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 …

The law of reciprocity in acoustics and elastodynamics codifies a relation of symmetry
between action and reaction in fluids and solids. In its simplest form, it states that the …

Phononic crystals (PCs) and metamaterials (MMs) can exhibit abnormal properties, even far
beyond those found in nature, through artificial design of the topology or ordered structure of …

Non-reciprocal transmission of motion is potentially highly beneficial to a wide range of
applications, ranging from wave guiding to shock and vibration damping and energy …

In solid state physics, a bandgap (BG) refers to a range of energies where no electronic
states can exist. This concept was extended to classical waves, spawning the entire fields of …

Acoustic resonances in open systems, which are usually associated with resonant modes
characterized by complex eigenfrequencies, play a fundamental role in manipulating …

Materials made from active, living, or robotic components can display emergent properties
arising from local sensing and computation. Here, we realize a freestanding active …

Dissipation in mechanics, optics, acoustics, and electronic circuits is nowadays recognized
to be not always detrimental but can be exploited to achieve non-Hermitian topological …

In recent years, elastic metamaterials inspired from electromagnetic metamaterials have
been used to protect buildings during earthquakes, and their effectiveness in seismic wave …

Abstract Space− time modulated metamaterials support extraordinary rich applications, such
as parametric amplification, frequency conversion, and non-reciprocal transmission. The …