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 various bounds concerning out-of-equilibrium dynamics in few-level and many-
body quantum systems. We primarily focus on closed quantum systems but will also mention …

Protection of gauge invariance in experimental realizations of lattice gauge theories based
on energy-penalty schemes has recently stimulated impressive efforts both theoretically and …

Speed of state transitions in macroscopic systems is a crucial concept for foundations of
nonequilibrium statistical mechanics as well as various applications in quantum technology …

The postulate of gauge invariance in nature does not lend itself directly to implementations
of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge …

The transverse-field Ising model is one of the fundamental models in quantum many-body
systems, yet a full understanding of its dynamics remains elusive in higher than one …

We derive a universal nonperturbative bound on the distance between unitary evolutions
generated by time-dependent Hamiltonians in terms of the difference of their integral …

We propose a construction of kinetically constrained models using the Markovian quantum
dynamics under strong dissipation. Engineering the Gorini-Kossakowski-Sudarshan …

This book focus on examining the thermodynamic properties of various prominent field
theories concerning high-energy and condensed matter physics. We make the usage of the …

A fundamental result in modern quantum chaos theory is the Maldacena-Shenker-Stanford
upper bound on the growth of out-of-time-order correlators, whose infinite-temperature limit …