The Normal Casimir Force for Lateral Moving Planes with Isotropic Conductivities
We consider the two planes at zero temperature with isotropic conductivity that are in relative lateral motion with velocity <i>v</i> and interplane distance <i>a</i>. Two models of conductivity are taken into account—the constant and frequency-dependent Drude models. The nor...
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MDPI AG
2024-01-01
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| Online Access: | https://www.mdpi.com/2624-8174/6/1/11 |
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| author | Nail Khusnutdinov Natalia Emelianova |
| author_facet | Nail Khusnutdinov Natalia Emelianova |
| author_sort | Nail Khusnutdinov |
| collection | DOAJ |
| description | We consider the two planes at zero temperature with isotropic conductivity that are in relative lateral motion with velocity <i>v</i> and interplane distance <i>a</i>. Two models of conductivity are taken into account—the constant and frequency-dependent Drude models. The normal (perpendicular to planes) Casimir force is analyzed in detail for two systems—(i) two planes with identical conductivity and (ii) one plane that is a perfect metal. The velocity correction to the Casimir energy, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>Δ</mo><mi>v</mi></msub><mi mathvariant="script">E</mi></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∝</mo><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>v</mi><mn>2</mn></msup></semantics></math></inline-formula>, for small enough velocities is used for all considered cases. In the case of constant conductivity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>, the energy correction is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>Δ</mo><mi>v</mi></msub><mi mathvariant="script">E</mi><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∝</mo><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>η</mi><mo>/</mo><msup><mi>a</mi><mn>3</mn></msup><msup><mfenced separators="" open="(" close=")"><mi>v</mi><mo>/</mo><mi>η</mi></mfenced><mn>2</mn></msup></mrow></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>v</mi><mo>≪</mo><mi>η</mi><mo>≪</mo><mn>1</mn></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-04-24T17:54:32Z |
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| language | English |
| last_indexed | 2024-04-24T17:54:32Z |
| publishDate | 2024-01-01 |
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| series | Physics |
| spelling | doaj.art-fe41a5ff512b4c3a8d520c7cf96e8ee32024-03-27T14:00:25ZengMDPI AGPhysics2624-81742024-01-016114816310.3390/physics6010011The Normal Casimir Force for Lateral Moving Planes with Isotropic ConductivitiesNail Khusnutdinov0Natalia Emelianova1Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, Santo André 09210-170, SP, BrazilCentro de Matemática, Computação e Cognição, Universidade Federal do ABC, Santo André 09210-170, SP, BrazilWe consider the two planes at zero temperature with isotropic conductivity that are in relative lateral motion with velocity <i>v</i> and interplane distance <i>a</i>. Two models of conductivity are taken into account—the constant and frequency-dependent Drude models. The normal (perpendicular to planes) Casimir force is analyzed in detail for two systems—(i) two planes with identical conductivity and (ii) one plane that is a perfect metal. The velocity correction to the Casimir energy, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>Δ</mo><mi>v</mi></msub><mi mathvariant="script">E</mi></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∝</mo><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>v</mi><mn>2</mn></msup></semantics></math></inline-formula>, for small enough velocities is used for all considered cases. In the case of constant conductivity, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>, the energy correction is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mo>Δ</mo><mi>v</mi></msub><mi mathvariant="script">E</mi><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∝</mo><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>η</mi><mo>/</mo><msup><mi>a</mi><mn>3</mn></msup><msup><mfenced separators="" open="(" close=")"><mi>v</mi><mo>/</mo><mi>η</mi></mfenced><mn>2</mn></msup></mrow></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>v</mi><mo>≪</mo><mi>η</mi><mo>≪</mo><mn>1</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2624-8174/6/1/11dynamic Casimir effectlateral motionconstant conductivity |
| spellingShingle | Nail Khusnutdinov Natalia Emelianova The Normal Casimir Force for Lateral Moving Planes with Isotropic Conductivities Physics dynamic Casimir effect lateral motion constant conductivity |
| title | The Normal Casimir Force for Lateral Moving Planes with Isotropic Conductivities |
| title_full | The Normal Casimir Force for Lateral Moving Planes with Isotropic Conductivities |
| title_fullStr | The Normal Casimir Force for Lateral Moving Planes with Isotropic Conductivities |
| title_full_unstemmed | The Normal Casimir Force for Lateral Moving Planes with Isotropic Conductivities |
| title_short | The Normal Casimir Force for Lateral Moving Planes with Isotropic Conductivities |
| title_sort | normal casimir force for lateral moving planes with isotropic conductivities |
| topic | dynamic Casimir effect lateral motion constant conductivity |
| url | https://www.mdpi.com/2624-8174/6/1/11 |
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