THE SET OF THE INVARIANT MEASURES OF BOUNDED SPIN–FLIP PROCESSES WITH POTENTIAL

1986 ◽  
Vol 6 (2) ◽  
pp. 213-222
Author(s):  
Shouzheng Tang
Keyword(s):  
2018 ◽  
Author(s):  
Shannon Houck ◽  
Nicholas Mayhall

<div>Many multiconfigurational systems, such as single-molecule magnets, are difficult to study using traditional computational methods due to the simultaneous existence of both spin and spatial degeneracies. In this work, a new approach termed n-spin-flip Ionization Potential/Electron Affinity (<i>n</i>SF-IP or <i>n</i>SF-EA) is introduced which combines the spin-flip method of Anna Krylov with particle-number changing IP/EA methods. We demonstrate the efficacy of the approach by applying it to the strongly-correlated N<sub>2</sub><sup>+</sup> as well as several double exchange systems. We also demonstrate that when these systems are well-described by a double exchange model Hamiltonian, only 1SF-IP/EA is required to extract the double exchange parameters and accurately predict energies for the low-spin states. This significantly reduces the computational effort for studying such systems. The effects of including additional excitations (using a RAS-<i>n</i>SF-IP/EA scheme) are also examined, with particular emphasis on hole and particle excitations.</div>


2018 ◽  
Author(s):  
Shannon Houck ◽  
Nicholas Mayhall

<div>Many multiconfigurational systems, such as single-molecule magnets, are difficult to study using traditional computational methods due to the simultaneous existence of both spin and spatial degeneracies. In this work, a new approach termed n-spin-flip Ionization Potential/Electron Affinity (<i>n</i>SF-IP or <i>n</i>SF-EA) is introduced which combines the spin-flip method of Anna Krylov with particle-number changing IP/EA methods. We demonstrate the efficacy of the approach by applying it to the strongly-correlated N<sub>2</sub><sup>+</sup> as well as several double exchange systems. We also demonstrate that when these systems are well-described by a double exchange model Hamiltonian, only 1SF-IP/EA is required to extract the double exchange parameters and accurately predict energies for the low-spin states. This significantly reduces the computational effort for studying such systems. The effects of including additional excitations (using a RAS-<i>n</i>SF-IP/EA scheme) are also examined, with particular emphasis on hole and particle excitations.</div>


2003 ◽  
Vol 10 (2) ◽  
pp. 247-255
Author(s):  
A. Kharazishvili

Abstract A method of extending σ-finite quasi-invariant measures given on an uncountable group, by using a certain family of its subgroups, is investigated.


Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 80
Author(s):  
Sergey Kryzhevich ◽  
Viktor Avrutin ◽  
Nikita Begun ◽  
Dmitrii Rachinskii ◽  
Khosro Tajbakhsh

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the number of ergodic measures and the minimality of the symbolic model) to ITMs. Further, we proved a version of the closing lemma and studied how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally.


2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Sadashige Matsuo ◽  
Kazuyuki Kuroyama ◽  
Shunsuke Yabunaka ◽  
Sascha R. Valentin ◽  
Arne Ludwig ◽  
...  

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