An analogy of the Fokker-Planck equation (FPE) with Schrödinger allows us to use quantum mechanics technique find analytical solution FPE in a number cases.However, previous studies have been limited potential discrete eigenvalue spectrum.Here, we will show how this approach can be also applied mixed spectrum bounded and free states.We solve boundaries located at x = ±L/2 take limit L → ∞, considering examples constant Pöschl-Teller potential.An oversimplified was proposed earlier by M.T....

Favorably scaling numerical time-dependent many-electron techniques such as density functional theory (TDDFT) with adiabatic exchange-correlation potentials typically fail in capturing highly correlated electron dynamics. We propose a method based on natural orbitals, i.e., the eigenfunctions of one-body reduced matrix, that is almost inexpensive numerically TDDFT, but which capable describing phenomena doubly excited states, autoionization, Fano profiles photoelectron spectra, and...

Natural orbital theory is a computationally useful approach to the few- and many-body quantum problems. While natural orbitals have been known applied for many years in electronic structure applications, their potential time-dependent problems started being investigated only recently. Correlated two-particle systems are of particular importance because two-body reduced density matrix expanded exactly this case. However, case carry phases that allow certain gauge transformations first kind....

Recently introduced time-dependent renormalized-natural-orbital theory (TDRNOT) is tested on nonsequential double ionization (NSDI) of a numerically exactly solvable one-dimensional model He atom subject to few-cycle, 800-nm laser pulses. NSDI atoms in strong fields prime example nonperturbative, highly correlated electron dynamics. As such, an important ``worst-case'' benchmark for any few and many-body technique beyond linear response. It found that TDRNOT reproduces the celebrated...

An airplane-boarding model, introduced earlier by Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)], is studied with the aim of determining precisely its asymptotic power-law scaling behavior for a large number passengers $N$. Based on Monte Carlo simulation data very system sizes up to $N={2}^{16}=65\phantom{\rule{0.16em}{0ex}}536$, we have analyzed numerically mean boarding time $\ensuremath{\langle}{t}_{b}\ensuremath{\rangle}$ other related quantities. In analogy critical phenomena, used...

Recently introduced time-dependent renormalized-natural-orbital theory (TDRNOT) is based on the equations of motion for so-called natural orbitals, i.e., eigenfunctions one-body reduced density matrix. Exact TDRNOT can be formulated any two-electron system in either spin configuration. In this paper, method tested against high-order harmonic generation (HHG) and Fano profiles absorption spectra with help a numerically exactly solvable one-dimensional model He atom, starting from spin-singlet...

Hematite at room temperature is a weak ferromagnetic material. Its permanent magnetization three orders smaller than for magnetite. Thus, hematite colloids allow us to explore different physical range of particle interaction parameters compared ordinary colloids. In this paper we investigate colloid consisting particles with cubic shape. We search energetically favorable structures in an external magnetic field analytical and numerical methods molecular dynamics simulations analyze whether...

Recently introduced time-dependent renormalized-natural-orbital theory (TDRNOT) is extended towards a multicomponent approach in order to describe ${{\mathrm{H}}_{2}}^{+}$ beyond the Born-Oppenheimer approximation. Two kinds of natural orbitals, describing electronic and nuclear degrees freedom are introduced, exact equations motion for them derived. The benchmarked by comparing numerically results Schr\"odinger equation an model system with corresponding TDRNOT predictions. Ground-state...

Recently a two-dimensional chiral fluid was experimentally demonstrated. It obtained from cubic-shaped hematite colloidal particles placed in rotating magnetic field. Here we look at building blocks of that fluid, by analyzing short chain behavior We find equilibrium structures chains static fields and observe dynamics fields. verify there are three planar motion regimes one where the cube goes out plane In this regime interesting -- rotates slower than order to catch up with field, it rolls...

Vortex patterns in ensembles of magnetic particles driven by a rotating field are studied. The driving arises due to the lubrication forces between acting direction perpendicular radius vector particles. Since cannot be equilibrated radial dipolar attraction and steric repulsion, ensemble is nonequilibrium state. Different regimes found for dynamics ensembles---solid-body rotation at low frequency stick-slip motion external layers aggregate with respect internal structure as increased....

The $N$-particle wavefunction has too many dimensions for a direct time propagation of many-body system according to the time-dependent Schrödinger equation (TDSE). On other hand, density functional theory (TDDFT) tells us that single-particle is, in principle, sufficient. However, practicable motion (EOM) accurate evolution is unknown. It thus an obvious idea propagate quantity which not as reduced but less dimensional than $N$-body wavefunction. Recently, we have introduced...

Recently a two-dimensional chiral fluid was experimentally demonstrated. It obtained from cubic-shaped hematite colloidal particles placed in rotating magnetic field. Here we look at building blocks of that fluid, by analyzing short chain behavior We find equilibrium structures chains static fields and observe dynamics fields. verify there are three planar motion regimes one where the cube goes out plane In this regime interesting -- rotates slower than order to catch up with field, it rolls...

Abstract Power-law distributions and other skew distributions, observed in various models real systems, are considered. A model, describing evolving systems with increasing number of elements, is considered to study the distribution over element sizes. Stationary power-law found. Certain non-stationary obtained analyzed, based on exact solutions numerical simulations.

In this work we show that macroscopic experiments can be used to investigate microscopic systems. Such enable testing the assumptions and results obtained by theoretical considerations or simulations not under microscope (e.g., orientation of a spherical particle). To emulate dynamics single hematite cube immersed in water subjected rotating magnetic field, cubic magnet is firmly positioned 3D printed superball shell. The dimensionless parameters systems equalized using glycerol-water...