메뉴 건너뛰기




Volumn 262, Issue 9, 2012, Pages 4000-4039

Exponential return to equilibrium for hypoelliptic quadratic systems

Author keywords

Chains of oscillators; Generalized Langevin equation; Hypoellipticity; Quadratic operators; Rate of convergence; Return to equilibrium

Indexed keywords


EID: 84857910164     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2012.02.008     Document Type: Article
Times cited : (55)

References (34)
  • 1
    • 0036574560 scopus 로고    scopus 로고
    • Collective and single particle diffusion on surfaces
    • Ala-Nissila T., Ferrando R., Ying S.C. Collective and single particle diffusion on surfaces. Adv. Phys. 2002, 51:949-1078.
    • (2002) Adv. Phys. , vol.51 , pp. 949-1078
    • Ala-Nissila, T.1    Ferrando, R.2    Ying, S.C.3
  • 2
    • 59149089908 scopus 로고    scopus 로고
    • Langevin equation with colored noise for constant temperature molecular dynamics simulations
    • Ceriotti M., Bussi G., Parrinello M. Langevin equation with colored noise for constant temperature molecular dynamics simulations. Phys. Rev. Lett. 2009, 102(2):020601.
    • (2009) Phys. Rev. Lett. , vol.102 , Issue.2 , pp. 020601
    • Ceriotti, M.1    Bussi, G.2    Parrinello, M.3
  • 3
    • 0034349280 scopus 로고    scopus 로고
    • Non-equilibrium statistical mechanics of strongly anharmonic chains of oscillators
    • Eckmann J.-P., Hairer M. Non-equilibrium statistical mechanics of strongly anharmonic chains of oscillators. Comm. Math. Phys. 2000, 212(1):105-164.
    • (2000) Comm. Math. Phys. , vol.212 , Issue.1 , pp. 105-164
    • Eckmann, J.-P.1    Hairer, M.2
  • 4
    • 0037631305 scopus 로고    scopus 로고
    • Spectral properties of hypoelliptic operators
    • Eckmann J.-P., Hairer M. Spectral properties of hypoelliptic operators. Comm. Math. Phys. 2003, 235:233-253.
    • (2003) Comm. Math. Phys. , vol.235 , pp. 233-253
    • Eckmann, J.-P.1    Hairer, M.2
  • 5
    • 0033114736 scopus 로고    scopus 로고
    • Entropy production in nonlinear, thermally driven Hamiltonian systems
    • Eckmann J.-P., Pillet C.-A., Rey-Bellet L. Entropy production in nonlinear, thermally driven Hamiltonian systems. J. Stat. Phys. 1999, 95(1-2):305-331.
    • (1999) J. Stat. Phys. , vol.95 , Issue.1-2 , pp. 305-331
    • Eckmann, J.-P.1    Pillet, C.-A.2    Rey-Bellet, L.3
  • 6
    • 0033243772 scopus 로고    scopus 로고
    • Non-equilibrium statistical mechanics of anharmonic chains coupled to two heat baths at different temperatures
    • Eckmann J.-P., Pillet C.-A., Rey-Bellet L. Non-equilibrium statistical mechanics of anharmonic chains coupled to two heat baths at different temperatures. Comm. Math. Phys. 1999, 201(3):657-697.
    • (1999) Comm. Math. Phys. , vol.201 , Issue.3 , pp. 657-697
    • Eckmann, J.-P.1    Pillet, C.-A.2    Rey-Bellet, L.3
  • 7
    • 5444253857 scopus 로고    scopus 로고
    • Periodic homogenization for hypoelliptic diffusions
    • Hairer M., Pavliotis G.A. Periodic homogenization for hypoelliptic diffusions. J. Stat. Phys. 2004, 117(1-2):261-279.
    • (2004) J. Stat. Phys. , vol.117 , Issue.1-2 , pp. 261-279
    • Hairer, M.1    Pavliotis, G.A.2
  • 8
    • 39749089200 scopus 로고    scopus 로고
    • From ballistic to diffusive behavior in periodic potentials
    • Hairer M., Pavliotis G.A. From ballistic to diffusive behavior in periodic potentials. J. Stat. Phys. 2008, 131(1):175-202.
    • (2008) J. Stat. Phys. , vol.131 , Issue.1 , pp. 175-202
    • Hairer, M.1    Pavliotis, G.A.2
  • 9
    • 22544444988 scopus 로고    scopus 로고
    • Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians
    • Springer-Verlag, Berlin
    • Helffer B., Nier F. Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians. Lecture Notes in Math. 2005, vol. 1862. Springer-Verlag, Berlin.
    • (2005) Lecture Notes in Math. , vol.1862
    • Helffer, B.1    Nier, F.2
  • 10
    • 33846585128 scopus 로고    scopus 로고
    • Short and long time behavior of the Fokker-Planck equation in a confining potential and applications
    • Hérau F. Short and long time behavior of the Fokker-Planck equation in a confining potential and applications. J. Funct. Anal. 2007, 244(1):95-118.
    • (2007) J. Funct. Anal. , vol.244 , Issue.1 , pp. 95-118
    • Hérau, F.1
  • 11
    • 42749083551 scopus 로고    scopus 로고
    • Tunnel effect for Kramers-Fokker-Planck type operators
    • Hérau F., Hitrik M., Sjöstrand J. Tunnel effect for Kramers-Fokker-Planck type operators. Ann. Henri Poincaré 2008, 9(2):209-274.
    • (2008) Ann. Henri Poincaré , vol.9 , Issue.2 , pp. 209-274
    • Hérau, F.1    Hitrik, M.2    Sjöstrand, J.3
  • 12
    • 77955479104 scopus 로고    scopus 로고
    • Tunnel effect for the Kramers-Fokker-Planck type operators: return to equilibrium and applications
    • Article ID rnn057
    • Hérau F., Hitrik M., Sjöstrand J. Tunnel effect for the Kramers-Fokker-Planck type operators: return to equilibrium and applications. Int. Math. Res. Not. 2008, 2008. Article ID rnn057.
    • (2008) Int. Math. Res. Not. , vol.2008
    • Hérau, F.1    Hitrik, M.2    Sjöstrand, J.3
  • 13
    • 79959325321 scopus 로고    scopus 로고
    • Tunnel effect and symmetries for Kramers Fokker-Planck type operators
    • Hérau F., Hitrik M., Sjöstrand J. Tunnel effect and symmetries for Kramers Fokker-Planck type operators. J. Inst. Math. Jussieu 2011, 10(3):567-634.
    • (2011) J. Inst. Math. Jussieu , vol.10 , Issue.3 , pp. 567-634
    • Hérau, F.1    Hitrik, M.2    Sjöstrand, J.3
  • 14
    • 1142264370 scopus 로고    scopus 로고
    • Isotropic hypoellipticity and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
    • Hérau F., Nier F. Isotropic hypoellipticity and trend to equilibrium for the Fokker-Planck equation with a high-degree potential. Arch. Ration. Mech. Anal. 2004, 171(2):151-218.
    • (2004) Arch. Ration. Mech. Anal. , vol.171 , Issue.2 , pp. 151-218
    • Hérau, F.1    Nier, F.2
  • 16
    • 67349280631 scopus 로고    scopus 로고
    • Spectra and semigroup smoothing for non-elliptic quadratic operators
    • Hitrik M., Pravda-Starov K. Spectra and semigroup smoothing for non-elliptic quadratic operators. Math. Ann. 2009, 344(4):801-846.
    • (2009) Math. Ann. , vol.344 , Issue.4 , pp. 801-846
    • Hitrik, M.1    Pravda-Starov, K.2
  • 17
    • 77952485125 scopus 로고    scopus 로고
    • Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics
    • Hitrik M., Pravda-Starov K. Semiclassical hypoelliptic estimates for non-selfadjoint operators with double characteristics. Comm. Partial Differential Equations 2010, 35(6):988-1028.
    • (2010) Comm. Partial Differential Equations , vol.35 , Issue.6 , pp. 988-1028
    • Hitrik, M.1    Pravda-Starov, K.2
  • 18
    • 84857919837 scopus 로고    scopus 로고
    • Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics, preprint
    • M. Hitrik, K. Pravda-Starov, Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics, preprint, 2011, http://arxiv.org/abs/1105.4801.
    • (2011)
    • Hitrik, M.1    Pravda-Starov, K.2
  • 20
    • 51249162728 scopus 로고
    • Symplectic classification of quadratic forms and general Mehler formulas
    • Hörmander L. Symplectic classification of quadratic forms and general Mehler formulas. Math. Z. 1995, 219(3):413-449.
    • (1995) Math. Z. , vol.219 , Issue.3 , pp. 413-449
    • Hörmander, L.1
  • 21
    • 0008112282 scopus 로고
    • Perturbation Theory for Linear Operators
    • Springer-Verlag, Berlin
    • Kato T. Perturbation Theory for Linear Operators. Classics Math. 1995, Springer-Verlag, Berlin.
    • (1995) Classics Math.
    • Kato, T.1
  • 22
  • 25
    • 79955061011 scopus 로고    scopus 로고
    • Asymptotic analysis for the Generalized Langevin Equation
    • Ottobre M., Pavliotis G.A. Asymptotic analysis for the Generalized Langevin Equation. Nonlinearity 2011, 24:1629-1653.
    • (2011) Nonlinearity , vol.24 , pp. 1629-1653
    • Ottobre, M.1    Pavliotis, G.A.2
  • 26
    • 43349100976 scopus 로고    scopus 로고
    • Contraction semigroups of elliptic quadratic differential operators
    • Pravda-Starov K. Contraction semigroups of elliptic quadratic differential operators. Math. Z. 2008, 259(2):363-391.
    • (2008) Math. Z. , vol.259 , Issue.2 , pp. 363-391
    • Pravda-Starov, K.1
  • 27
    • 79251589994 scopus 로고    scopus 로고
    • Subelliptic estimates for quadratic differential operators
    • Pravda-Starov K. Subelliptic estimates for quadratic differential operators. Amer. J. Math. 2011, 133(1):39-89.
    • (2011) Amer. J. Math. , vol.133 , Issue.1 , pp. 39-89
    • Pravda-Starov, K.1
  • 28
    • 84857917355 scopus 로고    scopus 로고
    • Subelliptic estimates for overdetermined systems of quadratic differential operators, Osaka
    • in press.
    • K. Pravda-Starov, Subelliptic estimates for overdetermined systems of quadratic differential operators, Osaka J. Math. (2011), in press.
    • (2011) J. Math.
    • Pravda-Starov, K.1
  • 29
    • 33748951433 scopus 로고    scopus 로고
    • Open classical systems
    • Springer, Berlin, Open Quantum Systems II
    • Rey-Bellet L. Open classical systems. Lecture Notes in Math. 2006, vol. 1881:41-78. Springer, Berlin.
    • (2006) Lecture Notes in Math. , vol.1881 , pp. 41-78
    • Rey-Bellet, L.1
  • 30
    • 0003299394 scopus 로고
    • The Fokker-Planck Equation
    • Springer-Verlag, Berlin
    • Risken H. The Fokker-Planck Equation. Springer Ser. Synergetics 1989, vol. 18. Springer-Verlag, Berlin.
    • (1989) Springer Ser. Synergetics , vol.18
    • Risken, H.1
  • 31
    • 0002048980 scopus 로고
    • Parametrices for pseudodifferential operators with multiple characteristics
    • Sjöstrand J. Parametrices for pseudodifferential operators with multiple characteristics. Ark. Mat. 1974, 12:85-130.
    • (1974) Ark. Mat. , vol.12 , pp. 85-130
    • Sjöstrand, J.1
  • 32
    • 0002367726 scopus 로고    scopus 로고
    • Function spaces associated to global I-Lagrangian manifolds
    • World Sci. Publ., River Edge, NJ
    • Sjöstrand J. Function spaces associated to global I-Lagrangian manifolds. Structure of Solutions of Differential Equations 1996, World Sci. Publ., River Edge, NJ.
    • (1996) Structure of Solutions of Differential Equations
    • Sjöstrand, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.