Related papers: Evolution of Discrete Symmetries
We develop a classification of perfectly transmitting resonances occuring in effectively one-dimensional optical media which are decomposable into locally reflection symmetric parts. The local symmetries of the medium are shown to yield…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We introduce the concept of parity symmetry in restricted spatial domains -- local parity -- and explore its impact on the stationary transport properties of generic, one-dimensional aperiodic potentials of compact support. It is shown…
We will analyze through a first order perturbative formulation the local loss of symmetry when a source of electromagnetic and gravitational field interacts with an agent that perturbs the original geometry associated to the source. As the…
A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite…
Exploring the deep insights into localization, disorder, and wave transport in non-Hermitian systems is an emergent area of research of relevance in different areas of physics. Engineered photonic lattices, with spatial regions of optical…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
Symmetries play a central role in physics, organizing dynamics, constraining interactions, and determining the effective number of physical degrees of freedom. In parallel, modern artificial intelligence methods have demonstrated a…
The spectral and localization properties of $\mathcal{PT}$-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are…
One-dimensional scattering mediated by non-Hermitian Hamiltonians is studied. A schematic set of models is used which simulate two point interactions at a variable strength and distance. The feasibility of the exact construction of the…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
Symmetry is one of the most beautiful yet mysterious concepts in science. In chemical systems, presence of local symmetries at specific fragments often serve as driving forces behind many physicochemical properties, including stability,…
A flexible control of wave scattering in complex media is of relevance in different areas of classical and quantum physics. Recently, a great interest has been devoted to scattering engineering in non-Hermitian systems, with the prediction…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are the manifestation of the continuous space translational symmetry being spontaneously broken into a discrete one. We argue…
We consider a one-dimensional mono-atomic lattice with random perturbations of masses spread over a finite number of particles. Assuming Newtonian dynamics and linear nearest-neighbour interactions and allowing for a provision of pinning…
We derive symmetry-based conditions for tight-binding Hamiltonians with flatbands to have compact localized eigenstates occupying a single unit cell. The conditions are based on unitary operators commuting with the Hamiltonian and…
One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices…
We prove the transversality result necessary for defining local Morse chain complexes with finite cyclic group symmetry. Our arguments use special regularized distance functions constructed using classical covering lemmas, and an inductive…
Quasiperiodic mosaic systems with the quasiperiodic potential being added periodically with a fixed lattice interval have attracted significant attention due to their peculiar spectral properties with exactly known mobility edges, which…