Related papers: Biot-Savart law in quantum matter
We consider Bloch electrons in the presence of the uniform electromagnetic field in two- and three-dimensions. It is renowned that the quantized Hall effect occurs in such systems. We suppose a weak and homogeneous electric field…
Bloch equations give a quantum description of the coupling between an atom and a driving electric force. In this article, we address the asymptotics of these equations for high frequency electric fields, in a weakly coupled regime. We prove…
It has long been known that quantum particles moving in a periodic lattice and subject to a constant force field undergo an oscillatory motion that is referred to as Bloch Oscillations (BOs). However, it is also known that, under quite…
We study the degeneracy of the ground-state energy $E$ of the two-component Bose-Hubbard model and of the perturbative correction $E_1$. We show that the degeneracy properties of $E$ and $E_1$ are closely related to the connectivity…
We consider dynamics of a charged particle in a finite along the $x$ direction square lattice in the presence of normal to the lattice plane magnetic field and in-plane electric field aligned with the $y$ axis. For vanishing magnetic field…
We consider the kinematics of bi-partite quantum states as determined by observable quantities, in particular the Bloch vectors of the subsystems. In examining the simplest case of a pair of two-level systems, there is a remarkable…
One common approach to computing the magnetic field produced by a filamentary current-carrying coil is to approximate the coil as a series of straight segments. The Biot-Savart field from each straight segment is known analytically.…
Knots have a twisted history in quantum physics. They were abandoned as failed models of atoms. Only much later was the connection between knot invariants and Wilson loops in topological quantum field theory discovered. Here we show that…
Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic…
Thermoelectric transport coefficients up to linear order in the applied magnetic field are microscopically studied using Kubo-Luttinger linear response theory and thermal Green's functions. We derive exact formulas for the thermoelectric…
We employ the density functional Kohn-Sham method in the local spin-density approximation to study the electronic structure and magnetism of quasi one-dimensional periodic arrays of few-electron quantum dots. At small values of the lattice…
We present a systematic derivation of the Biot-Savart equation from the Nonlinear Schr\"odinger equation, in the limit when the curvature radius of vortex lines and the inter-vortex distance are much greater than the vortex healing length,…
Synthetic gauge fields have provided physicists with a unique tool to explore a wide range of fundamentally important phenomena. However, most experiments have been focusing on synthetic vector gauge fields. The very rich physics brought by…
We reveal how the vector field links are untied under the influence of anti-parity-time-symmetric couplings in a dissipative sublattice-symmetric topological photonic crystal lattice. The topology of the quasi-one-dimensional two-band…
Topologically ordered states are quantum states of matter with topological ground state degeneracy and quasi-particles carrying fractional quantum numbers and fractional statistics. The topological spin $\theta_a=2\pi h_a$ is an important…
The dynamics of vortex ring pairs in the homogeneous nonlinear Schr\"odinger equation is studied. The generation of numerically-exact solutions of traveling vortex rings is described and their translational velocity compared to revised…
We present an analytical strategy to solve the electric field generated by a planar region $\mathcal{A}$ enclosed by a contour $c$ which is kept with a fixed but non-uniform electric potential. The approach can be used in certain situations…
We investigate the Bloch bands and develop a linear response theory for nonlinear systems, where the interplay between topological parameters and nonlinearity leads to new band structures. The nonlinear system under consideration is…
The connection between symmetries and conservation laws is a cornerstone of physics. It underlies Bloch's theorem which explains wave phenomena in all linear periodic systems. Here we demonstrate that, in a nonlinear grating with memory,…
The object of the present work is to study the quantum Hall effect through its symmetries and topological aspects. We consider the model of an electron moving in a two-dimensional lattice in the presence of applied in-plain electric field…