Related papers: Continuum Model of Isospectrally Patterned Lattice…
Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized…
Bandlimited approaches to quantum field theory offer the tantalizing possibility of working with fields that are simultaneously both continuous and discrete via the Shannon Sampling Theorem from signal processing. Conflicting assumptions in…
Conformal field theory predicts finite-size scaling amplitudes of correlation lengths universally related to critical exponents on sphere-like, semi-finite systems $S^{d-1}\times\mathbb{R}$ of arbitrary dimensionality $d$. Numerical studies…
We study flat bands in bipartite tight-binding networks with discrete translational invariance. Chiral flat bands with chiral symmetry eigenenergy E = 0 and host compact localized eigenstates for finite range hopping. For a bipartite…
We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states…
We propose a simple model unifying two major approaches to the analysis of large multicomponent systems: interacting particle systems (IPS) and couple map lattices (CML) and show that in the weak interaction limit depending on fine…
This experimental study of driven intrinsic localized modes (ILMs) in an electronic circuit lattice with saturable nonlinearity follows the theoretical work of Hadzievski and coworkers. They proposed that a saturable nonlinearity could…
The experimental properties of intrinsic localized modes (ILM) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest neighbor intersite potentials. Here it is shown for a 1-D…
We study nonlinear excitations described by DNLS-type equations with so-called competing nonlinearities. These are the nonlinearities that consist of two power terms with coefficients of different sign. A key feature of these models is the…
The capability to temporarily arrest the propagation of optical signals is one of the main challenges hampering the ever more widespread use of light in rapid long-distance transmission as well as all-optical on-chip signal processing or…
We exhibit simple lattice systems, motivated by recently proposed cold atom experiments, whose continuum limits interpolate between real and $p$-adic smoothness as a spectral exponent is varied. A real spatial dimension emerges in the…
Continuous time-translation symmetry is often spontaneously broken in open quantum systems, and the condition for their emergence has been actively investigated. However, there are only a few cases in which its condition for appearance has…
We propose a phenomenological model for pattern formation in a vertically vibrated layer of granular material. This model exhibits a variety of stable cellular patterns including standing rolls and squares as well as localized objects…
We present the first experimental demonstration of a new type of bound states in the continuum, namely, compacton-like linear states in flat bands lattices. To this end, photonic Lieb lattices are employed, which exhibit three tight-binding…
At the International Linear Collider large beam polarization of both the electron and positron beams will enhance the signature of physics due to interactions that are beyond the Standard Model. Here we review our recently obtained results…
Radiative properties of lasing plasmonic bound state in continuum are analyzed. The topological charge of the lasing signal is analyzed in the far field as well as in the source plane of the finite sized plasmonic lattice. The physical…
In the presence of boundaries, the entanglement entropy in lattice models is known to exhibit oscillations with the (parity of the) length of the subsystem, which however decay to zero with increasing distance from the edge. We point out in…
We investigate experimentally parity-time (${\cal PT}$) symmetric scattering using $LRC$ circuits in an inductively coupled ${\cal PT}$- symmetric pair connected to transmission line leads. In the single-lead case, the ${\cal PT}$-symmetric…
We describe spatiotemporal patterns in a network of identical van der Pol oscillators coupled in a two-dimensional geometry. In this study, we show that the system under study demonstrates a plethora of different spatiotemporal structures…
Periodic photonic structures enable precise control over the light-matter interaction through band structure engineering. Certain lattice geometries exhibit dispersionless flat bands, characterized by vanishing group velocity and diverging…