{"title":"Axiomatic quasi-classical quantization of particle motion in the dissipative media","authors":"S. V. Sazonov","doi":"10.1088/1612-202x/ad3f97","DOIUrl":null,"url":null,"abstract":"\n <jats:p>A self-consistent quasi-classical generalization of the axiomatic quantization of the translational motion of a particle in a dissipative medium is proposed, which is modeled by a drag force <jats:inline-formula>\n <jats:tex-math/>\n <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\n <mml:mrow>\n <mml:mrow>\n <mml:msub>\n <mml:mi>F</mml:mi>\n <mml:mrow>\n <mml:mtext>d</mml:mtext>\n </mml:mrow>\n </mml:msub>\n </mml:mrow>\n </mml:mrow>\n </mml:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"lplad3f97ieqn1.gif\" xlink:type=\"simple\"/>\n </jats:inline-formula>, which depends in a power-law manner on the velocity <jats:inline-formula>\n <jats:tex-math/>\n <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\n <mml:mrow>\n <mml:mi>v</mml:mi>\n </mml:mrow>\n </mml:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"lplad3f97ieqn2.gif\" xlink:type=\"simple\"/>\n </jats:inline-formula>: <jats:inline-formula>\n <jats:tex-math/>\n <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\n <mml:mrow>\n <mml:mrow>\n <mml:msub>\n <mml:mi>F</mml:mi>\n <mml:mrow>\n <mml:mtext>d</mml:mtext>\n </mml:mrow>\n </mml:msub>\n </mml:mrow>\n <mml:mo>∼</mml:mo>\n <mml:mrow>\n <mml:msup>\n <mml:mi>v</mml:mi>\n <mml:mi>n</mml:mi>\n </mml:msup>\n </mml:mrow>\n </mml:mrow>\n </mml:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"lplad3f97ieqn3.gif\" xlink:type=\"simple\"/>\n </jats:inline-formula>, where <jats:inline-formula>\n <jats:tex-math/>\n <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\n <mml:mrow>\n <mml:mi>n</mml:mi>\n </mml:mrow>\n </mml:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"lplad3f97ieqn4.gif\" xlink:type=\"simple\"/>\n </jats:inline-formula> is an arbitrary real number. A detailed analysis of the quasi-classical coherent state is carried out. It is shown that under condition <jats:inline-formula>\n <jats:tex-math/>\n <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\">\n <mml:mrow>\n <mml:mi>n</mml:mi>\n <mml:mo><</mml:mo>\n <mml:mn>3</mml:mn>\n </mml:mrow>\n </mml:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"lplad3f97ieqn5.gif\" xlink:type=\"simple\"/>\n </jats:inline-formula> the dissipative medium suppresses the quantum properties of particle motion, performing the function of a classical measuring device. Otherwise, there is no suppression of quantum properties.</jats:p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1612-202x/ad3f97","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
A self-consistent quasi-classical generalization of the axiomatic quantization of the translational motion of a particle in a dissipative medium is proposed, which is modeled by a drag force Fd, which depends in a power-law manner on the velocity v: Fd∼vn, where n is an arbitrary real number. A detailed analysis of the quasi-classical coherent state is carried out. It is shown that under condition n<3 the dissipative medium suppresses the quantum properties of particle motion, performing the function of a classical measuring device. Otherwise, there is no suppression of quantum properties.
对耗散介质中粒子平移运动的公理量子化提出了一种自洽的准经典概括，其模型是阻力 F d，它以幂律方式取决于速度 v：F d ∼ v n，其中 n 为任意实数。对准经典相干态进行了详细分析。结果表明，在 n 3 条件下，耗散介质会抑制粒子运动的量子特性，发挥经典测量设备的功能。否则，量子特性不会受到抑制。
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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