Pub Date : 2023-04-18DOI: 10.4236/jamp.2023.117121
G. Ariunbold
Quantum dynamics for arbitrary system are traditionally realized by time evolutions of wave functions in Hilbert space and/or density operators in Liouville space. However, the traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this letter, we introduce a nonstandard iterative technique where time interval is divided into a large number of discrete subintervals with an ultrashort duration; and the Liouville space is briefly expanded with an additional (virtual) space only within these subintervals. We choose two-state spin raising and lowering operators for virtual space operators because of their simple algebra. This tremendously reduces the cost of time-consuming calculations. We implement our technique for an example of a charged particle in both harmonic and anharmonic potentials. The temporal evolutions of the probability for the particle being in the ground state are obtained numerically and compared to the analytical solutions. We further discuss the physics insight of this technique based on a thought-experiment. Successive processes intrinsically 'hitchhiking' via virtual space in discrete ultrashort time duration, are the hallmark of our simple iterative technique. We believe that this novel technique has potential for solving numerous problems which often pose a challenge when using the traditional approach based on time-ordered exponentials.
{"title":"Quantum Dynamics via a Hidden Liouville Space","authors":"G. Ariunbold","doi":"10.4236/jamp.2023.117121","DOIUrl":"https://doi.org/10.4236/jamp.2023.117121","url":null,"abstract":"Quantum dynamics for arbitrary system are traditionally realized by time evolutions of wave functions in Hilbert space and/or density operators in Liouville space. However, the traditional simulations may occasionally turn out to be challenging for the quantum dynamics, particularly those governed by the nonlinear Hamiltonians. In this letter, we introduce a nonstandard iterative technique where time interval is divided into a large number of discrete subintervals with an ultrashort duration; and the Liouville space is briefly expanded with an additional (virtual) space only within these subintervals. We choose two-state spin raising and lowering operators for virtual space operators because of their simple algebra. This tremendously reduces the cost of time-consuming calculations. We implement our technique for an example of a charged particle in both harmonic and anharmonic potentials. The temporal evolutions of the probability for the particle being in the ground state are obtained numerically and compared to the analytical solutions. We further discuss the physics insight of this technique based on a thought-experiment. Successive processes intrinsically 'hitchhiking' via virtual space in discrete ultrashort time duration, are the hallmark of our simple iterative technique. We believe that this novel technique has potential for solving numerous problems which often pose a challenge when using the traditional approach based on time-ordered exponentials.","PeriodicalId":56629,"journal":{"name":"应用数学与应用物理(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43883700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.111003
Jean-Francois Niglio
{"title":"Onto Orthogonal Projections in the Space of Polynomials <i>P<sub>n</sub></i>[<i>x</i>]","authors":"Jean-Francois Niglio","doi":"10.4236/jamp.2023.111003","DOIUrl":"https://doi.org/10.4236/jamp.2023.111003","url":null,"abstract":"","PeriodicalId":56629,"journal":{"name":"应用数学与应用物理(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70823103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.111014
C. Giannantoni
{"title":"Solution to the “Three-Body Problem” in the Light of the Maximum Ordinality Principle, as a “Suggestion” for a <i>Ri-Orientation</i> of the Present Scientific Perspective in “Favor” of the “Irreducible Quality”","authors":"C. Giannantoni","doi":"10.4236/jamp.2023.111014","DOIUrl":"https://doi.org/10.4236/jamp.2023.111014","url":null,"abstract":"","PeriodicalId":56629,"journal":{"name":"应用数学与应用物理(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70823796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.111019
H. Uechi, L. Uechi, Schun T. Uechi
{"title":"The Application of Thermomechanical Dynamics (TMD) to the Analysis of Nonequilibrium Irreversible Motion and a Low-Temperature Stirling Engine","authors":"H. Uechi, L. Uechi, Schun T. Uechi","doi":"10.4236/jamp.2023.111019","DOIUrl":"https://doi.org/10.4236/jamp.2023.111019","url":null,"abstract":"","PeriodicalId":56629,"journal":{"name":"应用数学与应用物理(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70823898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.112036
V. Feshchenko, G. Feshchenko
{"title":"Polarization Simultons in CARS by Polaritons","authors":"V. Feshchenko, G. Feshchenko","doi":"10.4236/jamp.2023.112036","DOIUrl":"https://doi.org/10.4236/jamp.2023.112036","url":null,"abstract":"","PeriodicalId":56629,"journal":{"name":"应用数学与应用物理(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70824121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.113042
A. Sel'kin, N. K. Yuldashev
{"title":"Surface Quantum-Dimensional Photocarrier Recombination in <i>CdTe</i> Microcrystals","authors":"A. Sel'kin, N. K. Yuldashev","doi":"10.4236/jamp.2023.113042","DOIUrl":"https://doi.org/10.4236/jamp.2023.113042","url":null,"abstract":"","PeriodicalId":56629,"journal":{"name":"应用数学与应用物理(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70824759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.4236/jamp.2023.115088
W. Qian
{"title":"On the Attribution of Mercury’s Perihelion Precession","authors":"W. Qian","doi":"10.4236/jamp.2023.115088","DOIUrl":"https://doi.org/10.4236/jamp.2023.115088","url":null,"abstract":"","PeriodicalId":56629,"journal":{"name":"应用数学与应用物理(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70826578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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