Publications

Articles in peer-reviewed journals

1. B. Claudon, J. Zylberman, C. Feniou, F. Debbasch, A. Peruzzo, J.P. Piquemal: Polylogarithmic-depth controlled-NOT gates without ancilla qubits, https://arxiv.org/abs/2312.13206, 2023.

2. F. Debbasch: Space-time from quantum Physics, https://arxiv.org/abs/2310.01447, 2023.

3. J. Zylberman, F. Debbasch: Quantum State Preparation with Walsh Series, accepted for publication in Phys. Rev. A, https://arxiv.org/abs/2307.08384, 2023.

4. U. Nzongani, J. Zylberman, C.E. Doncecchi, A. Pérez, F. Debbasch and P. Arnault: Quantum circuits for discrete-time quantum walks with position-dependent coin operator, Quantum Info. Proc., 22, 270, 2023.

5. F. Debbasch: Minimal Quantum Walk Simulation of Dirac Fermions in curved Space-Time, Quantum Studies: Math. and Found.  2023.

6. T. Fredon, J. Zylberman, P. Arnault and F. Debbasch: Quantum Spatial Search with Electric Potential: Long-Time Dynamics and Robustness to noise, Entropy 2022, 24(12), 1178, 2022.

7. J. Zylberman, G. Di Molfetta, M. Brachet, N.F. Loureiro and F. Debbasch: Quantum Simulations of  Hydrodynamics via the Madelung transformation, Phys. Rev. A 106, 032408, 2022.

8. J. Zylberman, F. Debbasch: Dirac Spatial Search with Electric Fields, Entropy 2021, 23(11), 1441, 2021.

9. F. Debbasch: Quantum Walks simulating non commutative geometry in the Landau problem, https://arxiv.org/abs/2009.11371, J. Math. Phys. 62205, 2021.

10. G. Jay, P. Arnault and F. Debbasch: Dirac Quantum Walks with conserved angular momentum, https://arxiv.org/abs/2007.06211, Quantum Studies: Math. and Found. 8(4), 419-430, 2021.

11. P. Arnault et al.: Quantum simulation of quantum relativistic diffusions via quantum walks, https://arxiv.org/abs/1911.09791, J. Phys. A, 53 (20), 2020.

12. F. Debbasch: Relativistic Wigner Function for Quantum Walks, https://arxiv.org/abs/1902.11077, Rec. Prog. Mat., 2(1), 13, 2020. doi:10.21926/rpm.2001002

13. F. Debbasch: Discrete Geometry from Quantum Walks, Condens. Matter, 4(2), 40, 2019.

14. G. Jay, F. Debbasch and J. Wang: A new method to building Dirac quantum walks coupled to electromagnetic fields, accepted for publication in Quantum Information Processing, https://arxiv.org/abs/1812.06729

15. F. Debbasch: Action Principles for quantum Automata and Lorentz Invariance of Discrete-Time Quantum Walks, https://arxiv.org/abs/1806.02313, Ann. Phys., 405, 340-364, 2019.

16. G. Jay, F. Debbasch, J. Wang: Dirac quantum walks on triangular and honeycomb lattices, https://arxiv.org/abs/1803.01304, Phys. Rev. A 99, 032113, 2019.

17. M. Hatifi, G; Di Moletta, F. Debbasch, M. Brachet: Quantum Walk Hydrodynamics, https://arxiv.org/abs/1709.10417, Scientific Reports 9, 2989, 2019.

18. P. Arnault and F. Debbasch: Quantum walks and gravitational waves, Ann. Phys., 383, 645-661, 2017.

19. P. Arnault, G. Di Molfetta, M. Brachet and F. Debbasch: Quantum walks and non-abelian discrete gauge theories, Phys. Rev. A94, 012335, 2016.

20. G. Di Moletta and F. Debbasch: Discrete-time Quantum Walks in random artificial Gauge Fields, Quantum Studies: Mathematics and Foundations 3(4), 293-311, 2016.

21. P. Arnault and F. Debbasch: Quantum walks and discrete gauge theories,  Phys. Rev. A93, 052301, 2016.

22. P. Arnault and F. Debbasch: Landau Levels for discrete time quantum walks in artificial magnetic fields, Physica A, 179-191, 2016. 

23. G. Di Molfetta, F. Debbasch and M. Brachet: Non-linear optical Galton board: thermalization and continuous limit. Phys. Rev. E92, 042923, 2015.

24. G. Di Molfetta, M. Brachet and F. Debbasch. Quantum walks in artificial electric and gravitational Fields, Physica A, 397, 157-168, 2014.

25. G. Di Molfetta, M. Brachet and F. Debbasch. Quantum walks as massless Dirac fermions in curved space-time. Phys. Rev. A. 88(4), 042301, 2013.

26. F. Debbasch and G. Di Molfetta. Discrete time quantum walks: continuous limit in 1 + 1 and 1 + 2 dimensions, J. theor. comput. nanoscience, 10(7), 1621-1625, 2013.

27. G. Di Molfetta and F. Debbasch. Discrete time Quantum Walks: continuous limit and symmetries, J. Math. Phys. 53, 123302 , 2012.

28. F. Debbasch, D. Espaze and  V. Foulonneau: Can diffusions propagate? J. Stat. Phys. 149(1), 37-49, 2012.

29. I. Bailleul and F. Debbasch: A probalistic view on the relativistic Boltzamnn equation, Class. Quant. Grav., 29, 965020, 2012.

30. F. Debbasch, D. Espaze, V. Foulonneau and J.P. Rivet: Thermal relaxation for the Relativistic Ornstein-Uhlenbeck Process, Physica A, 391(15), 3797-3804, 2012.

31. J.P. Rivet and F. Debbasch: Validating the diffusion approximation through conditional entropies, Mod. Phys. Lett. B, 25(6), 377-388, 2011.

32. F. Debbasch and J.P. Rivet: The Ludwig-Soret effect and stochastic processes, Jour, Chem. Therm. 43(3), 300-306, 2011.

33. F. Debbasch: On teaching thermodynamics, Eur. J. Phys. 32(1), 15, 2011.

34. J.P. Rivet and F. Debbasch: Validating the diffusion approximation through conditional entropies, Mod. Phys. Lett. B, 25(6):377-383, 2011.

35. F. Debbasch and J.P. Rivet: Thermodiffusion: from kinetics to stochastics, Physica A, 389(10): 2048, 2010.

36. C. Chevalier and F. Debbasch: Lateral diffusions: the influence of geometry fluctuations. EPL 89(3):38001, 2010.

37. F. Debbasch: Relativistic Thermodynamics: Always look back. Nature Physics, 5(10):708-9, 2009.

38. C. Chevalier, F. Debbasch, Y. Ollivier. Multiscale Cosmological Dynamics. Physica A, 388(24), 5029-35, 2009.

39. C. Chevalier, F. Debbasch, J.P. Rivet: Stochastics Models of Thermodiffusion.  Mod. Phys. Lett. B. 23(9), 1147-1155, 2009.

40. C. Chevalier, F. Debbasch and Y. Ollivier: Large-scale nonlinear effects of fluctuations in relativistic gravitation. Nonlinear Analysis Series A: Theory, Methods and Applications, 71(12), 199-202, 2009.

41. F. Debbasch and W. van Leeuwen: General relativistic Boltzmann equation II: Manifestly covariant treatment. Physica A, 388(9):1818-34, 2009.

42. F. Debbasch and W. van Leeuwen: General relativistic Boltzmann equation I: Covariant treatment. Physica A, 388 (7): 1079-1104, 2009. 

43. C. Chevalier and F. Debbasch: Thermal Statistical Ensembles of Classical Extreme Black Holes. Physica A, 388: 628-638, 2009. 

44. C. Chevalier and F. Debbasch: Relativistic diffusions: a unifying approach. J. Math. Phys., 49(4):043303, 2008.

45. C. Chevalier and F. Debbasch: A unifying approach to relativistic diffusions and H-theorems. Mod. Phys. Lett. B, 22:383-392, 2008.

46. C. Chevalier and F. Debbasch: Is Brownian motion sensitive to geometry fluctuations? J. Stat. Phys., 131:717-731, 2008.

47. F. Debbasch: Equilibrium distribution function of a relativistic dilute perfect gas. Physica A, 387:2443-2454, 2008.

48. F. Debbasch and J.P. Rivet: Time-dependent transport coefficients: an effective macroscopic description of small-scale dynamics? Comptes Rendus Physique de l’Acad´emie des Sciences, 9:767-772, 2008.

49. C. Chevalier and F. Debbasch: Multi-scale diffusion on an interface. Eur. Phys. Lett., 77:20005–20009, 2007.

50. C. Chevalier and F. Debbasch: Fluctuation-Dissipation Theorems in an Expanding Universe. J. Math. Phys., 48:023304, 2007.

51. C. Chevalier, M. Bustamante, F. Debbasch. Thermal Statistical Ensembles of Black Holes. Physica A, 376:293-307, 2007.

52. F. Debbasch, L. Herrera, P.R.C.T. Pereira and N.O. Santos: Stationary Cylindrical Anisotropic Fluid. Gen. Rel. Grav., 38:1825, 2006.

53. M. Rigotti , F. Debbasch. An H-theorem for the General Relativistic Ornstein-Uhlenbeck process. J. Math. Phys., 46:103303, 2005.

54. C. Cichowlas, C. Bonaïti, F. Debbasch and M. Brachet. Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows. Phys. Rev. Lett., 95:264502, 2005.

55. F. Debbasch and Y. Ollivier. Observing a Schwarzschild black-hole with finite precision. Astron. Astrophys., 433(2):397, 2005.

56. F. Debbasch. Mean field theory and geodesics in general relativity. Eur. Phys. J. B, 43(1):143, 2005.

57. F. Debbasch and M. Moreau. Diffusion on a curved surface: A geometrical approach. Phys. A, 343:81, 2004. 

58. F. Debbasch. A diffusion process in curved space-time. J. Math. Phys., 45(7):2744, 2004. 

59. F. Debbasch. What is a mean gravitational field? Eur. Phys. J. B, 37(2):257, 2004. 

60. F. Debbasch, J.P. Rivet and W.A. van Leeuwen. Invariance of the relativistic one-particle distribution function. Physica A, 301:181, 2001.

61. C. Barbachoux, F. Debbasch and J.P. Rivet. Covariant Kolmogorov equation and entropy current for the relativistic Ornstein-Uhlenbeck process. Eur. Phys. J. B., 24:487, 2001. 

62. C. Barbachoux, F. Debbasch and J.P. Rivet. The spatially one-dimensional relativistic Ornstein-Uhlenbck process in an arbitrary inertial frame. Eur. Phys. J. B., 19:37, 2001. 

63. C. Huepe, F. Debbasch and M.E. Brachet. Generic inflationary and non-inflationary behavior in toy-cosmology. Physica D, 144:20, 2000.

64. C. Barbachoux, F. Debbasch and J.P. Rivet. Hydrodynamic behavior of Brownian particles in a position-dependent constant force-field. J. Math. Phys., 40:2891, 1999. 

65. F. Debbasch and J.P. Rivet. A diffusion equation from the relativistic Ornstein- Uhlenbeck process. J. Stat. Phys., 90:1179, 1998. 

66. F. Debbasch, K. Mallick and J.P. Rivet. Relativistic Ornstein-Uhlenbeck process. J. Stat. Phys., 88:945, 1997. 

67. F. Debbasch and M.E. Brachet. Non-linear acoustics in Galilean and relativistic fluids. Physica D, 108:135, 1997. 

68. F. Debbasch and M.E. Brachet. Relativistic hydrodynamics of semiclassical fluids.Physica D, 82:255, 1995. 

69. F. Debbasch. Global potentials for general relativistic flows of ideal charged fluids.J. Math. Phys., 35:5718, 1994. 

70. F. Debbasch. Classical Mechanics and gauge theories. Am. J. Phys., 61:1131, 1993. 

71. F. Debbasch. Self-consistent stationary models of 2D barred galaxies. Nuov. Cim. B, 107:1099, 1992. 

72. F. Combes, F. Debbasch, D. Friedli, and D. Pfenniger. Box and peanut shapes generated by stellar bars. Astron. Astrophys., 233:32, 1990.

Proceedings

• 1. F. Debbasch: The gambler's ruin problem and quantum measurement. Proceedings of Quantum Simulation and Quantum Walks 2020, QSQW2020, https://arxiv.org/abs/2004.01335.

  2. D. Espaze, V. Foulonneau, F. Debbasch and G. Di Molfetta: Propagation in quantum walks and relativistic diffusions, Physica Scripta, 014044, 2012.

  3. C. Chevalier and F. Debbasch: Effective large-scale diffusions on fluctuating interfaces, JOP Conference Series, 246, 012027, 2010.

  4. C. Chevalier, F. Debbasch and Y. Ollivier: Gravitational waves and cosmological back-reaction, JOP Conference Series, 228, 012054, 2010

  5. C. Chevalier and F. Debbasch: Diffusion Processes on Manifolds. ‘Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz’. Lecture Notes and Monographs Series, Institute of Mathematical Statistics, 2009. 

  6. C. Chevalier, F. Debbasch and J.P. Rivet: A stochastic approach to thermodiffusion. Proceedings of the Second International Forum on Heat Transfer (IFHT08), Sept. 17-19, Tokyo, Japan, Heat Transfer Society of Japan, 2008. 

  7. C. Chevalier, F. Debbasch and J.P. Rivet: A review of finite speed transport models. Proceedings of the Second International Forum on Heat Transfer (IFHT08), Sept. 17-19, Tokyo, Japan, Heat Transfer Society of Japan, 2008. 

  8. C. Chevalier and F. Debbasch: Brownian Motion and Entropy Growth on irregular Surfaces. International Journal of Numerical Analysis and Modeling, Vol. 5, Special Issue on Modeling, Analysis and Simulations of Multiscale Nonlinear Systems, M. Peszynska, R. Showalter, A. Spagnuolo and N. Walkington: guest editors, pp. 36-46, 2008. 

  9. C. Chevalier and F. Debbasch: Multi-scale diffusions on biological interfaces. Proceedings of the Seventh International Conference on Complex Systems, Oct. 28- Nov.2 2007, Editors Ali Minai, Dan Braha, Yaneer Bar-Yam, 2008. 

  10. C. Chevalier and F. Debbasch: Is matter an emergent property of space-time? Proceedings of the Seventh International Conference on Complex Systems, Oct. 28- Nov.2 2007, Editors Ali Minai, Dan Braha, Yaneer Bar-Yam, 2008. 

  11. F. Debbasch and C. Chevalier: Relativistic Stochastic Processes. In O. Descalzi, O.A. Rosso and H.A. Larrondo, editors, Proceedings of ‘Medyfinol 2006, No- nequilibrium Statistical Mechanics and Nonlinear Physics, XV Conference on Nonequilibrium Statistical Mechanics and Nonlinear Physics, Mar del Plata, Argentina, Dec. 4-8 2006’. American Institute of Physics, A.I.P. Conference Proceedings 913, Melville, NY, 2007.

  12. C. Chevalier and F. Debbasch: Relativistic Transport and Fluctuation-Dissipation Theorems. Accepted for publication in “17th International Symposium on Transport Phenomena”, Toyama, Japan, 2006, M. Ishizuka, editor.

  13. C. Chevalier and F. Debbasch: Mean Field Theory and General Relativistic Black Holes. In F. Combes and R. Robert, editors: Statistical Mechanics of non-extensive systems, Paris 2005. Cr. Acad. Sc. (2006). 

  14. C. Chevalier and F. Debbasch: Mean Field Theory and Astrophysical Black holes. In J.M. Alimi and A. Fuzfa, editors: Albert Einstein Century Interna- tional Conference, Unesco, Paris 2005. AIP Conference Proceedings 861, AIP (2006). 

  15. F. Debbasch: Relativistic Stochastic Processes: a Review. In J.M. Alimi and A. Fuzfa, editors: Albert Einstein Century International Conference, Unesco, Paris 2005. AIP Conference Proceedings 861, AIP (2006). 

  16. C. Cichowlas, F. Debbasch and M. Brachet. Evolution of complex singularities and Kolmogorov scaling in truncated 3-D Euler flows. UTAM, Kyoto, 2005. 

  17. C. Huepe, F. Debbasch and M.E. Brachet. Hydrodynamical interpretation of relativistic charged scalar field dynamics. In M. Signore and F. Melchiorri, editors, Topological Defects in Cosmology, 1997. 

  18. M. Abid, M.E. Brachet, F. Debbasch and C. Nore. Galilean and relativistic nonlinear equations: a hydrodynamical tool? In E. Tirapeguy and W. Zeller, editors, Instabilities and Non-equilibrium Structures V.. Kluwer Academic Publishers, 1996.

Preprints

• 1. M. Bustamante, F. Debbasch, M. Brachet. General relativity as free membrane dynamics.

  2. F. Debbasch: On the classical and quantum Langevin dynamics.

Varia

• 1. F. Debbasch and G. Bonneau. Description hydrodynamique d’un plasma relativiste. Rapport CEA, 1991. 

  2. J.P. Rivet, F. Debbasch and C. Barbachoux. Bulletin de l’A.D.I.O.N., 31, 1997.