Numerical and semiclassical analysis of some generalized Casimir pistons
The Casimir force due to a scalar field in a cylinder of radius r with a spherical cap of radius R>r is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines the Casimir force. The spectral function of convex domains...
Gespeichert in:
| Veröffentlicht in: | Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2009-05, Vol.79 (5), Article 052105 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | 5 |
| container_start_page | |
| container_title | Physical review. A, Atomic, molecular, and optical physics |
| container_volume | 79 |
| creator | Schaden, M. |
| description | The Casimir force due to a scalar field in a cylinder of radius r with a spherical cap of radius R>r is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines the Casimir force. The spectral function of convex domains is obtained from a probability measure on convex surfaces that is induced by the Wiener measure on Brownian bridges the convex surfaces are the hulls of. Due to reflection positivity, the vacuum force on the piston by a scalar field satisfying Dirichlet boundary conditions is attractive in these geometries, but the strength and short-distance behavior of the force depend strongly on the shape of the piston casing. For a cylindrical casing with a hemispherical head, the force on the piston does not depend on the dimension of the casing at small piston elevation a |
| doi_str_mv | 10.1103/PhysRevA.79.052105 |
| format | Article |
| fullrecord | <record><control><sourceid>crossref_osti_</sourceid><recordid>TN_cdi_osti_scitechconnect_21300792</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1103_PhysRevA_79_052105</sourcerecordid><originalsourceid>FETCH-LOGICAL-c275t-360811903b795946ddca7f90af8b1acfd7ccc624c37020f568990bd51a9c99473</originalsourceid><addsrcrecordid>eNo1kE1LAzEQhoMoWKt_wFPA89ZJstlsjqWoFYqK6Dmks4mN7EfJrEL99bZU38u8DA_D8DB2LWAmBKjbl82OXsP3fGbsDLQUoE_YRIAtC1FJeXroGgppS3POLog-YZ-ythO2fPrqQk7oW-77hlPoErae6G_j2x0l4kPkNHSBf4Q-ZN-mn9DwhafUpcy3icahp0t2Fn1L4epvTtn7_d3bYlmsnh8eF_NVgdLosVAV1EJYUGtjtS2rpkFvogUf67XwGBuDiJUsURmQEHVVWwvrRgtv0e7fV1N2c7w70JgcYRoDbnDo-4Cjk0IBGCv3lDxSmAeiHKLb5tT5vHMC3MGY-zfmjHVHY-oXHFdgpg</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Numerical and semiclassical analysis of some generalized Casimir pistons</title><source>American Physical Society Journals</source><creator>Schaden, M.</creator><creatorcontrib>Schaden, M.</creatorcontrib><description>The Casimir force due to a scalar field in a cylinder of radius r with a spherical cap of radius R>r is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines the Casimir force. The spectral function of convex domains is obtained from a probability measure on convex surfaces that is induced by the Wiener measure on Brownian bridges the convex surfaces are the hulls of. Due to reflection positivity, the vacuum force on the piston by a scalar field satisfying Dirichlet boundary conditions is attractive in these geometries, but the strength and short-distance behavior of the force depend strongly on the shape of the piston casing. For a cylindrical casing with a hemispherical head, the force on the piston does not depend on the dimension of the casing at small piston elevation a<<R and numerically approaches F{sub cas}(a<<R)=-0.003 26(4)({Dirac_h}/2{pi})c/a{sup 2}. Semiclassically this asymptotic force is due to short, closed, and nonperiodic trajectories that reflect just once off the piston near its periphery. A semiclassical estimate reproduces the numerical results for the small-distance behavior of the force within statistical errors, whereas the proximity force approximation is off by one order of magnitude when R{approx}r.</description><identifier>ISSN: 1050-2947</identifier><identifier>EISSN: 1094-1622</identifier><identifier>DOI: 10.1103/PhysRevA.79.052105</identifier><language>eng</language><publisher>United States</publisher><subject>ASYMPTOTIC SOLUTIONS ; BOUNDARY CONDITIONS ; BROWNIAN MOVEMENT ; CASIMIR EFFECT ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; CYLINDRICAL CONFIGURATION ; DIRICHLET PROBLEM ; DISTANCE ; ERRORS ; GEOMETRY ; NUMERICAL ANALYSIS ; PROBABILITY ; SCALAR FIELDS ; SEMICLASSICAL APPROXIMATION ; SPECTRAL FUNCTIONS ; SURFACES</subject><ispartof>Physical review. A, Atomic, molecular, and optical physics, 2009-05, Vol.79 (5), Article 052105</ispartof><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c275t-360811903b795946ddca7f90af8b1acfd7ccc624c37020f568990bd51a9c99473</citedby><cites>FETCH-LOGICAL-c275t-360811903b795946ddca7f90af8b1acfd7ccc624c37020f568990bd51a9c99473</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,2862,2863,27903,27904</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/21300792$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Schaden, M.</creatorcontrib><title>Numerical and semiclassical analysis of some generalized Casimir pistons</title><title>Physical review. A, Atomic, molecular, and optical physics</title><description>The Casimir force due to a scalar field in a cylinder of radius r with a spherical cap of radius R>r is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines the Casimir force. The spectral function of convex domains is obtained from a probability measure on convex surfaces that is induced by the Wiener measure on Brownian bridges the convex surfaces are the hulls of. Due to reflection positivity, the vacuum force on the piston by a scalar field satisfying Dirichlet boundary conditions is attractive in these geometries, but the strength and short-distance behavior of the force depend strongly on the shape of the piston casing. For a cylindrical casing with a hemispherical head, the force on the piston does not depend on the dimension of the casing at small piston elevation a<<R and numerically approaches F{sub cas}(a<<R)=-0.003 26(4)({Dirac_h}/2{pi})c/a{sup 2}. Semiclassically this asymptotic force is due to short, closed, and nonperiodic trajectories that reflect just once off the piston near its periphery. A semiclassical estimate reproduces the numerical results for the small-distance behavior of the force within statistical errors, whereas the proximity force approximation is off by one order of magnitude when R{approx}r.</description><subject>ASYMPTOTIC SOLUTIONS</subject><subject>BOUNDARY CONDITIONS</subject><subject>BROWNIAN MOVEMENT</subject><subject>CASIMIR EFFECT</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>CYLINDRICAL CONFIGURATION</subject><subject>DIRICHLET PROBLEM</subject><subject>DISTANCE</subject><subject>ERRORS</subject><subject>GEOMETRY</subject><subject>NUMERICAL ANALYSIS</subject><subject>PROBABILITY</subject><subject>SCALAR FIELDS</subject><subject>SEMICLASSICAL APPROXIMATION</subject><subject>SPECTRAL FUNCTIONS</subject><subject>SURFACES</subject><issn>1050-2947</issn><issn>1094-1622</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNo1kE1LAzEQhoMoWKt_wFPA89ZJstlsjqWoFYqK6Dmks4mN7EfJrEL99bZU38u8DA_D8DB2LWAmBKjbl82OXsP3fGbsDLQUoE_YRIAtC1FJeXroGgppS3POLog-YZ-ythO2fPrqQk7oW-77hlPoErae6G_j2x0l4kPkNHSBf4Q-ZN-mn9DwhafUpcy3icahp0t2Fn1L4epvTtn7_d3bYlmsnh8eF_NVgdLosVAV1EJYUGtjtS2rpkFvogUf67XwGBuDiJUsURmQEHVVWwvrRgtv0e7fV1N2c7w70JgcYRoDbnDo-4Cjk0IBGCv3lDxSmAeiHKLb5tT5vHMC3MGY-zfmjHVHY-oXHFdgpg</recordid><startdate>20090501</startdate><enddate>20090501</enddate><creator>Schaden, M.</creator><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>20090501</creationdate><title>Numerical and semiclassical analysis of some generalized Casimir pistons</title><author>Schaden, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c275t-360811903b795946ddca7f90af8b1acfd7ccc624c37020f568990bd51a9c99473</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>ASYMPTOTIC SOLUTIONS</topic><topic>BOUNDARY CONDITIONS</topic><topic>BROWNIAN MOVEMENT</topic><topic>CASIMIR EFFECT</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>CYLINDRICAL CONFIGURATION</topic><topic>DIRICHLET PROBLEM</topic><topic>DISTANCE</topic><topic>ERRORS</topic><topic>GEOMETRY</topic><topic>NUMERICAL ANALYSIS</topic><topic>PROBABILITY</topic><topic>SCALAR FIELDS</topic><topic>SEMICLASSICAL APPROXIMATION</topic><topic>SPECTRAL FUNCTIONS</topic><topic>SURFACES</topic><toplevel>online_resources</toplevel><creatorcontrib>Schaden, M.</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Physical review. A, Atomic, molecular, and optical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schaden, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical and semiclassical analysis of some generalized Casimir pistons</atitle><jtitle>Physical review. A, Atomic, molecular, and optical physics</jtitle><date>2009-05-01</date><risdate>2009</risdate><volume>79</volume><issue>5</issue><artnum>052105</artnum><issn>1050-2947</issn><eissn>1094-1622</eissn><abstract>The Casimir force due to a scalar field in a cylinder of radius r with a spherical cap of radius R>r is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines the Casimir force. The spectral function of convex domains is obtained from a probability measure on convex surfaces that is induced by the Wiener measure on Brownian bridges the convex surfaces are the hulls of. Due to reflection positivity, the vacuum force on the piston by a scalar field satisfying Dirichlet boundary conditions is attractive in these geometries, but the strength and short-distance behavior of the force depend strongly on the shape of the piston casing. For a cylindrical casing with a hemispherical head, the force on the piston does not depend on the dimension of the casing at small piston elevation a<<R and numerically approaches F{sub cas}(a<<R)=-0.003 26(4)({Dirac_h}/2{pi})c/a{sup 2}. Semiclassically this asymptotic force is due to short, closed, and nonperiodic trajectories that reflect just once off the piston near its periphery. A semiclassical estimate reproduces the numerical results for the small-distance behavior of the force within statistical errors, whereas the proximity force approximation is off by one order of magnitude when R{approx}r.</abstract><cop>United States</cop><doi>10.1103/PhysRevA.79.052105</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1050-2947 |
| ispartof | Physical review. A, Atomic, molecular, and optical physics, 2009-05, Vol.79 (5), Article 052105 |
| issn | 1050-2947 1094-1622 |
| language | eng |
| recordid | cdi_osti_scitechconnect_21300792 |
| source | American Physical Society Journals |
| subjects | ASYMPTOTIC SOLUTIONS BOUNDARY CONDITIONS BROWNIAN MOVEMENT CASIMIR EFFECT CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS CYLINDRICAL CONFIGURATION DIRICHLET PROBLEM DISTANCE ERRORS GEOMETRY NUMERICAL ANALYSIS PROBABILITY SCALAR FIELDS SEMICLASSICAL APPROXIMATION SPECTRAL FUNCTIONS SURFACES |
| title | Numerical and semiclassical analysis of some generalized Casimir pistons |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-22T03%3A12%3A16IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref_osti_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Numerical%20and%20semiclassical%20analysis%20of%20some%20generalized%20Casimir%20pistons&rft.jtitle=Physical%20review.%20A,%20Atomic,%20molecular,%20and%20optical%20physics&rft.au=Schaden,%20M.&rft.date=2009-05-01&rft.volume=79&rft.issue=5&rft.artnum=052105&rft.issn=1050-2947&rft.eissn=1094-1622&rft_id=info:doi/10.1103/PhysRevA.79.052105&rft_dat=%3Ccrossref_osti_%3E10_1103_PhysRevA_79_052105%3C/crossref_osti_%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |