Wave turbulence describes the long-time statistical behavior of
out-of-equilibrium systems composed of weakly interacting waves. Non-Hermitian
media ranging from open quantum systems to active materials can sustain wave
propagation in so-called $PT$-symmetric states where gain and loss are
effectively balanced. Here, we derive the kinetic equations governing wave
turbulence in a prototypical non-Hermitian medium: a three-dimensional fluid
with odd viscosity. We calculate its exact anisotropic solution, the so-called
Kolmogorov-Zakharov spectrum, and validate the existence of this regime using
direct numerical simulations. This non-Hermitian wave turbulence generates a
direct cascade that is sustained down to the smallest scales, suppressing the
transition to strong turbulence typically observed in rotating fluids and
electron magnetohydrodynamics. Beyond odd viscous fluids, this qualitative
mechanism applies to any non-linear system of waves where non-Hermitian effects
are enhanced at small scales through gradient terms in the dynamical equations,
e.g. via odd elastic moduli or other non-reciprocal responses.

Dieser Artikel untersucht Zeitreisen und deren Auswirkungen.

PDF herunterladen: