TY - JOUR
T1 - Semi-classical limits in a crystal with exterior potentials and effective mass theorems
AU - Poupaud, F.
AU - Ringhofer, Christian
PY - 1996/1/1
Y1 - 1996/1/1
N2 - We study the semi-classical limit of the dynamics of electrons in a crystal under the influence of an external electric field. Two small parameters e and h are introduced. They are respectively related to the scaled lattice length and the scaled Planck constant. When ε/h and h go to zero, we prove that in the limit process the dynamics of electrons is described by a Vlasov equation. When h is fixed and ε tends to zero, the dynamics is governed by an effective Schrödinger equation. In both cases, the mass of electrons is replaced by a matrix, the so-called effective mass.
AB - We study the semi-classical limit of the dynamics of electrons in a crystal under the influence of an external electric field. Two small parameters e and h are introduced. They are respectively related to the scaled lattice length and the scaled Planck constant. When ε/h and h go to zero, we prove that in the limit process the dynamics of electrons is described by a Vlasov equation. When h is fixed and ε tends to zero, the dynamics is governed by an effective Schrödinger equation. In both cases, the mass of electrons is replaced by a matrix, the so-called effective mass.
UR - https://www.scopus.com/pages/publications/0040062089
UR - https://www.scopus.com/pages/publications/0040062089#tab=citedBy
U2 - 10.1080/03605309608821248
DO - 10.1080/03605309608821248
M3 - Article
AN - SCOPUS:0040062089
SN - 0360-5302
VL - 21
SP - 1897
EP - 1918
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 11-12
ER -