Michael Wilkinson - List of Publications

April 2017 

Remarks: Item 107 is a review article. Items 49 and 93 are non-refereed conference contributions. Items 13, 40, 43, 53, 73, 76 were contributions to special issues of refereed journals, mostly associated with conferences. Some of the most recent papers may be under review, in which case an arXiv reference is provided. The remaining items are all contributed articles in peer reviewed journals.


1. Critical Properties of Electron Eigenstates in Incommensurate
Systems
,
M. Wilkinson, Proc. Roy. Soc. Lond.,A391, 305-350, (1984).

2. Diabolical Points in the Spectra of Triangles,
M. V. Berry and M. Wilkinson, Proc. Roy. Soc. Lond., A392, 15-43, (1984). 

3. An Example of Phase Holonomy in WKB Theory,
M. Wilkinson, J. Phys. A17, 3459-3476, (1984).

Reprinted in Geometric Phases in Physics, eds. A. Shapere and F. Wilzcek,
World Scientific: Singapore, (1989).

4. Von Neumann Lattices of Wannier Functions for Bloch Electrons in
a Magnetic Field
,
M. Wilkinson, Proc. Roy. Soc. Lond., A403, 153-166, (1986).

5. Tunnelling between Tori in Phase Space,
M. Wilkinson, Physica, 21D, 341-354, (1986).

6. Narrowly Avoided Crossings,
M. Wilkinson, J. Phys., A20, 635-645, (1987).

7. An Exact Effective Hamiltonian for a Perturbed Landau Level
M. Wilkinson, J. Phys., A20, 1761-1771, (1987).

8. A Semiclassical Sum Rule for Matrix Elements of Classically Chaotic Systems,
M. Wilkinson, J. Phys., A20, 2415-2423, (1987).

9. Multidimensional Tunnelling between Excited States,
M. Wilkinson and J. H. Hannay, Physica, 27D, 201-212, (1987).

10. An Exact Renormalisation Group for Bloch Electrons in a Magnetic
Field
,
M. Wilkinson, J. Phys., A20, 4337-4354, (1987).

11. Random Matrix Theory in Semiclassical Quantum Mechanics of
Chaotic Systems

M. Wilkinson, J. Phys., A21, 1173-1190, (1988)

12. Statistical Aspects of Dissipation by Landau-Zener Transitions,
M. Wilkinson, J. Phys., A21, 4021-4037, (1988).

13. Nonlinear Dissipation in a Finite-Sized Quantum System,
M. Wilkinson, Physica, 157A, 58-63, (1989)

(Proceedings of Second International Conference on
Electrical, Transport and Optical Properties of Inhomogeneous
Materials
, Paris, (1988), eds. J. Lafait and D. B. Tanner.)

14. Statistics of Multiple Avoided Crossings,
M. Wilkinson, J. Phys., A22, 2795-2805, (1989).

15. Phase Space Lattices with Threefold Symmetry,
M. Wilkinson and E. J. Austin, J. Phys., A23, 2529-2554, (1990).

16. Dissipation by Identical Oscillators,
M. Wilkinson, J. Phys., A23, 3603-3611, (1990).

17. Diffusion and Dissipation in Complex Quantum Systems,
M. Wilkinson, Phys. Rev., A41, 4645-4652, (1990).

18. Suppression of Dissipation by Localisation,
M. Wilkinson and E. J. Austin, J. Phys., A23, L957-L963, (1990).

19. Localisation and Spectral Statistics of a Banded Random Matrix Ensemble.
M. Wilkinson, M. Feingold and D. M. Leitner, J. Phys., A24, 175-182, (1991).

20. Spectral Statistics in Semiclassical Random Matrix Ensembles,
M. Feingold, D. M. Leitner and  M. Wilkinson, Phys. Rev. Lett., 66, 986-989, (1991).

21. Adiabatic Transport of Localised Electrons,
M. Wilkinson, J. Phys., A24, 2615-2624, (1991).

22. Dynamics of a Generic Quantum System under a Periodic Perturbation,
M. Wilkinson and E. J. Austin, Phys. Rev., A46, 64-74, (1992).

23. Statistical Properties of Parameter-Dependent Chaotic Quantum Systems,
E. J. Austin and M. Wilkinson, Nonlinearity, 5, 1137-50, (1992).

24. A Sum Rule for the Dispersion Relations of the Rational Harper Equation,
Y. Last and M. Wilkinson, J. Phys., A25, 6123-33, (1992).

25. A Statistical Topographic Model for Exciton Luminescence,
M. Wilkinson, F. Yang, E. J. Austin and K. P. O'Donnell, J. Phys.: Condens. Matter, 4, 8863-78, (1992).

Corrigendum:  J. Phys.: Condens. Matter6, 3123, (1994).

26. Distribution of Matrix Elements of a Classically Chaotic System,
E. J. Austin and M. Wilkinson, Europhysics Lett., 20, 589-93, (1992).

27.  Densities of Degeneracies and Near-degeneracies,
M. Wilkinson and E. J. Austin, Phys. Rev., A47, 2601-9, (1993).

28. The Origin of the Stokes' Shift: A Geometrical Model of Exciton Spectra in 2D Semiconductors,
Fang Yang, M. Wilkinson, E. J. Austin and K. P. O'Donnell, Phys. Rev. Lett., 70, 323-6, (1993).

Reply to comment: Phys. Rev. Lett.70, 1287, (1993).
Erratum:  Phys. Rev. Lett., 72, 1945, (1994).

29. Electric Dipole Absorption by Ballistic Electrons in Small Metal Spheres,
E. J. Austin and M. Wilkinson, J. Phys.: Condens. Matter, 5, 8461-8484, (1993).

30. Absorption of Radiation by Ballistic Electrons in Conducting Discs,
M. Wilkinson and E. J. Austin, J. Phys.: Condens. Matter, 6, 4153-66, (1994).

31. Spectral Dimension and Dynamics for Harper's Hamiltonian,
M. Wilkinson and E. J. Austin, Phys. Rev., B50, 1420-29, (1994).

32. Generalised Wannier Functions and Renormalisation of Harper's Equation,
M. Wilkinson, J. Phys., A27, 8123-48, (1994).

33. A Random Matrix Model for the Non-perturbative Response of a Complex Quantum System,
M. Wilkinson and E. J. Austin, J. Phys., A28, 2277-96, (1995).

34. Transverse Scattering Resonances in Quantum Wires,
M. Wilkinson and E. J. Austin, Physica status solidi, b189, 197-208, (1995).

35. Universal Fluctuations of Chern Integers,
P. N. Walker and M. Wilkinson, Phys. Rev. Lett., 74, 4055-8, (1995).

36. A Brownian Motion Model for the Parameter Dependence of Matrix Elements,
M. Wilkinson and P. N. Walker, J. Phys., A28, 6143-60, (1995).

37. A Transfer Matrix approach to Tunnelling between KAM Tori,
S. Takada, P. N. Walker and M. Wilkinson, Phys. Rev., A52, 3546-53, (1995).

38. First Order Correction to the Renormalisation of the Phase Space Lattice Hamiltonian
R. J. Kay and M. Wilkinson, J. Phys., A29, 1515-39, (1996).

39. Semiclassical Limits of the Spectrum of Harper's Equation,
M. Wilkinson and R. J. Kay, Phys. Rev. Lett., 76, 1896-99, (1996).

40. Singularities in the Spectra of Random Matrices,
P. N. Walker, M. J. Sanchez and M. Wilkinson, J. Math. Phys., 37, 5019-32, (1996).

(Contribution to special issue on Mesoscopic Physics, ed. G. Jona-Lasinio).

41. Semiclassical Theory for Absorption of Radiation in Particles with Diffusive Electron Motion,
B. Mehlig and M. Wilkinson, J. Phys.:Condens. Matter, 9, 3277-90, (1997).

42. Conserved and Broken Symmetries in the Renormalisation of the Phase Space Lattice Hamiltonian,
M. Wilkinson and R. J. Kay, J. Phys., A30, 5551-68, (1997).

43. Distribution of Oscillator Strengths for Recombination of Excitons in Two Dimensions,
M. Wilkinson, P. N. Walker and K. Chinyama, Chaos Solitons and Fractals, 8, 1169-77, (1997).

(Contribution to special issue entitled Chaos and Quantum Transport
in the Mesoscopic Cosmos
', ed. K. Nakamura).

44. Magnetic Dipole Absorption of Radiation in Small Conducting Particles,
M. Wilkinson, B. Mehlig and P. N. Walker, J. Phys.: Condens. Matter, 10, 2739-58, (1998).

45. Non-local Conductivity and the Effective Potential in Small Metal Particles,
M. Wilkinson and B. Mehlig, European Physical Journal, B1, 397-8, (1998).

46. Wannier Functions for Lattices in a Magnetic Field,
M. Wilkinson, J. Phys.: Condensed Matter, 10, 7407-27, (1998).

47. Band Distributions for Quantum Chaos on the Torus,
I. Dana, M. Feingold and M. Wilkinson, Phys. Rev. Lett., 81, 3124-7, (1998).

48. Critical Point Screening in Random Wave Fields,
I. Freund and M. Wilkinson, J. Opt. Soc. Am., A15, 2892-902, (1998).

49.  Parametric Random Matrices: Static and Dynamic Applications,
M. Wilkinson, in Supersymmetry and Trace Formulae
eds. I. V. Lerner, J. P. Keating and D. E. Khmelnitskii, New York: Plenum, p.369-399, (1999).

(Chapter contributed to proceedings of NATO ASI conference).

50. Non-adiabatic Transitions in Multi-level Systems,
M. Wilkinson and M. A. Morgan, Phys. Rev. A, 61, 062104, (2000).

51. Wannier Functions for Lattices in a Magnetic Field II: Extension to Irrational Fields,
M. Wilkinson, J. Phys.: Condensed Matter, 12, 4993-5009, (2000).

52. Absorption of Low-frequency Radiation by Small Metallic Particles:
 a Semiclassical Random Phase Approximation
,
M. Wilkinson and B. Mehlig, J. Phys.: Condensed Matter, 12, 10481-98, (2000).

53. Non-university of Chaotic Classical Dynamics: Implications for Quantum Chaos,
M. Wilkinson, Physica Scripta, T90, 75-9, (2001).

(Proceedings of Nobel Symposium 116, Quantum Chaos Y2K, Backskog
Castle, Sweden, (2000), eds. K-F. Berggren and S. Aberg.)

54. Spectral Correlations: Understanding of Oscillatory Contributions,
B. Mehlig and M. Wilkinson, Phys. Rev. E, 63, 045203, (2001).

55. Semiclassical Trace Formulae using Coherent States,
B. Mehlig and M. Wilkinson, Ann. Phys. Leipzig, 10, 541-59, (2001).

56. Absorption of Energy at a Metallic Surface due to a Normal Electric Field,
M. Wilkinson, J. Phys.: Condensed Matter, 13, 2901-18, (2001).

57. A New Quantum Model for Ohmic Dissipation,
M. Wilkinson, J. Phys.: Condensed Matter, 13, 8087-103, (2001).

58. Energy Shell Bases,
M. Wilkinson, J. Phys. A, 34, 11149-66, (2001).

59. The Path-Coalescence Transition and its Applications,
M. Wilkinson and B. Mehlig, Phys. Rev. E, 68, 040101, (2003).

60. Screening of Charged Singularities of Random Fields,
M. Wilkinson, J. Phys. A, 37, 6763-71, (2004).

61. Coagulation by Random Velocity Fields as a Kramers Problem,
B. Mehlig and M. Wilkinson, Phys. Rev. Lett., 92, 250602, (2004).

62. Caustics in Turbulent Aerosols,
M. Wilkinson and B. Mehlig, Europhysics Letters, 71, 186-92, (2005).

63.  Aggregation of Inertial Particles in Random Flows,
B. Mehlig, M. Wilkinson, K. Duncan, T. Weber and M. Lunggren,
Phys. Rev. E, 72, 051104, (2005).

64. Clustering by Mixing Flows,
K. Duncan, B. Mehlig, S. Ostlund and M. Wilkinson,
Phys. Rev. Lett., 95, 240602, (2005).

65. Staggered Ladder Spectra,
E. Arvedson, M. Wilkinson, B. Mehlig and K. Nakamura,
Phys. Rev. Lett., 96, 030601, (2006).

66. Semilinear Response,
M. Wilkinson, B. Mehlig and D. Cohen,
 Europhysics Letters, 75, 709-15, (2006).

67. Generalised Ornstein-Uhlenbeck Processes,
V. Bezuglyy, B. Mehlig, M. Wilkinson, K. Nakamura and E. Arvedson,
J. Math. Phys.
, 47, 073301, (2006).

68. Caustic Activation of Rain Showers,
M. Wilkinson, B. Mehlig and V. Bezuglyy, Phys. Rev. Lett., 97, 048501, (2006).

Featured in Research Highlights section of Nature Physics, 2, August 2006,
also ScienceNOW Daily News webpage , 14th July 2006.

69. Strength Distribution of Repeatedly Broken Chains,
 M. Wilkinson and B. Mehlig, J. Stat. Phys., 127, 1279-86, (2007).

70. Colliding Particles in Highly Turbulent Flows,
B. Mehlig, V. Uski and M. Wilkinson, Phys. Fluids., 19, 098107, (2007).

71. Unmixing in Random Flows,
M. Wilkinson, B. Mehlig, S. Ostlund and K. P. Duncan, Phys. Fluids, 19, 113303, (2007).

72. Advective Collisions,
B. Andersson, K. Gustavsson, B. Mehlig and M. Wilkinson, Europhysics Lett., 80, 69001, (2007).

73. Precise Asymptotics for a Variable-Range Hopping Model,
B. Mehlig and M. Wilkinson, Prog. Theor. Phys. Suppl., 166, 136-42, (2007).

(Special issue for proccedings of conference 'Quantum Mechanics and Chaos', Osaka, 2006,
eds. K. Nakamura, T. Harayama and K. Takatsuka).

74. Stokes Trapping and Planet Formation,
M. Wilkinson, B. Mehlig and V. Uski,, Astrophys. J., Suppl., 176, 484, (2008).

75. Stick-Breaking Model for Variable-Range Hopping,
 M.Wilkinson, B. Mehlig and V. Bezuglyy, Phil. Mag. Lett., 88, 327, (2008).

76. Collisions of Particles Advected in Random Flows,
K. Gustavsson, B. Mehlig and M. Wilkinson, New J. Phys., 10, 075014, (2008).

(Invited contribution to special issue on 'Cloud Physics', eds.
G. Falkovich and S. Malinowski.)

77. Mutually Unbiased Bases for Continuous Variables,
S. Weigert and M. Wilkinson, Phys. Rev. A, 78, 020303(R), (2008).

78. Variable-range Projection Model for Turbulence-driven Collisions,
K. Gustavsson, B. Mehlig, M. Wilkinson and V. Uski,
Phys. Rev. Lett., 101, 174503, (2008).

79. Fingerprints of Random Flows?,
M. Wilkinson, V. Bezuglyy and B. Mehlig,
Phys. Fluids, 21, 043304, (2009).

80. Multiple Regimes of Diffusion,
B. Mehlig, M. Wilkinson, V. Bezuglyy, K. Gustavsson and K. Nakamura,
Phys. Rev. E, 80, 011139, (2009).

81. Poincare Indices of Rheoscopic Visualisations,
V. Bezuglyy, B. Mehlig and M. Wilkinson,
Eurohysics Lett., 89, 34003, (2010).

82. Correlation Dimension of Inertial Particles in Random Flows,
M. Wilkinson, B. Mehlig and K. Gustavsson, Eurohysics Lett., 89, 50002, (2010).

83. Perturbation Theory for a Stochastic Process with Ornstein-Uhlenbeck Noise,
M. Wilkinson, J. Stat. Phys., 139, 345-53 (2010).

84. Shock Fragmentation Model for Gravitational Collapse,
M. Wilkinson, B. Mehlig and M. A. Morgan,
Res. Astron. Astrophys., 11, 545-62, (2011).

85. Emergent Order in Rheoscopic Swirls,
M. Wilkinson, V. Bezuglyy and B. Mehlig, J. Fluid Mech., 667, 158-87, (2011).

86. Lyapunov Exponent for Small Particles in Smooth One-Dimensional Flows,
M. Wilkinson, J. Phys. A: Math. Theor., 44, 045502, (2011).

87. Universal Anomalous Exponent of Photoconduction,
M. Wilkinson, Europhys. Lett., 96, 67007, (2011).

88. Spherical Ornstein-Uhlenbeck Processes,
M. Wilkinson and A. Pumir, J. Stat. Phys., 145, 113-42, (2011).

89. Orientation Statistics of Small Particles in Turbulence,
A. Pumir and M. Wilkinson, New J. Phys., 13, 093030, (2011).

90. Clustering of Exponentially Separating Trajectories,
M. Wilkinson, B. Mehlig, K. Gustavsson and E. Werner,
Eur. Phys. J. B., 85, 18, (2012).

91. Super-diffusion in Optical Realisations of Anderson Localisation,
Y. Krivlolapov, L. Levi, S. Fishman, M. Segev and M. Wilkinson,
New J. Phys., 14, 043047, (2012).

92. Universal Anomalous Diffusion of Weakly Damped Particles,

V. Bezuglyy, M. Wilkinson and B. Mehlig,

Phys. Rev. E, 85, 061128, (2012).


93. Planet Formation by Concurrent Collapse,
M. Wilkinson and B. Mehlig,
AIP Conf. Proc., 1468, 375-88, (2012).

(Proceedings of 8th International Summer School and Conference on Nonlinear Dynamics, Maribor 2011,
eds. M. Robnik and V. G. Romanovski).


94Spectal Dimension of Fractal Sets,

M. Wilkinson, H. R. Kennard and M. A. Morgan,

J. Phys. A: Math. Theor., 45, 415102, (2012).


95. A Model for Alignment between Microscopic Rods and Vorticity,

M. Wilkinson and H. R. Kennard,

J. Phys. A: Math. Theor., 45, 455502, (2012).


96. A model for the shapes of advected triangles,
A. Pumir and M. Wilkinson, J. Stat. Phys., 152, 934-53, (2013).


97. Multiple collisions in turbulent flows,
M.Vo▀kuhle, E. Leveque, M. Wilkinson and A. Pumir, Phys. Rev. E, 88, 063008, (2013).


98. A Test-Tube Model for Rainfall,
M. Wilkinson, Europhys. Lett.. 106, 40001, (2014).


98C. Reply to comment: Europhys. Lett., 108, 30006, (2014).


99. Prevalence of the sling effect for enhancing collision rates in turbulent suspensions,
M.Vo▀kuhle, A. Pumir, E. Leveque and M. Wilkinson, J. Fluid Mech. 749, 841-52, (2014).


100. Triangular Constellations in Fractal Measures,

M. Wilkinson and J. Grant, Europhys. Lett., 107, 50006, (2014).


101. Convective Ripening and Initiation of Rainfall,
M. Wilkinson, Europhys. Lett., 108, 49001, (2014).


102. Collision Rate for Suspensions at large Stokes Numbers ľ comparing Navier-Stokes

and Synthetic Turbulence,
M.Vo▀kuhle, A. Pumir, E.Leveque and M. Wilkinson, J. Turbulence, 16, 15-25, (2015).


103. Advection Diffusion Equation with Absorbing Boundary,
J. Grant and M. Wilkinson, J. Stat. Phys., 160, 622-35, (2015).


104. Analysis of the Correlation Dimension for Inertial Particles,
K. Gustavsson, B. Mehlig and M. Wilkinson, Phys. Fluids, 27, 073305, (2015).


105. Power-law Distributions in Noisy Dynamical Systems,
M. Wilkinson, R. Guichardaz, M. Pradas and A. Pumir, Europhys. Lett., 111, 50005, (2015).


106. Large Deviation Analysis of Rapid Onset of Rain Showers,
M. Wilkinson, Phys. Rev. Lett., 116, 018501, (2016).

106S Supplementary Materials.

107. Collisional Aggregation due to Turbulence,
A. Pumir and M. Wilkinson, Ann. Rev. Cond. Matter Phys., 7, 141-70, (2016).

108. Non-Thermal Einstein Relations,
R. Guichardaz, A. Pumir and M. Wilkinson, Europhys. Lett., 115, 10009, (2016).

109. Deviation-Angle and Trajectory Statistics for Inertial Particles in Turbulence,
A. Bhatnagar, A. Gupta, D. Mitra, P. Perlekar, M. Wilkinson and R. Pandit, Phys. Rev. E.94, 063112, (2016).

110. Convergent Chaos,
M. Pradas, A. Pumir, G. Huber and M. Wilkinson, arXiv: 1701.08262, submitted to J. Phys. A: Math. Teor., (2017).

111. Stability in Chaos,
G. Huber, M. Pradas, A. Pumir and M. Wilkinson, submitted to Europhys. Lett., (2017).