scholarly journals The Non-Relativistic Many-Body Quantum-Mechanical Hamiltonian with Diamagnetic Current-Current Interaction

2021 ◽  
Author(s):  
Ladislaus Alexander Bányai
Keyword(s):  
Solid State ◽  
Analogous Result ◽  
Charged Particles ◽  
Coulomb Gauge ◽  
Quantum Mechanical ◽  
Photon Propagator ◽  
Coulomb Interactions ◽  
Many Body ◽  
Transverse Current ◽  
Current Interaction

AbstractWe extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting from the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

scholarly journals The Nonrelativistic Quantum-Mechanical Hamiltonian with Diamagnetic Current-Current Interaction

2021 ◽  
Author(s):  
Ladislaus Alexander Bányai
Keyword(s):  
Solid State ◽  
Analogous Result ◽  
Charged Particles ◽  
Coulomb Gauge ◽  
Quantum Mechanical ◽  
Photon Propagator ◽  
Coulomb Interactions ◽  
Nonrelativistic Quantum ◽  
Transverse Current ◽  
Current Interaction

We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting form the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

scholarly journals Quantum Mechanics and Electromagnetism. Non-Relativistic Theory.

2020 ◽  
Author(s):  
Ladislaus Alexander Banyai ◽  
Mircea Bundaru
Keyword(s):  
Quantum Mechanics ◽  
Charged Particles ◽  
Electromagnetic Theory ◽  
Coulomb Interactions ◽  
Many Body ◽  
Many Body Theory ◽  
Magnetic Forces ◽  
The Many ◽  
Body Theory ◽  
The Magnetic Field

We describe here the coherent formulation of electromagnetism in the nonrelativistic quantummechanical many-body theory. We use the mathematical frame of the field theory and its quantization in the spirit of the QED. This is necessary because of the manifold of misinterpretations emerging from the hystorical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions inspired from the classical electromagnetic theory of point-like charges. However, this later is known to be inconsistent due to the self-interaction. This way could not be continued further to include properly the magnetic forces between the charged particles and lead to a lot of confusion about the interpretation of the magnetic field in the Hamiltonian, as well as about the gauge invariance. We emphasize the importance of the distinction between the applied (external fields) and the field in the matter. All these problems are length properly solved within the non-relativistic QED, nevertheless the confusion dominates in all the problems related to the magnetic properties of the solid state.

Transport through several four-quantum-dot topological structures

2021 ◽  
pp. 2150393
Author(s):  
Qingshuang Zhi ◽  
Kongfa Chen ◽  
Zelong He
Keyword(s):  
Quantum Dot ◽  
Coupling Strength ◽  
Bound States ◽  
Resonance Peak ◽  
Coulomb Interactions ◽  
Many Body ◽  
Body Effect ◽  
Topological Structures ◽  
Resonance Band ◽  
Interdot Coupling

In this paper, several four-quantum-dot topological structures are designed. The influence of the interdot coupling strength and intradot Coulomb interactions on the conductance is discussed. The location of the anti-resonance band can be manipulated by tuning the interdot coupling strength, which suggests a physical scheme of an effective quantum switch. The Fano anti-resonance peak may evolve into a resonance peak. For the particular value of the interdot coupling strength, two Fano anti-resonances collapse and bound states in the continuum are formed. Moreover, many-body effect makes the number of anti-resonance bands increase. This study provides a theoretical basis for the design of quantum computing devices.

Many-Body Effects in Combined Quantum Mechanical/Molecular Mechanical Simulations of the Hydrated Manganous Ion

2002 ◽  
Vol 106 (41) ◽  
pp. 9529-9532 ◽  
Author(s):  
Hannes H. Loeffler ◽  
Jorge Iglesias Yagüe ◽  
Bernd M. Rode
Keyword(s):  
Quantum Mechanical ◽  
Many Body ◽  
Many Body Effects

Covariant form for the collision integral

2007 ◽  
Vol 73 (4) ◽  
pp. 599-611 ◽  
Author(s):  
D. B. MELROSE
Keyword(s):  
Quantum Electrodynamics ◽  
Relativistic Effects ◽  
Collision Integral ◽  
Covariant Theory ◽  
Debye Screening ◽  
Coulomb Interactions ◽  
Small Momentum Transfer ◽  
Moller Scattering ◽  
Transverse Current ◽  
Charge Interaction

AbstractThe collision integral that describes the evolution of a distribution of particles in a plasma due to Coulomb interactions between themselves or with other particles is generalized to include relativistic effects and the current–current interaction (in addition to the charge–charge interaction). This is achieved through a covariant version of a conventional derivation based on correlation functions for fluctuations in the plasma. The covariant theory is used to distinguish between longitudinal (charge–charge) and transverse (current–current) interactions. For highly relativistic particles, the current–current contribution is half the charge–charge contribution when Debye screening is unimportant, and is unaffected by Debye screening. It is shown that the classical theory is reproduced by a quantum electrodynamics calculation for electron–electron (Møller) scattering in the limit of small momentum transfer.

scholarly journals Dynamic simulations of many-body electrostatic self-assembly

2018 ◽  
Vol 376 (2115) ◽  
pp. 20170143 ◽  
Author(s):  
Eric B. Lindgren ◽  
Benjamin Stamm ◽  
Yvon Maday ◽  
Elena Besley ◽  
A. J. Stace
Keyword(s):  
Self Assembly ◽  
Experimental Studies ◽  
Charged Particles ◽  
Theoretical Chemistry ◽  
Many Body ◽  
Single Particles ◽  
Theme Issue ◽  
Dynamic Simulations ◽  
The Subject ◽  
Small Clusters

Two experimental studies relating to electrostatic self-assembly have been the subject of dynamic computer simulations, where the consequences of changing the charge and the dielectric constant of the materials concerned have been explored. One series of calculations relates to experiments on the assembly of polymer particles that have been subjected to tribocharging and the simulations successfully reproduce many of the observed patterns of behaviour. A second study explores events observed following collisions between single particles and small clusters composed of charged particles derived from a metal oxide composite. As before, observations recorded during the course of the experiments are reproduced by the calculations. One study in particular reveals how particle polarizability can influence the assembly process. This article is part of the theme issue ‘Modern theoretical chemistry’.

scholarly journals The Quantum-Mechanical Many-Body Problem: The Bose Gas

2006 ◽  
pp. 97-183 ◽  
Author(s):  
Elliott H. Lieb ◽  
Robert Seiringer ◽  
Jan Philip Solovej ◽  
Jakob Yngvason
Keyword(s):  
Body Problem ◽  
Bose Gas ◽  
Quantum Mechanical ◽  
Many Body
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