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Solutions of the wave equations for time-independent disordered media can exhibit Anderson localization where instead of wave propagation we observe their localization around different points in space. Photonic time crystals are spatially homogeneous media in which the refractive index changes periodically in time, leading to the formation of bands in the wave number domain. By analogy to Anderson localization in space, one might expect that the presence of temporal disorder in photonic time crystals would lead to Anderson localization in the time domain. Here, we show that indeed periodic modulations of the refractive index with the addition of temporal disorder lead to Anderson localization in time, where an electromagnetic field can emerge from the temporally modulated medium at a certain moment in time and then decay exponentially over time. Thus, we are dealing with a situation where, in a fluctuating three-dimensional medium, the birth and death of waves can occur, and the mechanism of this phenomenon corresponds to Anderson localization., Comment: 4 pages + supplementary material, 3 figures

Periodic driving of systems of particles can create crystalline structures in time. Such systems can be used to study solid-state physics phenomena in the time domain. In addition, it is possible to engineer the wave-number band structure of optical systems and to realize photonic time crystals by periodic temporal modulation of the material properties of the electromagnetic wave propagation medium. We introduce here a versatile averaged-permittivity approach which empowers emulating various condensed matter phases in the time dimension in a traveling wave resonator. This is achieved by utilizing temporal modulation of permittivity within a small segment of the resonator and the spatial shape of the segment. The required frequency and depth of the modulation are experimentally achievable, opening a pathway for research into the practical realisation of crystalline structures in time utilising microwave and optical systems., Comment: 4 pages + supplemental materials, 3 figures

We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two-dimensions (2D) in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equations in 2D by imposing global constraints of energy and enstrophy conservation. A comparative study of the statistical properties of its solutions with those obtained from the standard Navier-Stokes equations clearly show that a formally time-reversible system is able to reproduce the features of a 2D turbulent flow. Statistical quantities based on one- and two-point measurements show an excellent agreement between the two systems, for the inverse- and direct cascade regions. Moreover, we find that the conjecture holds very well for 2D turbulent flows with both conserved energy and enstrophy at finite Reynolds number, which goes beyond the original conjecture for three-dimensional turbulence in the limit of infinite Reynolds number., Comment: 8 pages, 6 figures