Speaker
Description
In this work, we study the semiclassical dynamics of non-Hermitian quantum systems in
phase space. The non-Hermitian semiclassical dynamics of Gaussian coherent states is
described by a system of equations for the motion of the center and of the metric associated
with the wave packet, which we call the intrinsic geometry of the state [1,2] . The inclusion of a
non-Hermitian part leads to the non-conservation of the norm, which can be interpreted as
either energy loss or gain. Analytical and numerical methods of solving the dynamics of non-
Hermitian quantum systems in phase space are studied and developed. Lastly, a connection is
made between the formalism of stochastic optimization of a certain class of control systems
and the semiclassical evolution generated by a quantum non-Hermitian Hamiltonian. An
example of a quadratic Hamiltonian is explored where we show the existence of the infinite
time limit of the center and the metric of the wave packet.
