Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Zeitschrift für Naturforschung A

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

N. Sukumar, Bimalendu Deb, Harjinder Singh

Published Feb 1, 1993• 0 citations
Publisher

Abstract

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 r no 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 development is in progress.

DOI
10.1515/zna-1993-1-230

Related papers

Phase associated with the single‐particle density of many‐electron systems

N. Sukumar, Bimalendu Deb

Abstract In excited states of atoms and molecules, as well as in time‐dependent situations, the one‐electron density no longer suffices to completely characterize the electronic state; in addition, one now requires information about the electronic phase or the current density. We show that, for a stationary electronic state, the continuity equation of quantum fluid dynamics represents a differential equation for the electronic phase, which must be solved subject to certain periodicity conditions. These periodicity conditions arise from the nodal topology of the wave function and give rise to quantized vortices of current. The consequences of writing an electronic “wave function” for a many‐electron system directly in terms of the single‐particle density and phase have been investigated. We have shown that such a procedure leads to the appearance of an “internal magnetic vector potential.” We also establish the connection between the electronic phase and the geometrical (“Berry”) phase accompanying the adiabatic transport of a quantal system around a closed loop in parameter space. This leads to a generalization of the current density concept and allows us to discuss the geometrical phase in terms of the circulation of this current in parameter space.

International Journal of Quantum Chemistry•Oct 1, 1991•6 citations

Cellular automata for quantum systems

Morton D. Kostin

Cellular automata for modelling quantum systems are presented. The mass at each site is updated according to rules that depend on the masses of neighbouring sites. An essential feature of these local rules is that mass and probability are conserved. In the limit of small spatial and time steps it is shown that the equation defining one class of automata reduces to the Schrodinger equation and the equation defining another class of automata reduces to the Dirac equation. Advantages of these methods are discussed.

Journal of Physics A Mathematical and General•Mar 7, 1993•9 citations

Current density partitioning in time-dependent current density functional theory

Martín A. Mosquera, Adam Wasserman

We adapt time-dependent current density functional theory to allow for a fragment-based solution of the many-electron problem of molecules in the presence of time-dependent electric and magnetic fields. Regarding a molecule as a set of non-interacting subsystems that individually evolve under the influence of an auxiliary external electromagnetic vector-scalar potential pair, the partition 4-potential, we show that there are one-to-one mappings between this auxiliary potential, a sharply-defined set of fragment current densities, and the total current density of the system. The partition electromagnetic (EM) 4-potential is expressed in terms of the real EM 4-potential of the system and a gluing EM 4-potential that accounts for exchange-correlation effects and mutual interaction forces between fragments that are required to yield the correct electron dynamics. We prove the zero-force theorem for the fragmented system, establish a variational formulation in terms of action functionals, and provide a simple illustration for a charged particle in a ring.

The Journal of Chemical Physics•Mar 19, 2014•6 citations

Many-body approach to time-dependent quantum transport

Anna-Maija Uimonen

In this thesis the electron transport through interacting quantum wires is studied.The time-dependent properties of the system are investigated by using the non-equilibrium Green function technique.This technique provides a way to include ultra-fast timedependent processes, arbitrary strong external fields and also brings forward an effective treatment of electron-electron and electron-phonon interactions.The electronelectron interactions are included via various self-energy approximations at Hartree-Fock, second-order Born and GW levels.These approximations are called conserving since they fulfill the physical conservation laws like the charge conservation law.The interacting central system is coupled to one-dimensional tight-binding leads, which are considered effectively as noninteracting.The system is perturbed by a bias voltage after which the time-evolution of the system is followed by Kadanoff-Baym equations.The non-equilibrium steady-state value of the current depends on the used self-energy approximation, which indicates the importance of the history-dependence in the calculation of current.This is an important observation in the aspect of time-dependent density functional theory, since it is one indication for the need of functionals with memory.The steady-state current is independent of the initial state, which is in accordance with the memory-loss theorem.The transient current shows small oscillations, which are consequence of the density oscillations especially in the first and last site.The density oscillations in the sites are effect of the electron transition from the lead to the central system and vice versa.

•Jan 1, 2009•0 citations

Ultracold Lattice Gas Automata for Single Trapped Ion Interacting with a Laser Field

Giovanni Costantini, Zakarya Zarezadeh

Abstract In the same context of lattice gauge theory, a notion of cellular automaton (CA) is considered as a description of the underlying dynamics of fields evaluated on a discrete lattice. The explorative approach of this work is initiated by taking the automata evolution as an elementary description of fields dynamics on one side and pivotal role of locality on other side to connect the notion of states and transformations to density operators in quantum electrodynamics. In order to parameterize the definition of proposed model in the context of lattice field theory the nonlinear interaction is introduced with neighboring cells. In this paper, analytical and explicit expression of atomic density matrix for single trapped ion interacting with laser field based on cellular automata dynamics are discussed. The definition is further explored by introducing some probabilistic theories as the theoretical framework then it is concluded that the graph of cellular automata in continuum time limit of the CA dynamics leads to Maxwell–Bloch equation.

Annalen der Physik•Jun 4, 2020•2 citations

Schrödinger fluid dynamics of many-electron systems in a time-dependent density-functional framework

Bimalendu Deb, Swapan Kumar Ghosh

For an N-electron system, a connection is explored between density-functional theory and quantum fluid dynamics, through a dynamical extension of the former. First, we prove the Hohenberg–Kohn theorem for a time-dependent harmonic perturbation under conditions which guarantee the existence of the corresponding steady (or quasiperiodic) states of the system. The corresponding one-particle time-dependent Schrödinger equation is then variationally derived starting from a fluid-dynamical Lagrangian density. The subsequent fluid-dynamical interpretation preserves the ’’particle’’ description of the system in the sense that the N-electron fluid has N components each of which is an independent-particle Schrödinger fluid characterized by a density function ρj and an irrotational velocity field uj, j = 1,⋅⋅⋅,N. However, the mean velocity u of the fluid is not irrotational, in general. The force densities and the stress tensor occurring in the Navier–Stokes equation are physically interpreted. The present work is another step towards the interpretation of physicochemical phenomena in three-dimensional space.

The Journal of Chemical Physics•Jul 1, 1982•159 citations
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 r no 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 development is in progress.
Abstract In excited states of atoms and molecules, as well as in time‐dependent situations, the one‐electron density no longer suffices to completely characterize the electronic state; in addition, one now requires information about the electronic phase or the current density. We show that, for a stationary electronic state, the continuity equation of quantum fluid dynamics represents a differential equation for the electronic phase, which must be solved subject to certain periodicity conditions. These periodicity conditions arise from the nodal topology of the wave function and give rise to quantized vortices of current. The consequences of writing an electronic “wave function” for a many‐electron system directly in terms of the single‐particle density and phase have been investigated. We have shown that such a procedure leads to the appearance of an “internal magnetic vector potential.” We also establish the connection between the electronic phase and the geometrical (“Berry”) phase accompanying the adiabatic transport of a quantal system around a closed loop in parameter space. This leads to a generalization of the current density concept and allows us to discuss the geometrical phase in terms of the circulation of this current in parameter space.
Cellular automata for modelling quantum systems are presented. The mass at each site is updated according to rules that depend on the masses of neighbouring sites. An essential feature of these local rules is that mass and probability are conserved. In the limit of small spatial and time steps it is shown that the equation defining one class of automata reduces to the Schrodinger equation and the equation defining another class of automata reduces to the Dirac equation. Advantages of these methods are discussed.
We adapt time-dependent current density functional theory to allow for a fragment-based solution of the many-electron problem of molecules in the presence of time-dependent electric and magnetic fields. Regarding a molecule as a set of non-interacting subsystems that individually evolve under the influence of an auxiliary external electromagnetic vector-scalar potential pair, the partition 4-potential, we show that there are one-to-one mappings between this auxiliary potential, a sharply-defined set of fragment current densities, and the total current density of the system. The partition electromagnetic (EM) 4-potential is expressed in terms of the real EM 4-potential of the system and a gluing EM 4-potential that accounts for exchange-correlation effects and mutual interaction forces between fragments that are required to yield the correct electron dynamics. We prove the zero-force theorem for the fragmented system, establish a variational formulation in terms of action functionals, and provide a simple illustration for a charged particle in a ring.
In this thesis the electron transport through interacting quantum wires is studied.The time-dependent properties of the system are investigated by using the non-equilibrium Green function technique.This technique provides a way to include ultra-fast timedependent processes, arbitrary strong external fields and also brings forward an effective treatment of electron-electron and electron-phonon interactions.The electronelectron interactions are included via various self-energy approximations at Hartree-Fock, second-order Born and GW levels.These approximations are called conserving since they fulfill the physical conservation laws like the charge conservation law.The interacting central system is coupled to one-dimensional tight-binding leads, which are considered effectively as noninteracting.The system is perturbed by a bias voltage after which the time-evolution of the system is followed by Kadanoff-Baym equations.The non-equilibrium steady-state value of the current depends on the used self-energy approximation, which indicates the importance of the history-dependence in the calculation of current.This is an important observation in the aspect of time-dependent density functional theory, since it is one indication for the need of functionals with memory.The steady-state current is independent of the initial state, which is in accordance with the memory-loss theorem.The transient current shows small oscillations, which are consequence of the density oscillations especially in the first and last site.The density oscillations in the sites are effect of the electron transition from the lead to the central system and vice versa.
Abstract In the same context of lattice gauge theory, a notion of cellular automaton (CA) is considered as a description of the underlying dynamics of fields evaluated on a discrete lattice. The explorative approach of this work is initiated by taking the automata evolution as an elementary description of fields dynamics on one side and pivotal role of locality on other side to connect the notion of states and transformations to density operators in quantum electrodynamics. In order to parameterize the definition of proposed model in the context of lattice field theory the nonlinear interaction is introduced with neighboring cells. In this paper, analytical and explicit expression of atomic density matrix for single trapped ion interacting with laser field based on cellular automata dynamics are discussed. The definition is further explored by introducing some probabilistic theories as the theoretical framework then it is concluded that the graph of cellular automata in continuum time limit of the CA dynamics leads to Maxwell–Bloch equation.
For an N-electron system, a connection is explored between density-functional theory and quantum fluid dynamics, through a dynamical extension of the former. First, we prove the Hohenberg–Kohn theorem for a time-dependent harmonic perturbation under conditions which guarantee the existence of the corresponding steady (or quasiperiodic) states of the system. The corresponding one-particle time-dependent Schrödinger equation is then variationally derived starting from a fluid-dynamical Lagrangian density. The subsequent fluid-dynamical interpretation preserves the ’’particle’’ description of the system in the sense that the N-electron fluid has N components each of which is an independent-particle Schrödinger fluid characterized by a density function ρj and an irrotational velocity field uj, j = 1,⋅⋅⋅,N. However, the mean velocity u of the fluid is not irrotational, in general. The force densities and the stress tensor occurring in the Navier–Stokes equation are physically interpreted. The present work is another step towards the interpretation of physicochemical phenomena in three-dimensional space.