Related papers: Metrics for two electron random potential systems
External potentials play a crucial role in modelling quantum systems, since, for a given inter- particle interaction, they define the system Hamiltonian. We use the metric space approach to quantum mechanics to derive, from the energy…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
Density functional theory is discussed in the context of one-particle systems. We show that the ground state density $\rho_0(x)$ and energy $E_0$ are simply related to a family of external potential energy functions with ground state wave…
This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…
In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent…
We introduce a rigorous, physically appealing, and practical way to measure distances between exchange-only correlations of interacting many-electron systems, which works regardless of their size and inhomogeneity. We show that this…
We prove that the electron density function of a real physical system can be uniquely determined by its values on any finite subsystem. This establishes the existence of a rigorous density-functional theory for any open electronic system.…
Using a TE/TM decomposition for an angular plane-wave spectrum of free random electromagnetic waves and matched boundary conditions, we derive the probability density function for the energy density of the vector electric field in the…
Accurate treatment of the electronic correlation in inhomogeneous electronic systems, combined with the ability to capture the correlation energy of the homogeneous electron gas, allows to reach high predictive power in the application of…
A numerical-analytical simulation of scattering by a three-barrier heterostructure of an electronic Gaussian wave packet, the spectral width of which is on the order of the distance between the levels of the doublet of quasi-stationary…
Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. The correction to the conductivity due to inelastic scatterings by oscillating potentials is shown to be a universal…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
We present a metric-space approach to quantify the performance of density-functional approximations for interacting many-body systems and to explore the validity of the Hohenberg-Kohn-type theorem on fermionic lattices. This theorem…
We study the properties of a family of distances between functions of a single variable. These distances are examples of integral probability metrics, and have been used previously for comparing probability measures on the line; special…
Understanding the behavior of quantum systems subject to magnetic fields is of fundamental importance and underpins quantum technologies. However, modeling these systems is a complex task, because of many-body interactions and because…
We develop a new density functional theory (DFT) and formalism for correlated electron systems by taking as reference an interacting electron system that has a ground state wavefunction which obeys exactly the Gutzwiller approximation for…
We extend density matrix embedding theory to periodic systems, resulting in an electronic band structure method for solid-state materials. The electron correlation can be captured by means of a local impurity model using various choices of…
We propose the idea that in Bohmian mechanics the wavefunction is related to a density of states and explore some of its consequences. Specifically, it allows a maximum-entropy interpretation of quantum probabilities, which creates a…
A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…