Equation-of-motion method for the study of defects in insulators: Application to a simple model ofTiO2

1987 ◽  
Vol 36 (12) ◽  
pp. 6640-6645 ◽  
Author(s):  
J. W. Halley ◽  
Herbert B. Shore
Keyword(s):  
Simple Model ◽  
Equation Of Motion ◽  
Motion Method

Theoretical Study on the Transport through a Quantum Dots Array with a Side Quantum Dot

2011 ◽  
Vol 340 ◽  
pp. 331-336
Author(s):  
Hai Tao Yin ◽  
Xiao Jie Liu ◽  
Wei Long Wan ◽  
Cheng Bao Yao ◽  
Li Na Bai ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Green Function ◽  
Energy Level ◽  
Quantum Dot ◽  
Quantum Interference ◽  
Theoretical Study ◽  
Equation Of Motion ◽  
Function Technique ◽  
Motion Method ◽  
Linear Conductance

We studied transport properties through a noninteracting quantum dots array with a side quantum dot employing the equation of motion method and Green function technique. The linear conductance has been calculated numerically. It is shown that an antiresonance always pinned at the energy level of side quantum dot. The conductance develops Fano line shape when the side quantum dot level is not aligned with that of the quantum dots in the array due to quantum interference through different channels.

scholarly journals Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method

2016 ◽  
Vol 194 ◽  
pp. 61-80 ◽  
Author(s):  
Lipeng Chen ◽  
Maxim F. Gelin ◽  
Vladimir Y. Chernyak ◽  
Wolfgang Domcke ◽  
Yang Zhao
Keyword(s):  
Relaxation Time ◽  
Electronic State ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Harmonic Oscillators ◽  
Conical Intersection ◽  
Coherent Motion ◽  
Conical Intersections ◽  
Dissipative Dynamics ◽  
Motion Method

The effect of a dissipative environment on the ultrafast nonadiabatic dynamics at conical intersections is analyzed for a two-state two-mode model chosen to represent the S2(ππ*)–S1(nπ*) conical intersection in pyrazine (the system) which is bilinearly coupled to infinitely many harmonic oscillators in thermal equilibrium (the bath). The system–bath coupling is modeled by the Drude spectral function. The equation of motion for the reduced density matrix of the system is solved numerically exactly with the hierarchy equation of motion method using graphics-processor-unit (GPU) technology. The simulations are valid for arbitrary strength of the system–bath coupling and arbitrary bath memory relaxation time. The present computational studies overcome the limitations of weak system–bath coupling and short memory relaxation time inherent in previous simulations based on multi-level Redfield theory [A. Kühl and W. Domcke, J. Chem. Phys. 2002, 116, 263]. Time evolutions of electronic state populations and time-dependent reduced probability densities of the coupling and tuning modes of the conical intersection have been obtained. It is found that even weak coupling to the bath effectively suppresses the irregular fluctuations of the electronic populations of the isolated two-mode conical intersection. While the population of the upper adiabatic electronic state (S2) is very efficiently quenched by the system–bath coupling, the population of the diabatic ππ* electronic state exhibits long-lived oscillations driven by coherent motion of the tuning mode. Counterintuitively, the coupling to the bath can lead to an enhanced lifetime of the coherence of the tuning mode as a result of effective damping of the highly excited coupling mode, which reduces the strong mode–mode coupling inherent to the conical intersection. The present results extend previous studies of the dissipative dynamics at conical intersections to the nonperturbative regime of system–bath coupling. They pave the way for future first-principles simulations of femtosecond time-resolved four-wave-mixing spectra of chromophores in condensed phases which are nonperturbative in the system dynamics, the system–bath coupling as well as the field-matter coupling.

Mikroskopisches Modell eines Ionenkristalles mit einem Brown’schen Untergitter. I. Allgemeine Theorie

1978 ◽  
Vol 33 (7) ◽  
pp. 808-814 ◽  
Author(s):  
C. H. Tillmanns ◽  
L. Merten ◽  
G. Börstel
Keyword(s):  
Complex System ◽  
Dipole Moment ◽  
Simple Model ◽  
Relaxation Process ◽  
Ionic Crystal ◽  
Equation Of Motion ◽  
System Of Equations ◽  
Ionic Crystals ◽  
Debye Relaxation ◽  
Rigid Ion Model

The rigid ion model is extended to ionic crystals with a Brownian sublattice. This sublattice is formed by particles which have the possibility to assume at least two positions along a direction overcoming a potential barrier. Such a Debye relaxation process is connected with a spontaneous dipole moment. Taking into account this additional dipole moment in the equation of motion for ionic crystals we get the corresponding equation for ionic crystals with a Brownian sublattice. In part II of this paper this complex system of equations, which depends on temperature, is solved for a simple model of a diatomic ionic crystal.

New applications of the equation-of-motion method: Optical properties

1993 ◽  
Vol 164-166 ◽  
pp. 877-880 ◽  
Author(s):  
D Weaire ◽  
D Hobbs ◽  
G.J Morgan ◽  
J.M Holender ◽  
F Wooten
Keyword(s):  
Optical Properties ◽  
Equation Of Motion ◽  
New Applications ◽  
Motion Method

scholarly journals Understanding how a falling ball chain can be speeded up by impact onto a surface

2019 ◽  
Vol 475 (2223) ◽  
pp. 20180578
Author(s):  
J. Pantaleone
Keyword(s):  
Simple Model ◽  
Inclination Angle ◽  
Free Fall ◽  
Equation Of Motion ◽  
Theoretical Description ◽  
Bending Angle

When a falling ball chain strikes a surface, a tension is created that pulls the chain downward. This causes a downward acceleration that is larger than free-fall, which has been observed by recent experiments. Here, a theoretical description of this surprising phenomenon is developed. The equation of motion for the falling chain is derived, and then solved for a general form of the tension. The size of the tension needed to produce the observed motion is relatively small and is explained here as coming from the rotation of a link just above where the chain collides with the surface. This simple model is used to calculate the size of the tension in terms of physically measurable quantities: the length and width of a link, the maximum bending angle at a junction, the inclination angle of the surface and the coefficients of friction and restitution between the chain and the surface. The model's predictions agree with the results of current experiments. New experiments are proposed that can test the model.

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