List of publications --- Christian Beck


1. Thermodynamics of Chaotic Systems , Cambridge University Press (1993) (with F. Schloegl) (paperback edition 1995).

2. Spatio-Temporal Chaos and Vacuum Fluctuations of Quantized Fields , World Scientific (2002)

Edited Books:

3. C. Beck, G. Benedek, A. Rapisarda, and C. Tsallis (eds.), Complexity, Metastability, and Nonextensivity,
World Scientific, Singapore (2005)

Book contributions:

4. Transitions from Chaotic to Brownian Motion Behaviour , in Solitons and Chaos , eds. I. Antoniou, F. Lambert, Springer, Berlin (1991)

5. Digital machines iterating chaotic maps: Roundoff induced periodicity , in Proc. Signal and Image Processing , GRETSI, Juan les Pins (1991)

6. A Dynamical System Approach to Quantum Mechanics with Imaginary Time , in Information Dynamics ,
eds. H. Atmanspacher and H. Scheingraber, Springer, Berlin (1991)

7. Effects of Roundoff Errors on Chaotic Dynamics , in EUSIPCO 92, eds. J. Vandewalle and A. Oosterlinck, Elsevier, New York (1992)

8. Stochastic processes from deterministic dynamics , in Chaos: The interplay between stochastic and deterministic behaviour ,
eds. P. Garbaczewski, M. Wolf, A. Weron (Springer, New York, 1995)

9. Coupled map lattices simulating fully developed turbulent flows , in Applied Nonlinear Dynamics and Stochastic Systems Near the Millenium ,
eds. J.B. Kadtke and A. Bulsara, American Institute of Physics (1997) (with A. Hilgers)

10. Dynamical systems with time scale separation: Averaging, stochastic modelling, and Central Limit Theorems ,
in Stochastic Climate Models , Birkhaeuser (2001) (with C. Roedenbeck and H. Kantz) (ps file available)

11. Multifractal analysis , in Encyclopedia of Nonlinear Science, ed. A. Scott, Routledge (2005), ps file available

12. String theory , in Encyclopedia of Nonlinear Science, ed. A. Scott, Routledge (2005), ps file available

13. Free energy , in Encyclopedia of Nonlinear Science, ed. A. Scott, Routledge (2005), ps file available

14. Chaotic quantization and the parameters of the standard model , hep-th/0305173, Proc. Idea-Finding Symposium Frankfurt, 3 (2003), EP Systema, ps file available

15. Superstatistical turbulence models,
PDF file available (physics/0506123), in Proceedings of MPA Garching (2005)

16. Superstatistics: Recent developments and applications,
PDF file available (cond-mat/0502306), in 'Complexity, Metastability and Nonextensivity',
eds. C. Beck, G. Benedek, A. Rapisarda, and C. Tsallis, World Scientific (2005)

17. Dark energy, chaotic fields, and fundamental constants,
PDF file available (astro-ph/0502211), in 'Frontiers of Fundamental Physics', eds. B.G. Sidharth, F. Honsell and A. de Angelis, p. 137, Springer, Berlin (2006)


18. Effects of phase space discretization on the long-time behaviour of dynamical systems , Physica 25D, 173 (1987) (with G. Roepstorff)

19. From dynamical systems to the Langevin equation , Physica 145A, 1 (1987) (with G. Roepstorff)

20. Scaling behaviour of random maps , Phys. Lett. 136A, 121 (1989)

21. Upper and lower bounds on the Renyi dimensions and the uniformity of multifractals , Physica 41D, 67 (1990)

22. Brownian motion from deterministic dynamics , Physica 169A, 324 (1990)

23. Ergodic properties of a kicked damped particle , Commun. Math. Phys. 130 , 51 (1990)

24. From stochastic processes to the hydrodynamic equations , Physica 165A , 270 (1990) (with G. Roepstorff)

25. Thermodynamic formalism for quantum mechanical systems , Physica 50D, 1 (1991)

26. Higher order correlation functions of chaotic maps: A graph theoretical approach , Nonlinearity 4, 1131 (1991)

27. Symbolic dynamics of successive quantum mechanical measurements , Phys. Rev. 46A, 6265 (1992) (with D. Graudenz)

28. Chaotic Motion in Single- and Double-Well Potentials , Physica 72D, 211 (1994) (with C. Schroer and G. Roepstorff)

29. Chaotic cascade model for turbulent velocity distributions , Phys. Rev. 49E, 3641 (1994)

30. Path integrals in the symbol space of chaotic mappings , J. Phys. A. Math. Gen. 28, 1889 (1995) (with T. Tel)

31. Sunspot activity curves and intermittent chaotic behavior , Int. J. Bif. Chaos 5, 1213 (1995) (with G. Guerbuez)

32. From the Perron-Frobenius equation to the Fokker-Planck equation , J. Stat. Phys. 79, 875 (1995)

33. From Ruelle's transfer operator to the Schroedinger operator , Physica 85D, 459 (1995)

34. Chaotic quantization of field theories , Nonlinearity 8, 423 (1995)

35. Dynamical systems of Langevin type , Physica 233A, 419 (1996)

36. Coupled map lattices simulating hydrodynamical turbulence , Physica 103D, 528 (1997)

37. Turbulent behaviour of stock exchange indices and foreign currency exchange rates , Int. J. Bif. Chaos 7, 1855 (1997) (with A. Hilgers)

38. Spontaneous symmetry breaking in a coupled map lattice simulation of quantized Higgs fields , Phys. Lett. 248A, 386 (1998)

39. Physical Meaning for Mandelbrot and Julia sets , Physica 125D, 171 (1999)

40. Hierarchical coupled map lattices as cascade models for hydrodynamical turbulence , Europhys. Lett. 45, 552 (1999) (with A. Hilgers)

41. Approach to Gaussian stochastic behaviour for systems driven by deterministic chaotic forces , Phys. Rev. 60E, 5385 (1999) (with A. Hilgers)

42. Application of generalized thermostatistics to fully developed turbulence , Physica A 277A, 115 (2000) ( dvi file , , available)

43. Non-extensive statistical mechanics and particle spectra in elementary interactions , Physica 286A, 164 (2000) ( ps file available) (hep-ph/0004225)

44. Measuring non-extensitivity parameters in a turbulent Couette-Taylor flow , Phys. Rev. 63E, 035303(R) (2001) (with G.L. Lewis and H.L. Swinney) ( ps file available)

45. A note on the application of non-extensive statistical mechanics to fully developed turbulence , J. Phys. (Math. Gen.) 34A , 4003 (2001) (with B.K. Shivamoggi)

46. Higher-order correlations of Tchebyscheff maps , Physica 156D , 1 (2001) (with A. Hilgers) ( ps file available)

47. Scaling exponents in fully developed turbulence from nonextensive statistical mechanics , Physica 295A , 195 (2001) ( ps file available)

48. On the small-scale statistics of Lagrangian turbulence , Phys. Lett. 287A , 240 (2001), ps file available (physics/0105058)

49. Dynamical foundations of nonextensive statistical mechanics , Phys. Rev. Lett. 87 , 180601 (2001) ps file available

50. Non-extensive statistical mechanics approach to fully developed hydrodynamic turbulence , Chaos, Solitons and Fractals 13 , 499 (2002)
ps file available

51. Non-additivity of Tsallis entropies and fluctuations of temperature , Europhys. Lett. 57 , 329 (2002)
ps file available (cond-mat/0105371)

52. Nonextensive methods in turbulence and particle physics , Physica 305A , 209 (2002)
ps file available

53. Generalized statistical mechanics and fully developed turbulence , Physica 306A , 189 (2002)
ps file available (cond-mat/0110071)

54. Chaotic strings and standard model parameters , Physica 171D , 72 (2002)
ps file available (hep-th/0105152)

55. Superstatistics (with E.G.D. Cohen) , Physica 322A, 267 (2003),
ps file available (cond-mat/0205097)

56. Lagrangian acceleration statistics in turbulent flows , Europhys. Lett. 64 , 151 (2003),
ps file available (cond-mat/0212566)

57. Beck replies , Phys. Rev. Lett. 90 , 218902 (2003)

58. Generalized statistical mechanics of cosmic rays , Physica 331A , 173 (2004)
ps file available (cond-mat/0301354)

59. Superstatistics: Theory and Applications , Cont. Mech. Therm. 16 , 293 (2004)
PDF file available (cond-mat/0303288)

60. Superstatistics in hydrodynamic turbulence , Physica 193D, 195 (2004),
ps file available (physics/0303061)

61. Defect turbulence and generalized statistical mechanics (with K.E. Daniels and E. Bodenschatz) , Physica 193D, 208 (2004)
ps file available (cond-mat/0302623)

62. Chaotic scalar fields as models for dark energy, Phys. Rev. 69D, 123515 (2004)
pdf file available (astro-ph/0310479)

63. Superstatistics, escort distributions, and applications,
ps file available (cond-mat/0312134), Physica 342A, 139 (2004)

64. Superstatistical generalization of the work fluctuation theorem (with E.G.D. Cohen),
ps file avaialable (cond-mat/0312399), Physica 344A, 393 (2004)

65. Nonextensive scalar field theories and dark energy models,
ps file available (cond-mat/0312433), Physica 340A, 459 (2004)

66. Could dark energy be measured in the lab? (with Michael C. Mackey),
PDF file available (astro-ph/0406504), Phys. Lett. B 605, 295 (2005)

67. Asymptotics of superstatistics (with Hugo Touchette),
ps file available (cond-mat/0408091), Phys. Rev. E 71, 016131 (2005)

68. Superstatistical Brownian motion,
PDF file available (cond-mat/0508263), Progr. Theor. Phys. Suppl. 162, 29 (2006)

69. Atmospheric turbulence and superstatistics (with E.G.D. Cohen and S. Rizzo),
PDF file available (cond-mat/0508257), Europhysics News 36, 189 (2005)

70. Nonconcave entropies in multifractals and the thermodynamic formalism (with H. Touchette),
PDF file available (cond-mat/0507379), J. Stat. Phys. 125, 455 (2006)

71. From time series to superstatistics (with E.G.D. Cohen and H.L. Swinney),
PDF file available (cond-mat/0507411), Phys. Rev. E 72, 056133 (2005)

72. Stretched exponentials from superstatistics,
PDF file available (cond-mat/0510841), Physica A 365, 96 (2006)

73. Laboratory tests on dark energy,
PDF file available (astro-ph/0512327), J. Phys. Conf. Ser. 31, 123 (2006)

74. Scaling behaviour of non-hyperbolic coupled map lattices (with S. Groote),
PDF file available (nlin.CD/0603397), Phys. Rev. E 74, 046216 (2006)

75. Zeropoint fluctuations and dark energy in Josephson junctions, (with M.C. Mackey)
PDF file available (astro-ph/0603067), Fluctuation and Noise Letters 7, C27 (2007)

76. Scaling properties of invariant densities of coupled Tchebyscheff maps (with S. Groote),
PDF file available (nlin.CD/0609052), Dyn. Systems 22, 219-248 (2007)

77. Measurability of vacuum fluctuations and dark energy (with M.C. Mackey),
PDF file available (astro-ph/0605418), Physica A 379, 101 (2007)

78. Statistics of 3-dimensional Lagrangian turbulence
PDF file available (cond-mat/0606655), Phys. Rev. Lett. 98, 064502 (2007)

79. Modelling train delays with q-exponential functions (with K. Briggs),
PDF file available (physics/0611097), Physica A 378, 498 (2007)

80. Central limit behavior of deterministic dynamical systems (with U. Tirnakli and C. Tsallis),
PDF file (cond-mat/0701622), Phys. Rev. E 75, 040106(R) (2007)

81. Complexity of chaotic fields and standard model parameters,
PDF file (hep-th/0702082), in
`The logic of nature, complexity and new physics: From quark gluon-plasma to superstrings, quantum gravity, and beyond', ed. A. Zichichi, p. 1-37 (World Scientific, 2008)

82. Electromagnetic dark energy (with M.C. Mackey),
PDF file (astro-ph/0703364), Int. J. Mod. Phys. D 17, 71-80 (2008)

83. Superstatistics, thermodynamics, and fluctuations (with S. Abe and E.G.D. Cohen),
PDF file (arXiv:0705.0148 [cond-mat]), Phys. Rev. E 76, 031102 (2007)

84. Superstatistics: Theoretical concepts and physical applications,
PDF file (arXiv:0705.3832 [cond-mat])
in R. Klages et al. (eds.): Anomalous Transport: Foundations and Applications, p. 433-457 (Wiley-VCH, 2008)

85. Possible measurable effects of dark energy in rotating superconductors (with C.J. de Matos),
PDF file (arXiv:0707.1797 [gr-qc]), Adv. Astron. 931920 (2009)

86. The dark energy scale in superconductors: Innovative theoretical and experimental concepts (with C.J. de Matos),
PDF file (arXiv:0709.2373 [gr-qc]), in `Dark Energy: Theory, Developments and Implication', p. 33-48, ed. K. Lefebvre and R. Garcia (Nova Publishers, New York) 2010

87. Correlations in superstatistical systems,
PDF file (arXiv:0709.3938 [cond-mat]), AIP Conf. Proc. 965, 60 (2007)

88. A superstatistical model of metastasis and cancer survival (with L. Leon Chen),
PDF file (arXiv:0711.4687 []), Physica A 387, 3162 (2008)

89. Chaotic quantization and the mass spectrum of fermions (with M. Maher),
PDF file (arXiv:0801.4720 [hep-th]), Chaos, Solitons and Fractals 37, 9 (2008)

90. Discrete symmetries of chaotic strings (with M. Schaefer),
PDF file (arXiv:0801.4892 []), Dynamical Systems 25, 253 (2010)

91. A closer look at time averages of the logistic map at the edge of chaos (with U. Tirnakli and C. Tsallis),
PDF file (arXiv:0802.1138 [cond-mat]), Phys. Rev. E 79, 056209 (2009)

92. Superstatistical distributions from a maximum entropy principle (with E. Van der Straeten),
PDF file (arXiv:0806.4332 [cond-mat]), Phys. Rev. E 78, 051101 (2008)

93. Axiomatic approach to the cosmological constant,
PDF file (arXiv:0810.0752 [gr-qc]), Physica A 388, 3384 (2009)

94. Recent developments in superstatistics,
PDF file (arXiv:0811.4363 [cond-mat]), Braz. J. Phys. 39, 357 (2009)

95. Superstatistical fluctuations in time series: application to share price dynamics and turbulence (with E. van der Straeten),
PDF file (arXiv:0901.2271 [physics]), Phys. Rev. E 036108 (2009)

96. Generalized information and entropy measures in physics,
PDF file (arXiv:0902.1235 [cond-mat]), Contemp. Phys. 50, 495-510 (2009)

97. Superstatistics in high energy physics: Application to cosmic ray energy spectra and e+e- annihilation,
PDF file (arXiv:0902.2459 [hep-ph]), Eur. Phys. J. A 40, 267 (2009)

98. Comment on `Proposed central limit behavior in deterministic dynamical systems' (with U. Tirnakli and C. Tsallis),
PDF file (arXiv:0906.1262 [cond-mat.stat-mech])

99. Dynamical modelling of superstatistical complex systems (with E. Van der Straeten),
PDF file (arXiv:0911.4816 [cond-mat.stat-mech]), Physica A 390, 951 (2011)

100. Generalized statistical mechanics for superstatistical systems,
PDF file (arXiv:1007.0903 [cond-mat.stat-mech]), Phil. Trans. Royal Soc. 369, 453 (2011)

101. Multifractal information production of the human genome (with A. Provata),
PDF file (arXiv:1011.3449), Europhys. Lett. 95, 58002 (2011)

102. Skewed superstatistical distributions from a Langevin and Fokker-Planck approach (with E. Van der Straeten),
PDF file (arXiv:1012.4631), Chin. Science Bull. 56 (No 34), 3633 (2011)

103. Multifractal analysis of nonhyperbolic coupled map lattices: Application to genomic sequences (with A. Provata),
PDF file (arXiv:1102.4237), Phys. Rev. E 83, 066210 (2011)

104. Testing axion physics in a Josephson junction environment,
PDF file (arXiv:1110.5871), Mod Phys. Lett. A 26, 2841 (2011)

105. Axion physics in a Josephson junction environment
PDF file (arXiv:1008.2085), Physica C 473, 21 (2012)

106. Statistical mechanics of the vacuum,
PDF file arXiv:1112.1583, Mod. Phys. Lett. B 26, 1250060 (2012)

107. Currents in complex polymers: an example of superstatistics for short time series (with C. Yalcin),
PDF files arXiv:1201.5011, Phys. Lett. A 376, 2344 (2012)

108. Coupled intermittent maps modelling the statistics of genomic sequences: a network approach (with A. Provata),
PDF file arXiv:1205.2249, Phys. Rev. E 86, 046101 (2012)

109. Statistics of Lagrangian quantum turbulence (with S. Miah),
PDF file Phys. Rev. E 87, 031002(R)(2013)

110. Renormalization group approach to chaotic strings (with S. Groote and H. Veermae),
PDF file Chaos Solitons Fractals 53, 18 (2013)

111. Fokker-Planck theory of superstatistics (with S. Abe and E.G.D. Cohen),
PDF file arXiv:1208.1957

112. Environmental superstatistics (with G.C. Yalcin),
arXiv:1212.5783, Physica A 392, 5431 (2013)

113. Hierarchical cascade model leading to 7-th order initial value problem (with G. Akram),
arXiv:1212.5784, Appl. Num. Math. 91, 89-97 (2015)

114. N coupled non-local harmonic oscillators leading to 2N-th order initial value problem (with G. Akram),

115. C. Beck, Possible resonance effect of axionic dark matter in S/N/S Josephson junctions,
Phys. Rev. Lett. 111, 231801 (2013) [arXiv:1309.3790]

116. P. Rabassa, C. Beck, Superstatistical analysis of sealevel fluctuations,
Physica A 417, 18 (2015) (arXiv:1405.6007)

117. S. Groote, H. Veermae, C. Beck, Renormalization aspects of chaotic strings,
J.Phys.: Conf. Ser. 532, 012008 (2014)

118. S. Miah, C. Beck, Lagrangian quantum turbulence model based on alternating superfluid/normal fluid stochastic dynamics,
EPL 108, 40004 (2014) (arXiv:1408.6690)

119. P. Rabassa, C. Beck, Extreme value laws for superstatistics,
Entropy 16, 5523 (2014) (arXiv:1409.2415)

120. C. Penrose, C. Beck, Superstatistics of Blaschke products, Dynamical Systems 31, 89 (2016)

121. C. Beck, Axion mass estimates from resonant Josephson junctions,
Physics Dark Universe 7-8, 6-11 (2015)

122. Dan Xu, C. Beck, Transitions from lognormal to chi-square superstatistics for financial time series,
arXiv:1506.01660, Physica A 453, 173 (2016)

123. C. Yalcin, P. Rabassa, and C. Beck, Extreme event statistics of daily rainfall: Dynamical systems approach,
arXiv:1508.03700, J.Phys.A Math.Theor. 49, 154001 (2016)

124. C. Beck, Cosmological flux noise and measured noise power spectra in SQUIDs,
Scientific Reports 6, 28275 (2016)

125. D. Xu and C. Beck, Symbolic dynamics techniques for complex systems: Application to share price dynamics, EPL 118, 30001 (2017)

126. C. Beck and E.G.D. Cohen, Superstatistics: Superposition of Maxwell-Boltzmann distributions, in G. Livadiotis (ed.): Kappa Distributions: Theory and Applications (Elsevier 2017)

127. C. Beck, Possible resonance effect of dark matter axions in SNS Josephson junctions, Proc. of Science (EPS-HEP2017)058 (2017)

128. B. Schaefer, C. Beck, K. Aihara, D. Witthaut, and M. Timme, Non-Gaussian power grid frequency fluctuations characterized by Levy-stable laws and superstatistics, Nature Energy, 3, 119-126 (2018)

129. P. Jizba, J. Korbel, H. Lavicka, M. Proks, V. Svoboda, and C. Beck, Transitions between superstatistical regimes: Validity, breakdown and applications, arXiv:1707.04838, Physica A 493, 29 (2018)

130. G.C. Yalcin and C. Beck, Generalized statistical mechanics of cosmic rays: Application to positron-electron spectral indices, Scientific Reports 8, 1764 (2018)

131. R. Martyr, B. Schaefer, C. Beck, and V. Latora, Benchmarking the performance of controllers for power grid transient stability, arXiv:1802.06647

132. G. Williams and C. Beck, Stochastic differential equations driven by deterministic chaotic maps: Analytic solutions of the Perron-Frobenius equation, Nonlinearity 31, 3484 (2018)

133. R. Martyr, J. Moriarty, and C. Beck, Optimal control of a commercial building's thermostatic load for off-peak demand response, to appear in J. Build. Perform. Sim. (2018), [arXiv:1806.01689]

134. J. Weber, M. Reyers, C. Beck, M. Timme, J.G. Pinto, D. Witthaut, B. Schaefer, Wind power persistence is governed by superstatistics, arXiv:1810.06391

135. J. Yan, C. Beck, Nonlinear Dynamics of Coupled Axion-Josephson Junction Systems, arXiv:1808.09417