"Quantum trajectory dynamics in imaginary time with the momentum-dependent
quantum potential"  by  Sophya Garashchuk

The quantum trajectory  dynamics is extended to the wavefunction evolution
in imaginary time.  For a nodeless wavefunction
 a simple exponential form  leads to the classical-like equations of motion
of  trajectories, representing the wavefunction,  in the  presence of the
momentum-dependent quantum potential in addition to  the external potential.
For a Gaussian wavefunction this quantum potential is a time-dependent
constant, generating zero quantum force yet contributing to the total
energy.  For anharmonic  potentials the momentum-dependent quantum potential
is cheaply estimated from the  global Least Squares  Fit  to the trajectory
momenta in the Taylor basis. Wavefunctions with nodes are described in  the
mixed
 coordinate space/trajectory  representation
 at little additional computational cost.  The nodeless wavefunction,
represented by the trajectory ensemble,  decays to the ground  state. The
mixed representation wavefunctions, with  lower energy contributions
projected out at each time step, decay to the excited energy states.
The imaginary-time quantum trajectory propagation can be also used for
direct evaluation of  the thermal reaction rate constants by evolving the
quantum  trajectory  ensemble, representing the
flux operator eigenvectors,  in imaginary time to the desired temperature
and, then, switching to the real-time dynamics to evaluate wavepacket
correlation functions.