Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators
Abstract We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice %${\mathbb{Z}}_{2N} \times \mathbb{Z}^2%$, and subjected to stochastic forcing mimicking heat baths of temperatures T1 and T2 on the hyperplanes at 0 and N. We introduce a...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Bricmont, Jean [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2007 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2007 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Berlin : Springer, 1965, 274(2007), 3 vom: 17. Juli, Seite 555-626 |
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| Übergeordnetes Werk: |
volume:274 ; year:2007 ; number:3 ; day:17 ; month:07 ; pages:555-626 |
| Links: |
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| DOI / URN: |
10.1007/s00220-007-0284-5 |
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| Katalog-ID: |
SPR002340097 |
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| 100 | 1 | |a Bricmont, Jean |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators |
| 264 | 1 | |c 2007 | |
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| 520 | |a Abstract We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice %${\mathbb{Z}}_{2N} \times \mathbb{Z}^2%$, and subjected to stochastic forcing mimicking heat baths of temperatures T1 and T2 on the hyperplanes at 0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile. | ||
| 650 | 4 | |a Zero Mode |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Lipschitz Constant |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Gibbs Measure |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Collision Kernel |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a BBGKY Hierarchy |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Kupiainen, Antti |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Communications in mathematical physics |d Berlin : Springer, 1965 |g 274(2007), 3 vom: 17. Juli, Seite 555-626 |w (DE-627)253721628 |w (DE-600)1458931-X |x 1432-0916 |7 nnns |
| 773 | 1 | 8 | |g volume:274 |g year:2007 |g number:3 |g day:17 |g month:07 |g pages:555-626 |
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10.1007/s00220-007-0284-5 doi (DE-627)SPR002340097 (SPR)s00220-007-0284-5-e DE-627 ger DE-627 rakwb eng Bricmont, Jean verfasserin aut Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2007 Abstract We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice %${\mathbb{Z}}_{2N} \times \mathbb{Z}^2%$, and subjected to stochastic forcing mimicking heat baths of temperatures T1 and T2 on the hyperplanes at 0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile. Zero Mode (dpeaa)DE-He213 Lipschitz Constant (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Collision Kernel (dpeaa)DE-He213 BBGKY Hierarchy (dpeaa)DE-He213 Kupiainen, Antti aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 274(2007), 3 vom: 17. Juli, Seite 555-626 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:274 year:2007 number:3 day:17 month:07 pages:555-626 https://dx.doi.org/10.1007/s00220-007-0284-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 274 2007 3 17 07 555-626 |
| spelling |
10.1007/s00220-007-0284-5 doi (DE-627)SPR002340097 (SPR)s00220-007-0284-5-e DE-627 ger DE-627 rakwb eng Bricmont, Jean verfasserin aut Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2007 Abstract We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice %${\mathbb{Z}}_{2N} \times \mathbb{Z}^2%$, and subjected to stochastic forcing mimicking heat baths of temperatures T1 and T2 on the hyperplanes at 0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile. Zero Mode (dpeaa)DE-He213 Lipschitz Constant (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Collision Kernel (dpeaa)DE-He213 BBGKY Hierarchy (dpeaa)DE-He213 Kupiainen, Antti aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 274(2007), 3 vom: 17. Juli, Seite 555-626 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:274 year:2007 number:3 day:17 month:07 pages:555-626 https://dx.doi.org/10.1007/s00220-007-0284-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 274 2007 3 17 07 555-626 |
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10.1007/s00220-007-0284-5 doi (DE-627)SPR002340097 (SPR)s00220-007-0284-5-e DE-627 ger DE-627 rakwb eng Bricmont, Jean verfasserin aut Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2007 Abstract We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice %${\mathbb{Z}}_{2N} \times \mathbb{Z}^2%$, and subjected to stochastic forcing mimicking heat baths of temperatures T1 and T2 on the hyperplanes at 0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile. Zero Mode (dpeaa)DE-He213 Lipschitz Constant (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Collision Kernel (dpeaa)DE-He213 BBGKY Hierarchy (dpeaa)DE-He213 Kupiainen, Antti aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 274(2007), 3 vom: 17. Juli, Seite 555-626 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:274 year:2007 number:3 day:17 month:07 pages:555-626 https://dx.doi.org/10.1007/s00220-007-0284-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 274 2007 3 17 07 555-626 |
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10.1007/s00220-007-0284-5 doi (DE-627)SPR002340097 (SPR)s00220-007-0284-5-e DE-627 ger DE-627 rakwb eng Bricmont, Jean verfasserin aut Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2007 Abstract We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice %${\mathbb{Z}}_{2N} \times \mathbb{Z}^2%$, and subjected to stochastic forcing mimicking heat baths of temperatures T1 and T2 on the hyperplanes at 0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile. Zero Mode (dpeaa)DE-He213 Lipschitz Constant (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Collision Kernel (dpeaa)DE-He213 BBGKY Hierarchy (dpeaa)DE-He213 Kupiainen, Antti aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 274(2007), 3 vom: 17. Juli, Seite 555-626 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:274 year:2007 number:3 day:17 month:07 pages:555-626 https://dx.doi.org/10.1007/s00220-007-0284-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 274 2007 3 17 07 555-626 |
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10.1007/s00220-007-0284-5 doi (DE-627)SPR002340097 (SPR)s00220-007-0284-5-e DE-627 ger DE-627 rakwb eng Bricmont, Jean verfasserin aut Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2007 Abstract We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice %${\mathbb{Z}}_{2N} \times \mathbb{Z}^2%$, and subjected to stochastic forcing mimicking heat baths of temperatures T1 and T2 on the hyperplanes at 0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile. Zero Mode (dpeaa)DE-He213 Lipschitz Constant (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Collision Kernel (dpeaa)DE-He213 BBGKY Hierarchy (dpeaa)DE-He213 Kupiainen, Antti aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 274(2007), 3 vom: 17. Juli, Seite 555-626 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:274 year:2007 number:3 day:17 month:07 pages:555-626 https://dx.doi.org/10.1007/s00220-007-0284-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 274 2007 3 17 07 555-626 |
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Enthalten in Communications in mathematical physics 274(2007), 3 vom: 17. Juli, Seite 555-626 volume:274 year:2007 number:3 day:17 month:07 pages:555-626 |
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Enthalten in Communications in mathematical physics 274(2007), 3 vom: 17. Juli, Seite 555-626 volume:274 year:2007 number:3 day:17 month:07 pages:555-626 |
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Bricmont, Jean @@aut@@ Kupiainen, Antti @@aut@@ |
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Bricmont, Jean |
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Bricmont, Jean misc Zero Mode misc Lipschitz Constant misc Gibbs Measure misc Collision Kernel misc BBGKY Hierarchy Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators |
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Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators Zero Mode (dpeaa)DE-He213 Lipschitz Constant (dpeaa)DE-He213 Gibbs Measure (dpeaa)DE-He213 Collision Kernel (dpeaa)DE-He213 BBGKY Hierarchy (dpeaa)DE-He213 |
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Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators |
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towards a derivation of fourier’s law for coupled anharmonic oscillators |
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Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators |
| abstract |
Abstract We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice %${\mathbb{Z}}_{2N} \times \mathbb{Z}^2%$, and subjected to stochastic forcing mimicking heat baths of temperatures T1 and T2 on the hyperplanes at 0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile. © Springer-Verlag 2007 |
| abstractGer |
Abstract We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice %${\mathbb{Z}}_{2N} \times \mathbb{Z}^2%$, and subjected to stochastic forcing mimicking heat baths of temperatures T1 and T2 on the hyperplanes at 0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile. © Springer-Verlag 2007 |
| abstract_unstemmed |
Abstract We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice %${\mathbb{Z}}_{2N} \times \mathbb{Z}^2%$, and subjected to stochastic forcing mimicking heat baths of temperatures T1 and T2 on the hyperplanes at 0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile. © Springer-Verlag 2007 |
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| title_short |
Towards a Derivation of Fourier’s Law for Coupled Anharmonic Oscillators |
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https://dx.doi.org/10.1007/s00220-007-0284-5 |
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Kupiainen, Antti |
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10.1007/s00220-007-0284-5 |
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2024-07-04T02:40:20.313Z |
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