The multi-configurational time-dependent Hartree approach in optimized second quantization: thermal ensembles and statistical sampling

In this article, a stochastic SIR-type model for COVID-19 epidemic is built using the standard field theoretical language based on creation and annihilation operators. From the model, we derive the time evolution of the mean number of infectious (active cases) and deceased individuals. In order to capture the effects of lockdown and social distancing, we use a time-dependent infection rate. The results are in good agreement with the data for three different waves of epidemic activity in South Korea.

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The multi-configurational time-dependent Hartree approach in optimized second quantization: Imaginary time propagation and particle number conservation

The Journal of Chemical Physics ◽

10.1063/1.5140984 ◽

2020 ◽

Vol 152 (3) ◽

pp. 034101 ◽

Cited By ~ 4

Author(s):

Thomas Weike ◽

Uwe Manthe

Keyword(s):

Particle Number ◽

Time Dependent ◽

Imaginary Time ◽

Second Quantization ◽

Number Conservation ◽

Particle Number Conservation ◽

Time Propagation

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SOLVING THE SINGLE LAYER MULTICONFIGURATION TIME-DEPENDENT HARTREE–FOCK EQUATION IN SECOND QUANTIZATION REPRESENTATION BASED ON A DECOMPOSITION OF THE OVERALL FOCK SPACE

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633612501052 ◽

2013 ◽

Vol 12 (01) ◽

pp. 1250105 ◽

Cited By ~ 3

Author(s):

WENLIANG LI ◽

X. WENWU ◽

H. KELI

Keyword(s):

Fock Space ◽

Single Layer ◽

Time Dependent ◽

Initial Condition ◽

Imaginary Time ◽

Second Quantization ◽

Hartree Fock ◽

Time Propagation ◽

Set Up ◽

Quantization Representation

Very recently, the multilayer multiconfiguration time-dependent Hartree (MCTDH) method based on a decomposition of the overall Fock space in second quantization representation was proposed [Wang H, Thoss M, J Chem Phys131:024114, 2009], and they have presented demonstrative numerical example on vibrationally coupled electron transport. Followed by the thinking, the strategies of the implement of the theory to deal with multielectron dynamics with consideration coulomb interaction were discussed in detail. Some demonstrative calculations have been carried out by using the single layer MCTDHF method. The influences of the different choice way of initial condition, such as the species of basis function, the type of decomposition of the full Fock space, the choice of the spin orbitals, the number of the single particle function and so on, on the imaginary time propagation are mainly studied. The bridge between the generalized theory and the calculation application has been set up.

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Hartree-Fock and Kohn-Sham time-dependent response theory in a second-quantization atomic-orbital formalism suitable for linear scaling

The Journal of Chemical Physics ◽

10.1063/1.2961039 ◽

2008 ◽

Vol 129 (5) ◽

pp. 054106 ◽

Cited By ~ 40

Author(s):

Thomas Kjærgaard ◽

Poul Jørgensen ◽

Jeppe Olsen ◽

Sonia Coriani ◽

Trygve Helgaker

Keyword(s):

Atomic Orbital ◽

Time Dependent ◽

Linear Scaling ◽

Response Theory ◽

Second Quantization ◽

Hartree Fock

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Atomic Spectroscopy in the FIM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100145157 ◽

1986 ◽

Vol 44 ◽

pp. 758-761

Author(s):

J. J. Hren ◽

S. D. Walck

Keyword(s):

Electron Microscope ◽

Electric Fields ◽

Atom Probe ◽

Atomic Spectroscopy ◽

Single Atom ◽

Statistical Sampling ◽

Commercial Instrument ◽

Available Technology ◽

High Electric Fields ◽

Field Ion Microscope

The field ion microscope (FIM) has had the ability to routinely image the surface atoms of metals since Mueller perfected it in 1956. Since 1967, the TOF Atom Probe has had single atom sensitivity in conjunction with the FIM. “Why then hasn't the FIM enjoyed the success of the electron microscope?” The answer is closely related to the evolution of FIM/Atom Probe techniques and the available technology. This paper will review this evolution from Mueller's early discoveries, to the development of a viable commercial instrument. It will touch upon some important contributions of individuals and groups, but will not attempt to be all inclusive. Variations in instrumentation that define the class of problems for which the FIM/AP is uniquely suited and those for which it is not will be described. The influence of high electric fields inherent to the technique on the specimens studied will also be discussed. The specimen geometry as it relates to preparation, statistical sampling and compatibility with the TEM will be examined.

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