Related papers: Twisting versus bending in quantum waveguides
We describe the effects of geometric torsion on the coherent motion of electrons along a thin twisted quantum ring. The geometric torsion inherent in the quantum ring triggers a quantum phase shift in the electrons' eigenstates, thereby…
We investigate the optical and quantum mechanical properties of a charged spinless particle confined in a two-dimensional quantum ring under the simultaneous influence of a spiral dislocation and an external magnetic field. The dislocation…
The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful in various fields of applied mathematics. To be more…
Atomic gases confined in curved geometries are characterized by distinctive features that are absent in their flat counterparts, such as periodic boundaries, local curvature, and nontrivial topologies. The recent experiments with…
We investigate the spectrum of the Dirichlet Laplacian in a unbounded strip subject to a new deformation of "shearing": the strip is built by translating a segment oriented in a constant direction along an unbounded curve in the plane. We…
We consider a time-harmonic wave problem, appearing for example in water-waves and in acoustics, in a setting such that the analysis reduces to the study of a 2D waveguide problem with a Neumann boundary condition. The geometry is symmetric…
We study measure perturbations of the Laplacian in $L^2(\R^2)$ supported by an infinite curve $\Gamma$ in the plane which is asymptotically straight in a suitable sense. We show that if $\Gamma$ is not a straight line, such a ``leaky…
We present an analysis of wave propagation and reflection in an acoustic waveguide with random sound soft boundary and a turning point. The waveguide has slowly bending axis and variable cross section. The variation consists of a slow and…
The momentum space of topological insulators and topological superconductors is equipped with a quantum metric defined from the overlap of neighboring valence band states or quasihole states. We investigate the quantum geometrical…
In this note we present preliminary study on the relation between the quantum entanglement of boundary states and the quantum geometry in the bulk in the framework of spin networks. We conjecture that the emergence of space with non-zero…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
This paper presents an analytical study of the coexistence of different transport regimes in quasi-one-dimensional surface-disordered waveguides (or electron conductors). To elucidate main features of surface scattering, the case of two…
Topological properties of the spectrum of shallow-water waves on a rotating spherical body are established. Particular attention is paid to its spectral flow, i.e. the modes whose frequencies transit between the Rossby and inertia-gravity…
In this scientific preface to the first issue of International Journal of Geometric Methods in Modern Physics, we briefly survey some peculiarities of geometric techniques in quantum models.
We investigate the dynamic transition of quantum turbulence (QT) in a confined potential field as the system evolves from purely two-dimensional (2D) to quasi-two-dimensional, and ultimately to three-dimensional (3D), by fixing the lateral…
Motivated by the example of a curved waveguide embedded in a photonic crystal, we examine the effects of geometry in a ``quantum channel'' of parabolic form. We study the linear case and derive exact as well as approximate expressions for…
The evolution of the quantum wave packet describing an atom trapped in the surface-tip junction of the scanning tunneling microscope is investigated by using the time-dependent Schroedinger equation, and by a quasi-classical Hamiltonian…
Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the…
A method is proposed for studying wave and particle transport in disordered waveguide systems of dimension higher than unity by means of exact one-dimensionalization of the dynamic equations in the mode representation. As a particular case,…
The importance of the quantum metric in flat-band systems has been noticed recently in many contexts such as the superfluid stiffness, the dc electrical conductivity, and ideal Chern insulators. Both the quantum metric of degenerate and…