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 …

We review the recent developments and the current status in the field of quantum-gas cavity
QED. Since the first experimental demonstration of atomic self-ordering in a system …

Over the last decade impressive progress has been made in the theoretical understanding
of transport properties of clean, one-dimensional quantum lattice systems. Many physically …

In Floquet engineering, periodic driving is used to realize novel phases of matter that are
inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe …

A bstract Continuing the previous initiatives [1, 2], we pursue the exploration of operator
growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort …

Explaining quantum many-body dynamics is a long-held goal of physics. A rigorous operator
algebraic theory of dynamics in locally interacting systems in any dimension is provided …

In contrast with extended Bloch waves, a single particle can become spatially localized due
to the so-called skin effect originating from non-Hermitian pumping. Here we show that in …

Markovian open quantum systems display complicated relaxation dynamics. The spectral
gap of the Liouvillian characterizes the asymptotic decay rate toward the steady state, but it …

The gap of the Liouvillian spectrum gives the asymptotic decay rate of a quantum dissipative
system, and therefore its inverse has been identified as the slowest relaxation time. Contrary …

We show that current noisy quantum computers are ideal platforms for the simulation of
quantum many-body dynamics in generic open systems. We demonstrate this using the IBM …