2008/12/18 by Laurent Amour, Amour, Laurent, Jérémy Faupin +5
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems #Crystallography and Radiation Phenomena
paper · doi:10.48550/arxiv.0812.3562
We consider a non-relativistic electron interacting with a classical magnetic field pointing along the x3-axis and with a quantized electromagnetic field. The system is translation invariant in the x3-direction and we consider the reduced Hamiltonian H(P3) associated with the total momentum P3 along the x3-axis. For a fixed momentum P3 sufficiently small, we prove that H(P3) has a ground state in the Fock representation if and only if E'(P3)=0, where P3 ↦ E'(P3) is the derivative of the map P3 ↦ E(P3) = inf σ(H(P3)). If E'(P3) ≠ 0, we obtain the existence of a ground state in a non-Fock representation. This result holds for sufficiently small values of the coupling constant.