Related papers: Metrics for two electron random potential systems
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
Bound states around an impurity are investigated for a two dimensional electron system in a strong magnetic field. Long-range Coulomb potential and related potentials are considered. Schr\"odinger equation is solved numerically to obtain…
A function has been proposed to evaluate the electron density model constructed by inverse Fourier transform using the observed structure amplitudes and trial phase set. The strategy of this function is applying an imaginary electron…
There are limits of validity of classical constitutive laws such as Fourier and Navier-Stokes equations, phenomena beyond those limits have been experimentally found many decades ago. However, it is still not clear what theory would be…
We propose to verify relations between quantities which characterize scaling properties of high energy density fluctuations in terms of factorial moments and newly introduced associated frequency moments. Typical examples are presented in…
We study orthogonality relations for Fourier frequencies and complex exponentials in Hilbert spaces $L^2(\mu)$ with measures $\mu$ arising from iterated function systems (IFS). This includes equilibrium measures in complex dynamics.…
Density matrix embedding theory (DMET) describes finite fragments in the presence of a surrounding environment. In contrast to most embedding methods, DMET explicitly allows for quantum entanglement between both. In this chapter, we discuss…
We present a first-principles-based (second-principles) scheme that permits large-scale materials simulations including both atomic and electronic degrees of freedom on the same footing. The method is based on a predictive…
Relations between particle and wave properties for charge carriers in periodic potentials of crystalline metals and semiconductors are derived. The particle aspects of electrons and holes in periodic potentials are considered using…
Density functional theory (DFT) is an essential building block for modern theoretical physics, chemistry, and engineering, especially those concerning electronic properties. Through decades of development, various program packages for…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
We calculate the single-particle states of a two-dimensional electron gas (2DEG) in a perpendicular quantizing magnetic field, which is periodic in one direction of the electron layer. We discuss the modulation of the electron density in…
These are introductory lectures to some aspects of the physics of strongly correlated electron systems. I first explain the main reasons for strong correlations in several classes of materials. The basic principles of dynamical mean-field…
In the recent paper [17] the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem with a positive semidefinite operator as unknown. The…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Correlation-driven phenomena in molecular periodic systems are challenging to predict computationally not only because such systems are periodically infinite but also because they are typically strongly correlated. Here we generalize the…
Two electrons move in a quasi one--dimensional wire under the influence of a short--range interaction. We restrict Hilbert space to those states where the two electrons are close to each other. Using supersymmetry, we present a complete…
The Hohenberg-Kohn theorem of density functional theory (DFT) for the case of electrons interacting with an external magnetic field (that couples to spin only) is examined in more detail than previously. A unexpected generalization is…
We study the interaction between entropy and Wasserstein distance in free probability theory. In particular, we give lower bounds for several versions of free entropy dimension along Wasserstein geodesics, as well as study their topological…
Stochastic density functional theory is applied to analyze the conductivity of strong two species electrolytes at arbitrary field strengths. The corresponding stochastic equations for the density of the electrolyte species are solved by…