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 …

Shortcuts to adiabaticity (STA) are fast routes to the final results of slow, adiabatic changes
of the controlling parameters of a system. The shortcuts are designed by a set of analytical …

This chapter introduces the basic ideas of P T-symmetric systems. It begins with a brief
discussion of closed (isolated) and open (non-isolated) systems and explains that P T …

We propose a simple method for simulating a general class of nonunitary dynamics as a
linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on …

Recent progress on nonlinear properties of parity-time (PT)-symmetric systems is
comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum …

The present status and development of strong-field nano-optics, an emerging field of
nonlinear optics, is discussed. A nonperturbative regime of light-matter interactions is …

Invisibility by metamaterials is of great interest, where optical properties are manipulated in
the real permittivity–permeability plane,. However, the most effective approach to achieving …

Real-time electronic structure methods provide an unprecedented view of electron dynamics
and ultrafast spectroscopy on the atto-and femtosecond time scale with vast potential to yield …

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define
a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We …

We propose a measure, which we call the dissipative spectral form factor (DSFF), to
characterize the spectral statistics of non-Hermitian (and nonunitary) matrices. We show that …