Related papers: Capacitance matrix revisited
The quantum density matrix generalises the classical concept of probability distribution to quantum theory. It gives the complete description of a quantum state as well as the observable quantities that can be extracted from it. Its…
We start from microscopic approach to many body physics and show the analytical steps and approximations required to arrive at the concept of quantum capacitance. These approximations are valid only in the semi-classical limit and the…
We propose a quantum Hamiltonian for a transmission line with charge discreteness. The periodic line is composed of an inductance and a capacitance per cell. In every cell the charge operator satisfies a nonlinear equation of motion because…
Leveraging topological properties in the response of electromagnetic systems can greatly enhance their potential. Although the investigation of singularity-based electromagnetics and non-Hermitian electronics has considerably increased in…
The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…
This paper gives a method that maps the static magnetic field due to a system of parallel current-carrying wires to a complex function. Using this function simplifies the calculation of the magnetic field energy density and inductance per…
This study clarifies the proper criteria to assess the modeling capacity of a general tensor model. The work analyze the problem based on the study of tensor ranks, which is not a well-defined quantity for higher order tensors. To process,…
Application of the generalized continuity equation reveals that the drift current in conductors is equivalent to a negative diffusion current. A phenomenological model of conductivity is developed using the generalized continuity equations.…
Matrix elements of potential energy are examined in detail. We consider a model problem - a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and…
We consider graphs made of one-dimensional wires connected at vertices, and on which may live a scalar potential. We are interested in a scattering situation where such a network is connected to infinite leads. We study the correlations of…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
The charge of an ideal parallel capacitor leads to the resolution of the wave equation for the electric field with prescribed initial conditions and boundary constraints. Independently of the capacitor's shape and the applied voltage, none…
Interatomic potentials approximate the potential energy of atoms as a function of their coordinates. Their main application is the effective simulation of many-atom systems. Here, we review empirical interatomic potentials designed to…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
We give a new quantum circuit approximation of quantum multiplexors based on the idea of complexity theory oracles. As an added bonus, our multiplexor approximation immediately gives a quantum circuit approximation of diagonal unitary…
We consider the power of Boolean circuits with MOD$_{6}$ gates. First, we introduce a few basic notions of computational complexity, and describe the standard models with which we study the complexity of problems. We then define the model…
This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in…
An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…
Systems of neutral interacting mesons are investigated, concerning in particular the validity of their description by an effective hamiltonian. First, I study its connection to quantum field theory and show that the spectrum of such systems…
Molecular dynamics simulations at a constant electric potential are an essential tool to study electrochemical processes, providing microscopic information on the structural, thermodynamic, and dynamical properties. Despite the numerous…