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One of the most celebrated accomplishments of modern physics is the description of fundamental principles of nature in the language of geometry. As the motion of celestial bodies is governed by the geometry of spacetime, the motion of…
Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts…
In this paper, we introduce and study parallel-plate waveguides formed by two penetrable metasurfaces having arbitrary isotropic sheet impedances. We investigate guided modes of this structure and derive the corresponding dispersion…
A model of joint random walk of two agents on an infinite plane is considered. The agents possess no means of mutual classical communication, but have access to quantum entanglement resource which is used according to a pre-arranged…
A nonrelativistic quantum mechanical particle moving freely on a curved surface feels the effect of the nontrivial geometry of the surface through the kinetic part of the Hamiltonian, which is proportional to the Laplace-Beltrami operator,…
Motivated by a recent prediction to engineer the dispersion relation of a waveguide constructed from atomic components [arXiv:2104.08121], we explore the possibility to create directional transport in an open, collective quantum system. The…
The conditions required for spontaneous parametric down-conversion in a waveguide with periodic nonlinearity in the presence of an unguided pump field are established. Control of the periodic nonlinearity and the physical properties of the…
We study for the first time the effect of the geometry of quantum wire networks on their nonlinear optical properties and show that for some geometries, the first hyperpolarizability is largely enhanced and the second hyperpolarizability is…
We elaborate that $s$-wave and $d$-wave superconductors described by mean field theories possess a nontrivial quantum geometry. From the overlap of two quasihole states at slightly different momenta, one can define a quantum metric that…
Coherent electron transport through a quantum channel in the presence of a general extended scattering potential is investigated using a T-matrix Lippmann-Schwinger approach. The formalism is applied to a quantum wire with Gaussian type…
Refractive gravitational waves are a generalisation of impulsive waves on a null hypersurface in which the metric is discontinuous but a weaker continuity condition for areas holds. A simple example of a plane wave is examined in detail and…
We have developed the mode matching technique that is based on the using the eigenmodes of circular cavities and the eigenwaves of circular waveguides as the basic functions for calculation the properties of nonuniform disc-loaded…
A classical optics waveguide structure is proposed to simulate resonances of short range one-dimensional potentials in quantum mechanics. The analogy is based on the well known resemblance between the guided and radiation modes of a…
The quantum geometry of Bloch wavefunctions underpins a wealth of emergent phenomena in quantum materials. Its imaginary part, the Berry curvature, has long been recognized as a key source for hallmark effects such as quantum Hall and…
The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise…
A widespread, intuitive and computationally inexpensive method to analyze light guidance through waveguide bends is by introducing an equivalent straight waveguide with refractive index profile modified to account for actual waveguide bend.…
An integrated coherent matter wave circuit is a single device, analogous to an integrated optical circuit, in which coherent de Broglie waves are created and then launched into waveguides where they can be switched, divided, recombined, and…
The phenomenological description of propagation of atomic matter waves inside a curved atom wave guide is presented based on the effective action principle. The evolutions in both temporal and spatial domains for the atomic matter wave in…
Wave equations containing spatial derivatives which are higher than second order arise naturally in the context of condensed matter systems. The solutions of such equations contain more than two modes and consequently, the range of possible…
In this paper, we give upper estimates for the number and sum of eigenvalues below the bottom of the essential spectrum counting multiplicities of quantum waveguides in two dimensions. We consider both straight and curved waveguides of…