Electron Charge and Current Densities, the Geometrie Phase and Cellular Automata

1993 ◽  
Vol 48 (1-2) ◽  
pp. 134-136
Author(s):  
N. Sukumar ◽  
B. M. Deb ◽  
Harjinder Singh
Keyword(s):  
Current Density ◽  
Electron System ◽  
Time Dependent ◽  
Gauge Potential ◽  
Electronic Charge ◽  
Electronic Density ◽  
Electronic Current ◽  
Finite Set ◽  
The Many ◽  
Electronic Density Distribution

Some consequences of the quantum fluid dynamics formulation are discussed for excited states of atoms and molecules and for time-dependent processes. It is shown that the conservation of electronic current density j(r) allows us to manufacture a gauge potential for each excited state of an atom, molecule or atom in a molecule. This potential gives rise to a tube of magnetic flux carried around by the many-electron system. In time-dependent situations, the evolution of the electronic density distribution can be followed with simple, site-dependent cellular automaton (CA) rules. The CA consists of a lattice of sites, each with a finite set of possible values, here representing finite localized elements of electronic charge and current density (since the charge density rno longer suffices to fully characterize a time-dependent system, it needs to be supplemented with information about the current density j).Our numerical results are presented elsewhere and further developmentis in progress.

scholarly journals Adiabatic Electronic Motion in Forming Covalent Bond

2018 ◽  
Author(s):  
Michihiro Okuyama ◽  
Fumihiko Sakata
Keyword(s):  
Current Density ◽  
Covalent Bond ◽  
Displacement Current ◽  
Dynamical Process ◽  
Electronic Density ◽  
Electronic Current ◽  
Electronic Motion ◽  
Null Value ◽  
Current Densities ◽  
The One

<div>In studying a dynamical process of the chemical reaction, it is decisive to get appropriate information from an electronic current density. To this end, we divide one-body electronic density into a couple of densities, that is, an electronic sharing density and an electronic contraction density. Since the one-body electronic current density defi ned directly through the microscopic electronic wave function gives null value under the Born-Oppenheimer molecular dynamics, we propose to employ the Maxwell's displacement current density de fined by means of the one-body electronic density obtained under the same approximation. Applying the electronic sharing and the electronic contraction current densities to a hydrogen molecule, we show these densities give important physical quantities for analyzing a dynamical process of the covalent bond.</div>

Many-Electron Problem in Terms of the Density: From Thomas–Fermi to Modern Density-Functional Theory

2003 ◽  
Vol 02 (02) ◽  
pp. 301-322 ◽  
Author(s):  
Manoj K. Harbola ◽  
Arup Banerjee
Keyword(s):  
Density Functional Theory ◽  
Perturbation Theory ◽  
Electron Density ◽  
Current Density ◽  
Density Functional ◽  
Electron System ◽  
Time Dependent ◽  
Functional Theory ◽  
Thomas Fermi ◽  
Alkali Metal Clusters

In this paper we focus on the use of electron density and current-density as basic variables in describing a many-electron system. We start with a discussion of the seminal Thomas–Fermi theory and its extension by Bloch for time-dependent hamiltonians. We then present modern density-functional theory (for both time-independent and time-dependent hamiltonians) and approximations involved in implementing it. Also discussed is perturbation theory in terms of electron density and its use for calculating various response properties and related quantities. In particular, van der Waals coefficient C6 is calculated using density and current density in time-dependent perturbation theory. Throughout the paper, results for alkali-metal clusters are presented to demonstrate the strength of density-based theories.

scholarly journals Adiabatic Electronic Motion in Forming Covalent Bond

2018 ◽  
Author(s):  
Michihiro Okuyama ◽  
Fumihiko Sakata
Keyword(s):  
Current Density ◽  
Covalent Bond ◽  
Displacement Current ◽  
Dynamical Process ◽  
Electronic Density ◽  
Electronic Current ◽  
Electronic Motion ◽  
Null Value ◽  
Current Densities ◽  
The One

<div>In studying a dynamical process of the chemical reaction, it is decisive to get appropriate information from an electronic current density. To this end, we divide one-body electronic density into a couple of densities, that is, an electronic sharing density and an electronic contraction density. Since the one-body electronic current density defi ned directly through the microscopic electronic wave function gives null value under the Born-Oppenheimer molecular dynamics, we propose to employ the Maxwell's displacement current density de fined by means of the one-body electronic density obtained under the same approximation. Applying the electronic sharing and the electronic contraction current densities to a hydrogen molecule, we show these densities give important physical quantities for analyzing a dynamical process of the covalent bond.</div>

scholarly journals Application of time-dependent current-density-functional theory to nonlocal exchange-correlation effects in polymers

2003 ◽  
Vol 118 (3) ◽  
pp. 1044-1053 ◽  
Author(s):  
M. van Faassen ◽  
P. L. de Boeij ◽  
R. van Leeuwen ◽  
J. A. Berger ◽  
J. G. Snijders
Keyword(s):  
Density Functional Theory ◽  
Current Density ◽  
Density Functional ◽  
Time Dependent ◽  
Correlation Effects ◽  
Functional Theory ◽  
Exchange Correlation

Effect of High Electronic Current Density on the Motion ofAu195andSb125in Gold

1966 ◽  
Vol 145 (2) ◽  
pp. 507-518 ◽  
Author(s):  
H. Michael Gilder ◽  
David Lazarus
Keyword(s):  
Current Density ◽  
Electronic Current

scholarly journals THE DYNAMIC RESPONSE OF OFFSHORE STRUCTURES TO TIME-DEPENDENT FORCES

1964 ◽  
Vol 1 (9) ◽  
pp. 29
Author(s):  
William S. Gaither ◽  
David P. Billington
Keyword(s):  
Degrees Of Freedom ◽  
Wind Waves ◽  
Offshore Structures ◽  
Time Dependent ◽  
Wave Forces ◽  
Ocean Bottom ◽  
Single Wave ◽  
Single Degree Of Freedom ◽  
The Many ◽  
Floating Objects

This paper is addressed to the problem of structural behavior in an offshore environment, and the application of a more rigorous analysis for time-dependent forces than is currently used. Design of pile supported structures subjected to wave forces has, in the past, been treated in two parts; (1) a static analysis based on the loading of a single wave, and (2) a dynamic analysis which sought to determine the resonant frequency by assuming that the structure could be approximated as a single-degree-of-freedom system. (Ref. 4 and 6) The behavior of these structures would be better understood if the dynamic nature of the loading and the many degrees of freedom of the system were included. A structure which is built in the open ocean is subjected to periodic forces due to wind, waves, floating objects, and due occasionally to machinery mounted on the structure. To resist motion, the structure relies on the stiffness of the elements from which it is built and the restraints of the ocean bottom into which the supporting legs are driven.

scholarly journals Linear Increasing in Radial Electronic Density Distribution for K and L Shells throughout Some Be-Like Ions

2013 ◽  
Vol 10 (4) ◽  
pp. 1218-1222
Author(s):  
Baghdad Science Journal
Keyword(s):  
Density Distribution ◽  
Nuclear Data ◽  
Atomic Data ◽  
Arithmetic Sequence ◽  
Electronic Density ◽  
Hartree Fock ◽  
Linear Behavior ◽  
Data Tables ◽  
Electronic Density Distribution ◽  
Hf Wave

Maximum values of one particle radial electronic density distribution has been calculated by using Hartree-Fock (HF)wave function with data published by[A. Sarsa et al. Atomic Data and Nuclear Data Tables 88 (2004) 163–202] for K and L shells for some Be-like ions. The Results confirm that there is a linear behavior restricted the increasing of maximum points of one particle radial electronic density distribution for K and L shells throughout some Be-like ions. This linear behavior can be described by using the nth term formula of arithmetic sequence, that can be used to calculate the maximum radial electronic density distribution for any ion within Be like ions for Z

scholarly journals CORTICAL PHASE TRANSITIONS, NONEQUILIBRIUM THERMODYNAMICS AND THE TIME-DEPENDENT GINZBURG–LANDAU EQUATION

2012 ◽  
Vol 26 (06) ◽  
pp. 1250035 ◽  
Author(s):  
WALTER J. FREEMAN ◽  
ROBERTO LIVI ◽  
MASASHI OBINATA ◽  
GIUSEPPE VITIELLO
Keyword(s):  
Phase Transitions ◽  
Landau Equation ◽  
Power Laws ◽  
Time Dependent ◽  
Many Body ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Characteristic Space ◽  
The Many ◽  
The Brain

The formation of amplitude modulated and phase modulated assemblies of neurons is observed in the brain functional activity. The study of the formation of such structures requires that the analysis has to be organized in hierarchical levels, microscopic, mesoscopic, macroscopic, each with its characteristic space-time scales and the various forms of energy, electric, chemical, thermal produced and used by the brain. In this paper, we discuss the microscopic dynamics underlying the mesoscopic and the macroscopic levels and focus our attention on the thermodynamics of the nonequilibrium phase transitions. We obtain the time-dependent Ginzburg–Landau equation for the nonstationary regime and consider the formation of topologically nontrivial structures such as the vortex solution. The power laws observed in functional activities of the brain is also discussed and related to coherent states characterizing the many-body dissipative model of brain.

scholarly journals Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1342
Author(s):  
Ofir E. Alon
Keyword(s):  
Angular Momentum ◽  
Infinite Number ◽  
Mean Field ◽  
Solvable Model ◽  
Time Dependent ◽  
Angular Momentum Operator ◽  
Many Body ◽  
The Many ◽  
Bose Einstein ◽  
Number Of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.

scholarly journals Impact of the transverse direction on the many-body tunneling dynamics in a two-dimensional bosonic Josephson junction

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Anal Bhowmik ◽  
Sudip Kumar Haldar ◽  
Ofir E. Alon
Keyword(s):  
Josephson Junction ◽  
Quantum Dynamics ◽  
Transverse Direction ◽  
General Rule ◽  
Time Dependent ◽  
Two Dimensional ◽  
Many Body ◽  
Initial State ◽  
The Many ◽  
Tunneling Dynamics

AbstractTunneling in a many-body system appears as one of the novel implications of quantum physics, in which particles move in space under an otherwise classically-forbidden potential barrier. Here, we theoretically describe the quantum dynamics of the tunneling phenomenon of a few intricate bosonic clouds in a closed system of a two-dimensional symmetric double-well potential. We examine how the inclusion of the transverse direction, orthogonal to the junction of the double-well, can intervene in the tunneling dynamics of bosonic clouds. We use a well-known many-body numerical method, called the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method. MCTDHB allows one to obtain accurately the time-dependent many-particle wavefunction of the bosons which in principle entails all the information of interest about the system under investigation. We analyze the tunneling dynamics by preparing the initial state of the bosonic clouds in the left well of the double-well either as the ground, longitudinally or transversely excited, or a vortex state. We unravel the detailed mechanism of the tunneling process by analyzing the evolution in time of the survival probability, depletion and fragmentation, and the many-particle position, momentum, and angular-momentum expectation values and their variances. As a general rule, all objects lose coherence while tunneling through the barrier and the states which include transverse excitations do so faster. In particular for the later states, we show that even when the transverse direction is seemingly frozen, prominent many-body dynamics in a two-dimensional bosonic Josephson junction occurs. Implications are briefly discussed.

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