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 …

Topological quantum computation has emerged as one of the most exciting approaches to
constructing a fault-tolerant quantum computer. The proposal relies on the existence of …

The distribution of quantum states over long distances is limited by photon loss.
Straightforward amplification as in classical telecommunications is not an option in quantum …

In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization
group transformation. When applied to the Kondo problem, this numerical renormalization …

Many trial wave functions for fractional quantum Hall states in a single Landau level are
given by functions called conformal blocks, taken from some conformal field theory. Also …

The dichotomy between fermions and bosons is at the root of many physical phenomena,
from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent …

We propose a quantum nondemolition method—a giant optical Faraday rotation near the
resonant regime to measure a single-electron spin in a quantum dot inside a microcavity …

We describe an occupation-number-like picture of fractional quantum Hall states in terms of
polynomial wave functions characterized by a dominant occupation-number configuration …

The fractional quantum Hall effect, being one of the most studied phenomena in condensed
matter physics during the past 30 years, has generated many ground-breaking new ideas …

We introduce exactly solvable gapless quantum systems in d dimensions that support
symmetry-protected topological (SPT) edge modes. Our construction leads to long-range …