메뉴 건너뛰기




Volumn 8, Issue 2, 2013, Pages 144-158

Generalized elastic model: Fractional langevin description, fluctuation relation and linear response

Author keywords

Fox H function; Fractional Langevin equation; Linear response; Subdiffusion

Indexed keywords

EXTERNAL PERTURBATIONS; FLUCTUATION RELATIONS; FRACTIONAL LANGEVIN EQUATIONS; H FUNCTION; LINEAR RESPONSE; SCALING PROPERTIES; SINGLE-FILE SYSTEMS; SUBDIFFUSION;

EID: 84876928733     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20138209     Document Type: Article
Times cited : (11)

References (62)
  • 2
    • 28844478780 scopus 로고    scopus 로고
    • Linear response to perturbation of non-exponential renewal processes
    • F. Barbi, M. Bologna, P. Grigolini. Linear response to perturbation of non-exponential renewal processes. Phys. Rev. Lett., 95 (2005), 220601.
    • (2005) Phys. Rev. Lett , vol.95 , pp. 220601
    • Barbi, F.1    Bologna, M.2    Grigolini, P.3
  • 3
    • 0035305938 scopus 로고    scopus 로고
    • Fractional Fokker-Planck equation solution, and application
    • E. Barkai. Fractional Fokker-Planck equation, solution, and application. Phys. Rev. E, 63 (2001), 046118.
    • (2001) Phys. Rev. e , vol.63 , pp. 046118
    • Barkai, E.1
  • 5
    • 0010653914 scopus 로고
    • Elementary example of establishing thermal equilibrium in a system coupled to thermostat. in on some statistical methods in mathematical physics
    • in Russian
    • N. N. Bogolyubov, Elementary example of establishing thermal equilibrium in a system coupled to thermostat. in On some statistical methods in mathematical physics. Acad. Sci. Ukrainian SSR, Kiev, 1945, pp. 115-137, in Russian.
    • (1945) Acad. Sci. Ukrainian SSR, Kiev , pp. 115-137
    • Bogolyubov, N.N.1
  • 6
    • 0040307478 scopus 로고
    • Anomalous diffusion in disordered media: Statistical mechanisms models and physical applications
    • J.-P. Bouchaud, A. Georges. Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep., 195 (1990), 127-293.
    • (1990) Phys. Rep , vol.195 , pp. 127-293
    • Bouchaud, J.-P.1    Georges, A.2
  • 7
    • 40849121133 scopus 로고    scopus 로고
    • Critical exponent of the fractional Langevin equation
    • S. Burov and E. Barkai, Critical exponent of the fractional Langevin equation. Phys. Rev. Lett., 100 (2008), 070601.
    • (2008) Phys. Rev. Lett , vol.100 , pp. 070601
    • Burov, S.1    Barkai, E.2
  • 8
    • 23544467877 scopus 로고
    • Quantum particle in a washboard potential I. Linear mobility and the Einstein relation
    • Y. C. Chen, J. L. Lebowitz. Quantum particle in a washboard potential. I. Linear mobility and the Einstein relation. Phys. Rev. B, 46 (1992), 10743-10750.
    • (1992) Phys. Rev. B , vol.46 , pp. 10743-10750
    • Chen, Y.C.1    Lebowitz, J.L.2
  • 9
    • 33748565282 scopus 로고
    • Dispersion and absorption in dielectrics I. Alternating current characteristics
    • K. S. Cole, R. H. Cole. Dispersion and absorption in dielectrics I. Alternating current characteristics. J. Chem. Phys., 9 (1941), 341-352.
    • (1941) J. Chem. Phys , vol.9 , pp. 341-352
    • Cole, K.S.1    Cole, R.H.2
  • 10
    • 59349102367 scopus 로고    scopus 로고
    • Ergodic properties of fractional Brownian-Langevin motion
    • W. H. Deng, E. Barkai, Ergodic properties of fractional Brownian-Langevin motion. Phys. Rev. E, 79 (2009), 011112.
    • (2009) Phys. Rev. e , vol.79 , pp. 011112
    • Deng, W.H.1    Barkai, E.2
  • 11
    • 6144273098 scopus 로고
    • Statistical Mechanics of Assemblies of Coupled Oscillators
    • G. W. Ford, M. Kac, P. Mazur. Statistical Mechanics of Assemblies of Coupled Oscillators. J. Math. Phys., 6 (1965), No. 4, 504-515.
    • (1965) J. Math. Phys , vol.6 , Issue.4 , pp. 504-515
    • Ford, G.W.1    Kac, M.2    Mazur, P.3
  • 14
    • 0345218900 scopus 로고
    • A method of analyzing experimental results obtained from elasto-viscous bodies
    • A. Gemant. A method of analyzing experimental results obtained from elasto-viscous bodies., Physics, 7 (1936), 311-317.
    • (1936) Physics , vol.7 , pp. 311-317
    • Gemant, A.1
  • 15
    • 4344623697 scopus 로고    scopus 로고
    • Non-Markovian stochastic resonance
    • I. Goychuk, P. Hänggi, Non-Markovian stochastic resonance. Phys. Rev. Lett., 91 (2003), 070601.
    • (2003) Phys. Rev. Lett , vol.91 , pp. 070601
    • Goychuk, I.1    Hänggi, P.2
  • 16
    • 45849155671 scopus 로고    scopus 로고
    • Theory of non-Markovian stochastic resonance
    • I. Goychuk, P. Hänggi, Theory of non-Markovian stochastic resonance. Phys. Rev. E, 69 (2004), 021104.
    • (2004) Phys. Rev. e , vol.69 , pp. 021104
    • Goychuk, I.1    Hänggi, P.2
  • 17
    • 27944452210 scopus 로고    scopus 로고
    • Non-Markovian stochastic resonance: Three state model of ion channel gating
    • I. Goychuk, P. Hänggi, J. L. Vega, S. Miret-Artes. Non-Markovian stochastic resonance: three state model of ion channel gating. Phys. Rev. E, 71 (2005), 061906.
    • (2005) Phys. Rev. e , vol.71 , pp. 061906
    • Goychuk, I.1    Hänggi, P.2    Vega, J.L.3    Miret-Artes, S.4
  • 18
    • 33344478864 scopus 로고    scopus 로고
    • Current and universal scaling in anomalous transport
    • (Rapid Communication)
    • I. Goychuk, E. Heinsalu, M. Patriarca, G. Schmid, P. Hänggi. Current and universal scaling in anomalous transport. Phys. Rev. E, 73 (2006), 020101 (Rapid Communication).
    • (2006) Phys. Rev. e , vol.73 , pp. 020101
    • Goychuk, I.1    Heinsalu, E.2    Patriarca, M.3    Schmid, G.4    Hänggi, P.5
  • 19
    • 36249021544 scopus 로고    scopus 로고
    • Anomalous escape governed by thermal 1/f noise
    • I. Goychuk and P. Hänggi. Anomalous escape governed by thermal 1/f noise., Phys. Rev. Lett., 99 (2007), 200601.
    • (2007) Phys. Rev. Lett , vol.99 , pp. 200601
    • Goychuk, I.1    Hänggi, P.2
  • 20
    • 35448949473 scopus 로고    scopus 로고
    • Anomalous relaxation and dielectric response
    • I. Goychuk, Anomalous relaxation and dielectric response. Phys. Rev. E, 76 (2007), 040102(R).
    • (2007) Phys. Rev. e , vol.76 , pp. 040102
    • Goychuk, I.1
  • 21
    • 70449103071 scopus 로고    scopus 로고
    • Viscoelastic subdiffusion: From anomalous to normal
    • I. Goychuk. Viscoelastic subdiffusion: from anomalous to normal. Phys. Rev. E, 80 (2009), 046125.
    • (2009) Phys. Rev. e , vol.80 , pp. 046125
    • Goychuk, I.1
  • 22
    • 77957753703 scopus 로고    scopus 로고
    • Subdiffusive Brownian ratchets rocked by a periodic force
    • I. Goychuk. Subdiffusive Brownian ratchets rocked by a periodic force. Chem. Phys., 375 (2010), 450-457.
    • (2010) Chem. Phys , vol.375 , pp. 450-457
    • Goychuk, I.1
  • 23
    • 84973168602 scopus 로고    scopus 로고
    • Subdiffusive dynamics in washboard potentials: Two different approaches and different universality classes
    • J Klafter, S C. Lim, R. Metzler, editors Ch. 13
    • I. Goychuk, P. Hänggi. Subdiffusive dynamics in washboard potentials: two different approaches and different universality classes. in J. Klafter, S. C. Lim, R. Metzler, editors. Fractional Dynamics, Recent Advances. World Scientific, Singapore, 2011, Ch. 13, pp. 307-329.
    • (2011) Fractional Dynamics, Recent Advances. World Scientific, Singapore , pp. 307-329
    • Goychuk, I.1    Hänggi, P.2
  • 24
    • 84897583775 scopus 로고    scopus 로고
    • Viscoelastic subdiffusion: Generalized Langevin equation approach
    • I. Goychuk. Viscoelastic subdiffusion: generalized Langevin equation approach. Adv. Chem. Phys., 150 (2012), 187-253.
    • (2012) Adv. Chem. Phys , vol.150 , pp. 187-253
    • Goychuk, I.1
  • 25
    • 84860662682 scopus 로고    scopus 로고
    • Is subdiffusional transport slower than normal?
    • I. Goychuk. Is subdiffusional transport slower than normal?. Fluct. Noise Lett., 11 (2012), 1240009.
    • (2012) Fluct. Noise Lett , vol.11 , pp. 1240009
    • Goychuk, I.1
  • 26
    • 84861929335 scopus 로고    scopus 로고
    • Fractional Brownian motors and stochastic resonance
    • I. Goychuk, V. Kharchenko. Fractional Brownian motors and stochastic resonance. Phys. Rev. E, 85 (2012), 051131.
    • (2012) Phys. Rev. e , vol.85 , pp. 051131
    • Goychuk, I.1    Kharchenko, V.2
  • 27
    • 48849092363 scopus 로고    scopus 로고
    • Random time-scale invariant diffusion and transport coefficients
    • Y. He, S. Burov, R. Metzler, E. Barkai. Random time-scale invariant diffusion and transport coefficients. Phys. Rev. Lett., 101 (2008), 058101.
    • (2008) Phys. Rev. Lett , vol.101 , pp. 058101
    • He, Y.1    Burov, S.2    Metzler, R.3    Barkai, E.4
  • 28
    • 33646360565 scopus 로고    scopus 로고
    • Fractional Fokker-Planck dynamics: Numerical algorithm and simulations
    • E. Heinsalu, M. Patriarca, I. Goychuk, G. Schmid, P. Hänggi. Fractional Fokker-Planck dynamics: Numerical algorithm and simulations. Phys. Rev. E, 73 (2006), 046133.
    • (2006) Phys. Rev. e , vol.73 , pp. 046133
    • Heinsalu, E.1    Patriarca, M.2    Goychuk, I.3    Schmid, G.4    Hänggi, P.5
  • 29
    • 34748840212 scopus 로고    scopus 로고
    • Use and abuse of a fractional Fokker-Planck dynamics for time-dependent driving
    • E. Heinsalu, M. Patriarca, I. Goychuk, P. Hänggi, Use and abuse of a fractional Fokker-Planck dynamics for time-dependent driving. Phys. Rev. Lett., 99 (2007), 120602.
    • (2007) Phys. Rev. Lett , vol.99 , pp. 120602
    • Heinsalu, E.1    Patriarca, M.2    Goychuk, I.3    Hänggi, P.4
  • 30
    • 65849244097 scopus 로고    scopus 로고
    • Fractional Fokker-Planck subdiffusion in alternating force fields
    • E. Heinsalu, M. Patriarca, I. Goychuk, P. Hänggi. Fractional Fokker-Planck subdiffusion in alternating force fields. Phys. Rev. E, 79 (2009), 041137.
    • (2009) Phys. Rev. e , vol.79 , pp. 041137
    • Heinsalu, E.1    Patriarca, M.2    Goychuk, I.3    Hänggi, P.4
  • 33
    • 84860535495 scopus 로고    scopus 로고
    • Flashing subdiffusive ratchets in viscoelastic media
    • V. Kharchenko, I. Goychuk. Flashing subdiffusive ratchets in viscoelastic media. New J. Phys., 14 (2012), 043042.
    • (2012) New J. Phys , vol.14 , pp. 043042
    • Kharchenko, V.1    Goychuk, I.2
  • 35
    • 0007679582 scopus 로고
    • Wiener spirals and some other interesting curves in a Hilbert space
    • English transl Kluwer, Dordrecht
    • English transl. Wiener spirals and some other interesting curves in a Hilbert space, in V. M. Tikhomirov, editor. Selected Works of A. N. Kolmogorov, vol. I, Mechanics and Mathematics. Kluwer, Dordrecht, 1991, pp. 303-307.
    • (1991) Selected Works of A. N. Kolmogorov, Mechanics and Mathematics , vol.1 , pp. 303-307
    • Tikhomirov, V.M.1
  • 36
    • 33847327575 scopus 로고
    • The fluctuation-dissipation theorem
    • R. Kubo. The fluctuation-dissipation theorem. Rep. Prog. Phys., 29 (1966), 255-284.
    • (1966) Rep. Prog. Phys , vol.29 , pp. 255-284
    • Kubo, R.1
  • 38
    • 0347975171 scopus 로고    scopus 로고
    • Fractional kinetics in Kac-Zwanzig heat bath models
    • R. Kupferman. Fractional kinetics in Kac-Zwanzig heat bath models. J. Stat. Phys., 114 (2004), 291-326.
    • (2004) J. Stat. Phys , vol.114 , pp. 291-326
    • Kupferman, R.1
  • 39
    • 46349096647 scopus 로고    scopus 로고
    • Nonergodicity mimics inhomogeneity in single particle tracking
    • A. Lubelski, I. M. Sokolov, J. Klafter. Nonergodicity mimics inhomogeneity in single particle tracking. Phys. Rev. Lett., 100 (2008), 250602.
    • (2008) Phys. Rev. Lett , vol.100 , pp. 250602
    • Lubelski, A.1    Sokolov, I.M.2    Klafter, J.3
  • 40
    • 0035509430 scopus 로고    scopus 로고
    • Fractional Langevin equation
    • E. Lutz. Fractional Langevin equation. Phys. Rev. E, 64 (2001), 051106.
    • (2001) Phys. Rev. e , vol.64 , pp. 051106
    • Lutz, E.1
  • 41
    • 5544237990 scopus 로고
    • Forced thermal ratchets
    • M. O. Magnasco. Forced thermal ratchets. Phys. Rev. Lett., 71 (1993), 1477-1481.
    • (1993) Phys. Rev. Lett , vol.71 , pp. 1477-1481
    • Magnasco, M.O.1
  • 42
    • 0343368357 scopus 로고    scopus 로고
    • The fractional Langevin Equation: Brownian motion revisited
    • F. Mainardi, P. Pironi. The fractional Langevin Equation: Brownian motion revisited. Extracta Mathematicae, 11 (1996), 140.
    • (1996) Extracta Mathematicae , vol.11 , pp. 140
    • Mainardi, F.1    Pironi, P.2
  • 44
    • 0000501589 scopus 로고
    • Fractional Brownian motions, fractional noises and applications
    • B. B. Mandelbrot, J. W. van Ness. Fractional Brownian motions, fractional noises and applications. SIAM Review, 10 (1968), No. 4, 422-437.
    • (1968) SIAM Review , vol.10 , Issue.4 , pp. 422-437
    • Mandelbrot, B.B.1    Van Ness, J.W.2
  • 46
    • 64349105027 scopus 로고    scopus 로고
    • Artificial Brownian motors: Bontrolling transport on the nanoscale
    • P. Hänggi, F. Marchesoni. Artificial Brownian motors: bontrolling transport on the nanoscale. Rev. Mod. Phys., 81 (2009), 387-442.
    • (2009) Rev. Mod. Phys , vol.81 , pp. 387-442
    • Hänggi, P.1    Marchesoni, F.2
  • 47
    • 0002550838 scopus 로고
    • On the dynamical theory of gases
    • J. C. Maxwell. On the dynamical theory of gases. Phil. Trans. R. Soc. Lond., 157 (1867), 49-88.
    • (1867) Phil. Trans. R. Soc. Lond , vol.157 , pp. 49-88
    • Maxwell, J.C.1
  • 48
    • 0002641421 scopus 로고    scopus 로고
    • The random walks guide to anomalous diffusion: A fractional dynamics approach
    • R. Metzler, J. Klafter. The random walks guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep., 339 (2000) 1-77.
    • (2000) Phys. Rep , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 49
    • 0002567920 scopus 로고
    • Random walks on lattices.2
    • E. M. Montroll, G.H. Weiss. Random walks on lattices.2. J. Math. Phys., 6 (1965), No. 2, 167.
    • (1965) J. Math. Phys , vol.6 , Issue.2 , pp. 167
    • Montroll, E.M.1    Weiss, G.H.2
  • 50
    • 5244221149 scopus 로고
    • Models of hierarchically constrained dynamics for glassy relaxation
    • R. G. Palmer, D. L. Stein, E. Abrahams, P. W. Anderson. Models of hierarchically constrained dynamics for glassy relaxation. Phys. Rev. Lett., 53 (1984), 958-961.
    • (1984) Phys. Rev. Lett , vol.53 , pp. 958-961
    • Palmer, R.G.1    Stein, D.L.2    Abrahams, E.3    Anderson, P.W.4
  • 51
    • 0036179557 scopus 로고    scopus 로고
    • Brownian motors: Noisy transport far from equilibrium
    • P. Reimann. Brownian motors: noisy transport far from equilibrium. Phys. Rep., 361 (2002), 57-265.
    • (2002) Phys. Rep , vol.361 , pp. 57-265
    • Reimann, P.1
  • 52
    • 0141508296 scopus 로고
    • Anomalous transit time dispersion in amorphous solids
    • H. Scher, E. M. Montroll. Anomalous transit time dispersion in amorphous solids. Phys. Rev. B, 12 (1975), 2455-2477.
    • (1975) Phys. Rev. B , vol.12 , pp. 2455-2477
    • Scher, H.1    Montroll, E.M.2
  • 53
    • 78651281631 scopus 로고    scopus 로고
    • Efficiency of autonomous soft nanomachines at maximum power
    • U. Seifert. Efficiency of autonomous soft nanomachines at maximum power. Phys. Rev. Lett., 106 (2011), 020601.
    • (2011) Phys. Rev. Lett , vol.106 , pp. 020601
    • Seifert, U.1
  • 54
    • 21744432613 scopus 로고    scopus 로고
    • Kinetic characterization of heat bath and the energetics of thermal ratchet models
    • K. Sekimoto. Kinetic characterization of heat bath and the energetics of thermal ratchet models. J. Phys. Soc. Jpn., 66 (1997) 1234-1237.
    • (1997) J. Phys. Soc. Jpn , vol.66 , pp. 1234-1237
    • Sekimoto, K.1
  • 55
    • 34250415771 scopus 로고
    • Asymptotic solutions of continuous time random walks
    • M. F. Shlesinger. Asymptotic solutions of continuous time random walks. J. Stat. Phys., 10 (1974), 421-434.
    • (1974) J. Stat. Phys , vol.10 , pp. 421-434
    • Shlesinger, M.F.1
  • 56
    • 31144434675 scopus 로고    scopus 로고
    • From diffusion to anomalous diffusion: A century after Einstein's Brownian motion
    • I.M. Sokolov, J. Klafter. From diffusion to anomalous diffusion: a century after Einstein's Brownian motion. Chaos, 15 (2005), 026103.
    • (2005) Chaos , vol.15 , pp. 026103
    • Sokolov, I.M.1    Klafter, J.2
  • 57
    • 33749485301 scopus 로고    scopus 로고
    • Field-induced dispersion in subdiffusion
    • I. M. Sokolov, J. Klafter. Field-induced dispersion in subdiffusion. Phys. Rev. Lett., 97 (2006), 140602.
    • (2006) Phys. Rev. Lett , vol.97 , pp. 140602
    • Sokolov, I.M.1    Klafter, J.2
  • 59
    • 84861636748 scopus 로고    scopus 로고
    • Efficiency of isothermal molecular machines at maximum power
    • C. Van den Broeck, N. Kumar, K. Lindenberg. Efficiency of isothermal molecular machines at maximum power. Phys. Rev. Lett., 108, (2012) 210602.
    • (2012) Phys. Rev. Lett , vol.108 , pp. 210602
    • Broeck Den C.Van1    Kumar, N.2    Lindenberg, K.3
  • 61
    • 18844402460 scopus 로고
    • Nonlinear generalized Langevin equations
    • R. Zwanzig. Nonlinear generalized Langevin equations. J. Stat. Phys., 9 (1973), 215-220.
    • (1973) J. Stat. Phys , vol.9 , pp. 215-220
    • Zwanzig, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.