A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

Both theoretical and experimental studies of topological phases in non-Hermitian systems
have made a remarkable progress in the last few years of research. In this article, we review …

In closed quantum systems, dynamical phase transitions are identified by the nonanalytic
behavior of the return probability as a function of time. In this work, we study the nonunitary …

It has been argued that it is incompatible to maintain unitary time evolution for time-
dependent non-Hermitian Hamiltonians when the metric operator is explicitly time …

We provide further nontrivial solutions to the recently proposed time-dependent Dyson and
quasi-Hermiticity relation. Here, we solve them for the generalized version of the non …

A universal scheme is introduced to speed up the dynamics of a driven open quantum
system along a prescribed trajectory of interest. This framework generalizes counterdiabatic …

In many classical and quantum systems described by an effective non-Hermitian
Hamiltonian, spectral phase transitions, from an entirely real-energy spectrum to a complex …

Thermodynamics is the phenomenological theory of heat and work. Here we analyze to
what extent quantum thermodynamic relations are immune to the underlying mathematical …

A series of geometric concepts are formulated for PT-symmetric quantum mechanics and
they are further unified into one entity, ie, an extended quantum geometric tensor (QGT). The …

In this paper, the Lewis-Riesenfeld invariant theory is generalized for the study of systems
with non-Hermitian time-dependent Hamiltonians. Explicitly time-dependent pseudo …