Related papers: A comprehensive study of the velocity, momentum an…
The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed.…
In this paper we propose and analyse a new formulation and pointwise divergence-free mixed finite element methods for the numerical approximation of Darcy--Brinkman equations in vorticity--velocity--pressure form, coupled with a transport…
The properties of the Volume operator in Loop Quantum Gravity, as constructed by Ashtekar and Lewandowski, are analyzed for the first time at generic vertices of valence greater than four. The present analysis benefits from the general…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
The geometric structure of an energy band in a solid is fundamental for a wide range of many-body phenomena in condensed matter and is uniquely characterized by the distribution of Berry curvature over the Brillouin zone. In analogy to an…
We examine the Bloch-Peierls-Berry dynamics under a classical nonequilibrium dynamical formulation. In this formulation all coordinates in phase space formed by the position and crystal momentum space are treated on equal footing.…
We calculate the force and impulse operators for a charged particle in the field of an Aharonov-Bohm flux line. The force operator is formally the Lorentz force, with the magnetic field operator modified to include quantum corrections due…
The Berry connection is a gauge-dependent quantity frequently used to describe the optical response of solids. Its evaluation requires a k-derivative with respect to the cell periodic-part of the Bloch-functions and is commonly calculated…
Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schr\"odinger equation with an…
This work explores simple relations that follow from the momentum-integral equation absent a pressure gradient. The resulting expressions enable us to relate the boundary-layer characteristics of a velocity profile, $u(y)$, to an assumed…
Starting with the quantum Liouville equation, we write the density operator as the product of elements respectively in the left and right ideals of an operator algebra and find that the Schrodinger picture may be expressed through two…
Quantum geometry is a key quantity that distinguishes electrons in a crystal from those in the vacuum. Its study continues to provide insights into quantum materials, uncovering new design principles for their discovery. However, unlike the…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…
We present high-precision ab initio calculations of the static and dynamic polarizability of the barium monohydroxide ($^{138}$BaOH) molecule, using relativistic coupled-cluster theory. By thoroughly investigating the dependence of the…
We derive the semiclassical Bloch dynamics with the second-order Berry phase correction in the presence of the slow-varying scalar potential as perturbation. Our mathematical derivation is based on a two-scale WKB asymptotic analysis. For a…
We present a compact and general derivation of the generalized Bloch-Wangsness-Redfield kinetic equations for systems with the static spin Hamiltonian utilizing the concept of the Liouville space. We show that the assumptions of short…
The Berry curvature is a geometrical property of an energy band which can act as a momentum space magnetic field in the effective Hamiltonian of a wide range of systems. We apply the effective Hamiltonian to a spin-1/2 particle in two…
We present a model-independent framework to determine finite-volume corrections of matrix elements of spatially-separated current-current operators. We define these matrix elements in terms of Compton-like amplitudes, i.e. amplitudes…
The finite entropy of black holes suggests that local regions of spacetime are described by finite-dimensional factors of Hilbert space, in contrast with the infinite-dimensional Hilbert spaces of quantum field theory. With this in mind, we…
We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We…