L 2 estimate on a singular integral operator.
AU - László Erdös
AU - Vougalter, Vitali
ID - 2739
IS - 2
JF - Communications in Mathematical Physics
TI - Pauli operator and Aharonov-Casher theorem for measure valued magnetic fields
VL - 225
ER -