Publications
    1988
  1. M. Czachor, "Should one expect E=hv for any massless field?", in Problems in Quantum Physics, edited by L. Kostro et al. World Scientific, Singapore (1988).
  2. M. Czachor, "On some class of random variables leading to violation of the Bell inequality", Phys. Lett. A 129, 291 (1988); new version (2017) arXiv:1710.06126 [quant-ph]
    1989
  3. M. Czachor, "Mackinnon's soliton reexamined", Phys.Lett. A 139, 193 (1989)
    1991
  4. M. Czachor, "Mobility and nonseparability", Found.Phys.Lett. 4, 351 (1991) [pdf]
  5. M. Czachor, "On Sachs approach to unification of general relativity and electrodynamics", Phys.Essays 4, 76 (1991)
    1992
  6. M. Czachor, "Non-locality in nonlinear quantum mechanics", in Bell's theorem and the foundations of modern physics, edited by F. Selleri and A. van der Merwe, World Scientific, Singapore (1992) 
  7. M. Czachor, "On classical models of spin", Found.Phys.Lett. 5, 249 (1992), quant-ph/0205010 [pdf]
    1994
  8. M. Czachor, "Bell theorem without inequalities: A single particle formulation" Phys.Rev. A 49, 2231 (1994). [pdf]
    1995
  9. M. Czachor, M.Kuna and W.A.Majewski, "Lyapunov instability of squeezing: An approach via quantum Lyapunov exponents", Acta Phys.Polon. B 26, 1047 (1995)
    1996
  10. M. Czachor, "Nonlinear Schroedinger equation and two-level atoms", Phys.Rev.A 53, 1310 (1996). [pdf]
  11. M. Czachor and L. You, "Nonsimultaneous spontaneous emission from atomic wave packets", in Coherence and Quantum Optics VII, edited by J. H. Eberly, L. Mandel and E. Wolf, Plenum Press, New York (1996) 
  12. M. Czachor, "Lie-Poisson and Lie-Nambu structures in linear and nonlinear QM", Acta Phys. Polon. B 27, 2319 (1996)
    1997
  13. M. Czachor and M. Kuna, "Off-shell triple bracket generalization of the Dirac equation", in Group 21 - Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, edited by H.-D. Doebner, P. Nattermann, and W. Scherer, p. 451-455 (World Scientific, Singapore, 1997)
  14. M. Czachor, "Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles", Phys. Rev. A 55, 72 (1997), quant-ph/9609022
  15. M. Czachor, "Nambu-type generalization of the Dirac equation", Phys. Lett. A 225, 1 (1997), quant-ph/9601015.
  16. M. Czachor, "Relativistic corrections to the Ekert test for eavesdropping", Proceedings of SPIE vol. 3297, p. 141-147 (1997), quant-ph/0205187.
  17. M. Czachor, book review Quantum Relativity: A Synthesis of the Ideas of Einstein and Heisenberg, Class. Quant. Gravity 14, 1012 (1997).
    1998
  18. M. Czachor and M. Marciniak, "Density matrix interpretation of solutions of Lie-Nambu equations", Phys. Lett. A 239, 353-358 (1998), quant-ph/9707013.
  19. M. Czachor, "Structure of nonlinear gauge transformations", Phys. Rev. A 57, R2263-R2266 (1998), quant-ph/9711053.
  20. M. Czachor, "Nonlocal-looking equations can make nonlinear quantum dynamics local", Phys. Rev. A 57, 4122 (1998), quant-ph/9708052.
  21. M. Czachor and M. Kuna, "Complete positivity of nonlinear evolution: A case study", Phys. Rev. A 58, 128 (1998), quant-ph/9708029.
  22. M. Czachor, "Remarks on search algorithms and nonlinearity", Acta Phys. Slov. 48, 157 (1998), quant-ph/9802051 (the eprint is more detailed than the published version).
  23. S. B. Leble and M. Czachor, "Darboux-integrable nonlinear Liouville-von Neumann equation", Phys. Rev. E 58, 7091 (1998), quant-ph/9804052.
    1999
  24. M. Czachor, "Lie-Nambu and beyond", Int. J. Theor. Phys. 38, 475-500 (1999), quant-ph/9711054 [pdf]
  25. M. Czachor and L. You, "Spatially sequential turn-on of spontaneous emission from atomic wave packets", Int. J. Theor. Phys. 38, 277-289 (1999), quant-ph/9802059. [pdf]
  26. M. Czachor, "Bargmann-Wigner spinors", in Photon and Poincare Group, ed. V. V. Dvoeglazov, p. 32-62 (Nova Science, 1999), hep-th/9701135.
  27. M. Czachor and J. Naudts, "Microscopic foundation of nonextensive statistics", Phys. Rev. E 59, R2498 (1999), quant-ph/9809061.
  28. M. Kuna, M. Czachor, and S. B. Leble, "Nonlinear von Neumann-type equations: Darboux invariance and spectra", Phys. Lett. A 225, 42-48 (1999), quant-ph/9810023.
  29. M. Czachor, "Quantum cryptography with polarizing interferometers", Phys. Lett. A 257, 107-112 (1999), quant-ph/9812030.
    2000
  30. M. Czachor, M. Kuna, S. B. Leble, and J. Naudts, "Nonlinear von Neumann-type equations", in Trends in Quantum Mechanics, ed. H.-D. Doebner et al., 209-226 (World Scientific, Singapore, 2000), quant-ph/9904110.
  31. M. Czachor, H.-D. Doebner, M. Syty, K. Wasylka, "Von Neumann equations with time-dependent Hamiltonians and supersymetric quantum meachanics", Phys. Rev. E 61, 3325-3329 (2000), quant-ph/9907059.
  32. M. Syty, K. Wasylka, M. Czachor, "The beauty of Harzians", in Quantum Theory and Symmetries, eds. H.-D. Doebner et al. 171-175 (World Scientific, Singapore, 2000).
  33. M. Czachor, "Non-canonical quantum optics", J. Phys. A: Math. Gen. 33, 8081-8103 (2000), quant-ph/0003091.
    2001
  34. J. Naudts and M. Czachor, "Dynamic and thermodynamic stability of non-extensive systems", in Nonextensive statistical mechanics and its applications, ed. S. Abe and Y. Okamato, Lecture Notes in Physics 560, 243-252 (Springer, 2001).
  35. N. V. Ustinov, M. Czachor, M. Kuna, S. B. Leble, "Darboux integration of idr /dt=[H,f(r )]", Phys. Lett. A 279, 333-340 (2001), quant-ph/0005030.
    2002
  36. M. Czachor, J. Naudts, "Thermostatistics based on Kolmogorov-Nagumo averages: Unifying framework for extensive and nonextensive generalizations", Phys. Lett. A 298, 369-374 (2002), [pdf]
  37. M. Czachor, H.-D. Doebner, "Correlation experiments in nonlinear quantum mechanics", Phys. Lett. A 301, 139-152 (2002), quant-ph/0110008.
  38. N. V. Ustinov, M. Czachor, "Darboux-integrable equations with non-Abelian nonlinearities", in Probing the structure of quantum mechanics: Nonlinearity, nonlocality, computation, axiomatics, D. Aerts, M. Czachor, T. Durt (Editors), 335-353 (World Scientific, Singapore, 2002), nlin.SI./0011013.
  39. D. Aerts, M. Czachor, T. Durt, "Probing the structure of quantum mechanics", in Probing the structure of quantum mechanics: Nonlinearity, nonlocality, computation, axiomatics, D. Aerts, M. Czachor, T. Durt (Editors), 1-19 (World Scientific, Singapore, 2002).
    2003
  40. J. L. Cieśliński, M. Czachor, N. V. Ustinov, "Darboux covariant equations of von Neumann type and their generalizations, J. Math. Phys. 44 (2003) 1763, nlin.SI/0205061 [pdf]
  41. D. Aerts, M. Czachor, L. Gabora, M. Kuna, A. Posiewnik, J. Pykacz, M. Syty, "Quantum morphogenesis: A variation on Thom's catastrophe theory", Phys. Rev. E 67, 051926 (2003), quant-ph/0211105; Virtual Journal of Biological Physics, June 2003
  42. M. Czachor, M. Wilczewski, "Relativistic Bennett-Brassard cryptographic scheme, relativistic errors, and how to correct them", Phys. Rev. A 68, 010302(R) (2003), quant-ph/0211105; Virtual Journal of Quantum Information, August 2003
  43. M. Czachor, "States of light via reducible quantization", Phys. Lett. A 313, 380-388 (2003), quant-ph/0211009.
    2004
  44. D. Aerts, M. Czachor, "Quantum aspects of semantic analysis and symbolic artificial intelligence", J. Phys. A: Math. Gen. 37, L123-L132 (2004), quant-ph/0309022.
  45. M. Czachor, "Reducible representations of CAR and CCR with possible applications to field quantization", J. Nonlin. Math. Phys. Supplement 11, 78-84 (2004), hep-th/0304144.
    2005
  46. M. Czachor, "Comment on `Quantum entropy and special relativity', by . A. Peres, P.F. Scudo, and D. Terno", Phys. Rev. Lett. 94, 078901 (2005), quant-ph/0312040.
    2006
  47. D. Aerts, M. Czachor, L. Gabora, P. Polk, "Soliton kinetic equations with non-Kolmogorovian structure: A new tool for biological modeling?" AIP Conference Proceedings 810, 19-33 (2006).
  48. D. Aerts, M. Czachor, "Abstract DNA-type systems", Nonlinearity 19, 575-589 (2006), q-bio.PE/0411031.
  49. D. Aerts, M. Czachor, M. Pawłowski, "Entangled-state cryptographic protocol that remains secure even if nonlocal hidden variables exist and can be measured with arbitrary precision”, Phys. Rev. A 73, 034303 (2006); Erratum - Phys. Rev. A 73, 059901(E) (2006), quant-ph/0501003.
  50. M. Pawłowski, M. Czachor, "Degree of entanglement as a physically ill-posed problem: The case of entanglement with vacuum”, Phys. Rev. A 73, 042111 (2006), quant-ph/0512253.
  51. D. Aerts, M. Czachor, B. D'Hooghe, "Towards a quantum evolutionary scheme: violating Bell's inequalities in language", Evolutionary Epistemology, Language and Culture: A non-adaptationist, systems theoretical approach, Theory and Decision Library A: , Vol. 39 N. Gontier, J.P. Bendegem, D. Aerts, Eds. (Springer, Berlin, 2006) 453-478, quant-ph/0407150
    2007
  52. M. Czachor, J. Naudts, "Regularization as quantization in reducible representations of CCR", Int. J. Theor. Phys. 46, 73-104 (2007), hep-th/0408017 [pdf].
  53. D. Aerts, M. Czachor, "Cartoon computation: Quantum-like algorithms without quantum mechanics", J. Phys. A: Math. Theor. 40, F259-F266 (2007), Fast Track Communication, quant-ph/0611279.
  54. D. Aerts, M. Czachor, M. Pawłowski, "Security in quantum cryptography vs. nonlocal hidden variables" AIP Conference Proceedings 889, 71-78 (2007).
  55. M. Czachor, M. Wilczewski, "Cavity QED tests of representations of canonical commutation relations employed in field quantization", Int. J. Theor. Phys. 46, 1215-1228 (2007), quant-ph/0509117 [pdf].
  56. M. Czachor, "Elementary gates for cartoon computation", J. Phys. A: Math. Theor. 40, F753-F759 (2007), Fast Track Communication, arXiv:0706.0967 [quant-ph].
  57. D. Aerts, M. Czachor, J. Dehaene, B. De Moor, B. D'Hooghe, "Macroscopic models for quantum systems and computers", J. Phys.: Conference Series 70, 012001 (2007).
  58. D. Aerts, M. Czachor, "Two-state dynamics for replicating two-strand systems", Open Systems and Information Dynamics 14, 397-410 (2007)
    (figures in color are available here).
    2008
  59. D. Aerts, M. Czachor, "Tensor-product vs. geometric-product coding", Phys. Rev. A 77, 012316 (2008), arXiv:0709.1268 [quant-ph].
  60. D. Aerts, E. D'Hondt, B. D'Hooghe, M. Czachor, J. Dehaene, B. De Moor, "A macroscopic device for quantum computation", Int. J. Theor. Phys. 47, 200-211 (2008).
  61. M. Czachor, "Teleportation seen from spacetime: on 2-spinor aspects of quantum information processing", Class. Quantum Grav. 25, 205003 (2008), arXiv:0803.3289 [quant-ph].
    2009
  62. D. Aerts, M. Czachor, Ł. Orłowski, "Teleportation of geometric structures in 3D", J. Phys. A: Math. Theor. 42, 135307 (2009), arXiv:0809.0579 [quant-ph].
  63. M. Wilczewski, M. Czachor, "Theory versus experiment for vacuum Rabi oscillations in lossy cavities ", Phys. Rev. A 79, 033836 (2009), arXiv:0811.3177 [quant-ph].
  64. M. Wilczewski, M. Czachor, "Theory versus experiment for vacuum Rabi oscillations in lossy cavities (II): Direct test of uniqueness of vacuum ", Phys. Rev. A 80, 013802 (2009), arXiv:0904.1618 [quant-ph]
  65. M. Czachor, K. Wrzask, "Automatic regularization by quantization in reducible representations of CCR: Point-form quantum optics with classical sources", Int. J. Theor. Phys. 48, 2511 (2009), arXiv:0806.3510v3 [math-ph], DOI: 10.1007/s10773-009-0038-6
  66. D. Aerts, M. Czachor, B. De Moor, "Geometric analogue of holographic reduced representation", Journal of Mathematical Psychology 53, 389-398 (2009), arXiv:0710.2611 [cs.AI], [pdf]
    2010
  67. M. Czachor, "Two-spinors, oscillator algebras, and qubits: aspects of manifestly covariant approach to relativistic quantum information", Quantum Information Processing 9, 171-232 (2010), arXiv:1002.0066v3 [quant-ph], DOI 10.1007/s11128-010-0163-4 [pdf].
    2011
  68. A.Patyk-Łońska, M. Czachor, D. Aerts, "A comparison of geometric analogues of Holographic Reduced Representations, original Holographic Representations and Binary Spatter Codes", Proceedings of the Federated Conference on Computer Science and Information Systems, 221-228 (IEEE, 2011) [pdf].
  69. A.Patyk-Łońska, M. Czachor, D. Aerts, "Distributed representations based on geometric algebra: The continuous model", Informatica 35, 407–417 (2011). (essentially a journal version of the IEEE proceedings paper - contribution invited by the editors) [pdf]
  70. P. Stefańska, M.Wilczewski, M. Czachor, "Vacuum Rabi oscillation in nonzero-temperature open cavity", Open Systems and Information Dynamics 18, 363-373 (2011), arXiv:1012.1014v1 [quant-ph], [pdf]
  71. D. Aerts, J. Broekaert, M. Czachor, B. D'Hooghe, "A quantum-conceptual explanation of violations of expected utility in economics", Proceedings of QI2011-Fifth International Symposium on Quantum Interaction, Robert Gordon University, Aberdeen, Scotland, June 27-29, 2011. Quantum Interaction. Lecture Notes in Computer Science, 7052, pp. 192-198. http://uk.arxiv.org/abs/1004.2525. doi: 10.1007/978-3-642-24971-6_19.
  72. D. Aerts, S. Bundervoet, M. Czachor, B. D'Hooghe, L. Gabora, P. Polk,"On the foundations of the theory of evolution". In D. Aerts, J. Broekaert, B. D'Hooghe and N. Note (Eds.), Worldviews, Science and Us: Bridging Knowledge and Its Implications for Our Perspectives of the World (pp. 266-280). Singapore: World Scientific
  73. D. Aerts, M. Czachor, S. Sozzo, "Quantum interaction approach in cognition, artificial intelligence and robotics". In V. Privman and V. Ovchinnikov (Eds.), IARIA, Proceedings of the Fifth International Conference on Quantum, Nano and Micro Technologies, pp. 35-40, http://arxiv.org/abs/1104.3345
    2013
  74. M. Czachor, "Uderzenie w brzozę opływem końcówki lewego skrzydła - alternatywny scenariusz pierwszej fazy Katastrofy Smoleńskiej", materiały konferencyjne I Konferencji Smoleńskiej, 22 października 2012, Warszawa (2013)
  75. D. Aerts, M. Czachor, M. Kuna, S. Sozzo, "Systems, environments, and soliton rate equations: A non-Kolmogorovian framework for population dynamics", Ecological Modelling 267, 80-92 (2013).
    2014
  76. D. Aerts, J. Broekaert, M. Czachor, M. Kuna, S. Sozzo, B. Sinervo, "Quantum structure in competing lizard communities", Ecological Modelling 281, 38–51 (2014).
    2015
  77. M. Czachor, "Relativity of arithmetic as a fundamental symmetry of physics", Quantum Studies: Mathematics and Foundations (Springer Open Access, first online 7 Sep. 2015), arXiv:1412.8583 [math-ph], DOI: 10.1007/s40509-015-0056-4
    2016
  78. M. Czachor, A. Posiewnik, "Wavepacket of the Universe and its spreading", Int. J. Theor. Phys. 55, 2001-2011 (2016); arXiv:1312.6355 [gr-qc], DOI: 10.1007/s10773-015-2840-7
  79. M. Czachor, "Relativity of arithmetic as a fundamental symmetry of physics" (printed version), Quantum Stud.: Math. Found. 3, 123-133 (2016), DOI: 10.1007/s40509-015-0056-4
  80. D. Aerts, M. Czachor, M. Kuna, "Crystallization of space: Space-time fractals from fractal arithmetic", Chaos, Solitons and Fractals 83, 201-211 (2016), arXiv:1506.00487 [gr-qc] [pdf].
  81. D. Aerts, M. Czachor, M. Kuna, "Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus", Chaos, Solitons and Fractals 91, 461-468 (2016), arXiv:1603.05471 [math-ph] [pdf].
    2017
  82. M. Czachor, "If gravity is geometry, is dark energy just arithmetic?", Int. J. Theor. Phys. 56, 1364-1381 (2017), arXiv:1604.05738 [math-ph], DOI: 10.1007/s10773-017-3278-x.
  83. M. Czachor, "Information processing and Fechner's problem as a choice of arithmetic", in M. Burgin and W. Hofkirchner (eds.), Information Studies and the Quest for Interdisciplinarity: Unity Through Diversity, pp. 363-372, World Scientific, Singapore (2017); arXiv:1602.00587 [q-bio.NC].
    2018
  84. M. Czachor, "Co dalej z badaniami Katastrofy Smoleńskiej? - uwagi po dwóch latach", Kurier WNET, 2/2018 [pdf]; wersja rozszerzona [pdf]
  85. D. Aerts, M. Czachor, M. Kuna, "Simple fractal calculus from fractal arithmetic", Rep. Math. Phys. 81, 357-370 (2018), arXiv:1606.01337 [math.GN]