TY - JOUR
AB - We consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.
AU - Leopold, Nikolai K
AU - Mitrouskas, David Johannes
AU - Seiringer, Robert
ID - 9246
JF - Archive for Rational Mechanics and Analysis
SN - 00039527
TI - Derivation of the Landau–Pekar equations in a many-body mean-field limit
VL - 240
ER -
TY - JOUR
AB - We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state φ0⊗ξα, where φ0 is the electron ground state of the Pekar energy functional and ξα the associated coherent state of the phonons, can be approximated by a global phase for times small compared to α2. In the present note we prove that a similar approximation holds for t=O(α2) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to α−2 and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order α2, while the phonon fluctuations around the coherent state ξα can be described by a time-dependent Bogoliubov transformation.
AU - Mitrouskas, David Johannes
ID - 9333
JF - Letters in Mathematical Physics
SN - 03779017
TI - A note on the Fröhlich dynamics in the strong coupling limit
VL - 111
ER -