Quantum theory of multiscale coarse-graining
Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in q...
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Veröffentlicht in: | The Journal of chemical physics 2018-03, Vol.148 (10), p.102335-102335 |
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creator | Han, Yining Jin, Jaehyeok Wagner, Jacob W. Voth, Gregory A. |
description | Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology. |
doi_str_mv | 10.1063/1.5010270 |
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Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. 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Published by AIP Publishing.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c348t-bd2b87ffd7acd6b117bbeaebe2e3ea01d502a9bb2e02a8e56d6697c3067cde093</citedby><cites>FETCH-LOGICAL-c348t-bd2b87ffd7acd6b117bbeaebe2e3ea01d502a9bb2e02a8e56d6697c3067cde093</cites><orcidid>0000-0001-7194-1279 ; 0000-0002-3267-6748 ; 0000-0002-6577-2015 ; 0000000171941279 ; 0000000265772015 ; 0000000232676748</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jcp/article-lookup/doi/10.1063/1.5010270$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,784,794,4502,27915,27916,76145</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/29544317$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Han, Yining</creatorcontrib><creatorcontrib>Jin, Jaehyeok</creatorcontrib><creatorcontrib>Wagner, Jacob W.</creatorcontrib><creatorcontrib>Voth, Gregory A.</creatorcontrib><title>Quantum theory of multiscale coarse-graining</title><title>The Journal of chemical physics</title><addtitle>J Chem Phys</addtitle><description>Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.</description><subject>Algorithms</subject><subject>Computer simulation</subject><subject>Consistency</subject><subject>Granulation</subject><subject>Integrals</subject><subject>Mathematical models</subject><subject>Multiscale analysis</subject><subject>Optimization</subject><subject>Quantum statistics</subject><subject>Quantum theory</subject><subject>Statistical mechanics</subject><issn>0021-9606</issn><issn>1089-7690</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp90M1KxDAUBeAgijOOLnwBKbhRseO9aZs0Sxn8gwERdF2S9Hbs0DaatIt5eyszunDh6mw-DofD2CnCHEEkNzjPAIFL2GNThFzFUijYZ1MAjrESICbsKIQ1AKDk6SGbcJWlaYJyyq5fBt31Qxv17-T8JnJV1A5NXwerG4qs0z5QvPK67upudcwOKt0EOtnljL3d370uHuPl88PT4nYZ2yTN-9iU3OSyqkqpbSkMojSGNBnilJAGLDPgWhnDacycMlEKoaRNQEhbEqhkxi62vR_efQ4U-qIdB1HT6I7cEAoOmKpUZgAjPf9D127w3biu4IhZDiJXYlSXW2W9C8FTVXz4utV-UyAU3xcWWOwuHO3ZrnEwLZW_8uezEVxtQbB1r_vadf-0fQGJKHd7</recordid><startdate>20180314</startdate><enddate>20180314</enddate><creator>Han, Yining</creator><creator>Jin, Jaehyeok</creator><creator>Wagner, Jacob W.</creator><creator>Voth, Gregory A.</creator><general>American Institute of Physics</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0001-7194-1279</orcidid><orcidid>https://orcid.org/0000-0002-3267-6748</orcidid><orcidid>https://orcid.org/0000-0002-6577-2015</orcidid><orcidid>https://orcid.org/0000000171941279</orcidid><orcidid>https://orcid.org/0000000265772015</orcidid><orcidid>https://orcid.org/0000000232676748</orcidid></search><sort><creationdate>20180314</creationdate><title>Quantum theory of multiscale coarse-graining</title><author>Han, Yining ; Jin, Jaehyeok ; Wagner, Jacob W. ; Voth, Gregory A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c348t-bd2b87ffd7acd6b117bbeaebe2e3ea01d502a9bb2e02a8e56d6697c3067cde093</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algorithms</topic><topic>Computer simulation</topic><topic>Consistency</topic><topic>Granulation</topic><topic>Integrals</topic><topic>Mathematical models</topic><topic>Multiscale analysis</topic><topic>Optimization</topic><topic>Quantum statistics</topic><topic>Quantum theory</topic><topic>Statistical mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Han, Yining</creatorcontrib><creatorcontrib>Jin, Jaehyeok</creatorcontrib><creatorcontrib>Wagner, Jacob W.</creatorcontrib><creatorcontrib>Voth, Gregory A.</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>The Journal of chemical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Han, Yining</au><au>Jin, Jaehyeok</au><au>Wagner, Jacob W.</au><au>Voth, Gregory A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quantum theory of multiscale coarse-graining</atitle><jtitle>The Journal of chemical physics</jtitle><addtitle>J Chem Phys</addtitle><date>2018-03-14</date><risdate>2018</risdate><volume>148</volume><issue>10</issue><spage>102335</spage><epage>102335</epage><pages>102335-102335</pages><issn>0021-9606</issn><eissn>1089-7690</eissn><coden>JCPSA6</coden><abstract>Coarse-grained (CG) models serve as a powerful tool to simulate molecular systems at much longer temporal and spatial scales. Previously, CG models and methods have been built upon classical statistical mechanics. The present paper develops a theory and numerical methodology for coarse-graining in quantum statistical mechanics, by generalizing the multiscale coarse-graining (MS-CG) method to quantum Boltzmann statistics. A rigorous derivation of the sufficient thermodynamic consistency condition is first presented via imaginary time Feynman path integrals. It identifies the optimal choice of CG action functional and effective quantum CG (qCG) force field to generate a quantum MS-CG (qMS-CG) description of the equilibrium system that is consistent with the quantum fine-grained model projected onto the CG variables. A variational principle then provides a class of algorithms for optimally approximating the qMS-CG force fields. Specifically, a variational method based on force matching, which was also adopted in the classical MS-CG theory, is generalized to quantum Boltzmann statistics. The qMS-CG numerical algorithms and practical issues in implementing this variational minimization procedure are also discussed. Then, two numerical examples are presented to demonstrate the method. Finally, as an alternative strategy, a quasi-classical approximation for the thermal density matrix expressed in the CG variables is derived. This approach provides an interesting physical picture for coarse-graining in quantum Boltzmann statistical mechanics in which the consistency with the quantum particle delocalization is obviously manifest, and it opens up an avenue for using path integral centroid-based effective classical force fields in a coarse-graining methodology.</abstract><cop>United States</cop><pub>American Institute of Physics</pub><pmid>29544317</pmid><doi>10.1063/1.5010270</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0001-7194-1279</orcidid><orcidid>https://orcid.org/0000-0002-3267-6748</orcidid><orcidid>https://orcid.org/0000-0002-6577-2015</orcidid><orcidid>https://orcid.org/0000000171941279</orcidid><orcidid>https://orcid.org/0000000265772015</orcidid><orcidid>https://orcid.org/0000000232676748</orcidid></addata></record> |
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subjects | Algorithms Computer simulation Consistency Granulation Integrals Mathematical models Multiscale analysis Optimization Quantum statistics Quantum theory Statistical mechanics |
title | Quantum theory of multiscale coarse-graining |
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