Non-Unitary Evolution?

Mustapha Maamache

We provide a new perspective on non-Hermitian evolution in quantum mechanics by emphasizing the same method as in the Hermitian quantum evolution. We first give a precise description of the non unitary evolution, and collecting the basic results around it and postulating the norm preserving. This cautionary postulate imposing that the time evolution of a non Hermitian quantum system preserves the inner products between the associated states must not be read naively. We also give an example showing that the solutions of time-dependent non Hermitian Hamiltonian systems given by a linear combination of SU(1,1) and SU(2) are obtained thanks to time-dependent non-unitary transformation.

Bastien Lapierre, Pietro Pelliconi, Shinsei Ryu +1 more

We investigate the interplay between unitary and non-unitary driven many-body dynamics in (1+1)-dimensional quantum critical systems described by conformal field theory (CFT). By formulating a coherent state approach, we demonstrate that the growth of entanglement entropy and energy can be found analytically for a class of non-unitary driven CFTs, where the evolution alternates between real and imaginary time evolution, the latter corresponding to postselected weak measurements. We find that non-unitary evolution leads to the emergence of steady states at infinite times for the cases of periodic, quasiperiodic, and random drives. In a special class of drives, for mixed initial states, we uncover purification phase transitions that arise as a result of the competition between unitary evolution and weak measurements. We compare the CFT evolution with the corresponding non-unitary dynamics of critical lattice models, finding remarkable agreement.

Alex Khang, Kali Charan Rath

Gu, Lei

We pose the question of what effect the statistical fluctuation causes if it induces a non-unitary evolution. We apply this idea to the BCS model and study fluctuation around the mean-field average. We find that, dynamics of the thermalization influences the equilibrium besides the non-unitary evolution, and the resulting equilibrium state is no longer the canonical one. The pseudogap phenomenon can exist in this model.