Related papers: General Properties of Two-dimensional Conformal Tr…
We derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the…
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and…
Mechanical metamaterials are engineered materials that gain their remarkable mechanical properties, such as negative Poisson's ratios, negative compressibility, phononic bandgaps, and topological phonon modes, from their structure rather…
We describe space-time using split octonions over the reals and use their group of automorphisms, the non-compact form of Cartan's exceptional Lie group G2, as the main geometrical group of the model. Connections of the G2-rotations of…
The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the field of analytic complex functions, the generic…
Electromagnetic fields with complex spatial variation routinely arise in Nature. We study the response of a small molecule to monochromatic fields of arbitrary three-dimensional geometry. First, we consider the allowed configurations of the…
The geometry of two-dimensional crystalline membranes dictates their mechanical, electronic and chemical properties. The local geometry of a surface is determined from the two invariants of the metric and the curvature tensors. Here we…
We apply variational principles in the context of geometrothermodynamics. The thermodynamic phase space ${\cal T}$ and the space of equilibrium states ${\cal E}$ turn out to be described by Riemannian metrics which are invariant with…
We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are…
The electrodynamics of two-dimensional (2D) dielectric and conducting layers cannot be described by such three-dimensional macroscopic quantities as the dielectric constant $\epsilon$ or the refractive index $n$. By means of the proper…
We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the…
Breakthroughs in nanotechnology have enabled the large-scale fabrication of nanoparticles with varied compositions and structures. Yet, evaluating their electrical conductivities remains challenging due to high volume and individual…
Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding…
Beyond the constraints of conservative systems, altering wave propagation frequency emerges as a crucial factor across diverse physical domains. This Letter demonstrates bi-directional asymmetric frequency conversion -- either upward or…
Understanding and mastering the mechanical properties of metallic nanoparticles is crucial for their use in a wide range of applications. In this context, we use atomic-scale (Molecular Dynamics) and continuous (Finite Elements)…
We study the effects of a domain deformation to the nodal set of Laplacian eigenfunctions when the eigenvalue is degenerate. In particular, we study deformations of a rectangle that perturb one side and how they change the nodal sets…
We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure.…
Two-dimensional materials (2DM) and their derived heterostructures have electrical and optical properties that are widely tunable via several approaches, most notably electrostatic gating and interfacial engineering such as twisting. While…
I consider the effect of the finite width of the resonant level on its thermodynamics and tunneling transport properties in the single electron charging regime. The finite width of the levels results from their delocalization with formation…
Toroidal modes enable high-Q resonances, but electric toroidal excitations remain unexplored compared to magnetic ones. This work establishes electric-magnetic toroidal duality in a hexagonal metasurface. Using finite element simulations,…