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Stochastic cloaking: Concealing a region from diffusive particles

Connor Roberts1,*, Ziluo Zhang1,2, Helder Rojas3, Stefano Bo4, Carlos Escudero3, Sébastien Guenneau5,†, and Gunnar Pruessner1,‡

  • *Contact author: connor.roberts16@imperial.ac.uk
  • †Contact author: s.guenneau@imperial.ac.uk
  • ‡Contact author: g.pruessner@imperial.ac.uk
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Phys. Rev. Research 7, L032025 – Published 4 August, 2025

DOI: https://doi.org/10.1103/mwxh-g9d5

Abstract

We introduce “stochastic cloaking,” where a region of space is concealed from an ensemble of diffusing particles whose individual trajectories are governed by a stochastic (Langevin) equation. Our simulations reveal how different interpretations of the Langevin equation affect the cloaking performance of an annular single-layer invisibility cloak of smoothly varying diffusivity in two dimensions. Near-perfect cloaking is achieved under the Itô convention, indicated by the cloak preventing particles from accessing an inner core without disturbing the particle density outside the cloak. The cloak's performance can be further improved by regularizing its singular behavior. We believe our demonstration of stochastic cloaking is a significant milestone, comparable to earlier developments that extended cloaking from optics and acoustics to thermodynamics.

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References (37)

  1. R. A. Shelby, D. R. Smith, and S. Schultz, Experimental verification of a negative index of refraction, Science 292, 77 (2001).
  2. D. R. Smith, W. J. Padilla, D. Vier, S. C. Nemat-Nasser, and S. Schultz, Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett. 84, 4184 (2000).
  3. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, Cloaking devices, electromagnetic wormholes, and transformation optics, SIAM Rev. 51, 3 (2009).
  4. U. Leonhardt, Optical conformal mapping, Science 312, 1777 (2006).
  5. A. Ward and J. B. Pendry, Refraction and geometry in Maxwell's equations, J. Mod. Opt. 43, 773 (1996).
  6. J. B. Pendry, D. Schurig, and D. R. Smith, Controlling electromagnetic fields, Science 312, 1780 (2006).
  7. S. Guenneau, C. Amra, and D. Veynante, Transformation thermodynamics: Cloaking and concentrating heat flux, Opt. Express 20, 8207 (2012).
  8. R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, Experiments on transformation thermodynamics: Molding the flow of heat, Phys. Rev. Lett. 110, 195901 (2013).
  9. M. Raza, Y. Liu, E. H. Lee, and Y. Ma, Transformation thermodynamics and heat cloaking: A review, J. Opt. 18, 044002 (2016).
  10. S. A. Cummer and D. Schurig, One path to acoustic cloaking, New J. Phys. 9, 45 (2007).
  11. G. W. Milton, M. Briane, and J. R. Willis, On cloaking for elasticity and physical equations with a transformation invariant form, New J. Phys. 8, 248 (2006).
  12. N. G. Van Kampen, Itô versus Stratonovich, J. Stat. Phys. 24, 175 (1981).
  13. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, New York, 1992), Vol. 1.
  14. C. Escudero and H. Rojas, Itô versus Hänggi-Klimontovich, arXiv:2309.03654.
  15. R. Yuan and P. Ao, Beyond Itô versus Stratonovich, J. Stat. Mech. (2012) P07010.
  16. R. Mannella and P. V. McClintock, Itô versus Stratonovich: 30 years later, FNL 11, 1240010 (2012).
  17. K. Itô, Stochastic integral, Proc. Imp. Acad. Japan 20, 519 (1944).
  18. R. L. Stratonovich, A new representation for stochastic integrals and equations, SIAM J. Control 4, 362 (1966).
  19. A. Pacheco-Pozo, M. Balcerek, A. Wyłomanska, K. Burnecki, I. M. Sokolov, and D. Krapf, Langevin equation in heterogeneous landscapes: How to choose the interpretation, Phys. Rev. Lett. 133, 067102 (2024).
  20. A. W. Lau and T. C. Lubensky, State-dependent diffusion: Thermodynamic consistency and its path integral formulation, Phys. Rev. E 76, 011123 (2007).
  21. Á. Correales and C. Escudero, Itô vs Stratonovich in the presence of absorbing states, J. Math. Phys. 60, 123301 (2019).
  22. C. Escudero, Kinetic energy of the Langevin particle, Stud. Appl. Math. 145, 719 (2020).
  23. C. Escudero, Fluctuation-dissipation relation, Maxwell-Boltzmann statistics, equipartition theorem, and stochastic calculus, Phys. Scr. 98, 055214 (2023).
  24. G. Vaccario, C. Antoine, and J. Talbot, First-passage times in d-dimensional heterogeneous media, Phys. Rev. Lett. 115, 240601 (2015).
  25. P. Hänggi, Stochastic processes I: Asymptotic behaviour and symmetries, Helv. Phys. Acta 51, 183 (1978).
  26. Y. L. Klimontovich, Nonlinear Brownian motion, Phys. Usp. 37, 737 (1994).
  27. I. M. Sokolov, Ito, Stratonovich, Hänggi and all the rest: The thermodynamics of interpretation, Chem. Phys. 375, 359 (2010).
  28. R. Perez–Carrasco and J. Sancho, Stochastic algorithms for discontinuous multiplicative white noise, Phys. Rev. E 81, 032104 (2010).
  29. F. Sagués, J. M. Sancho, and J. García-Ojalvo, Spatiotemporal order out of noise, Rev. Mod. Phys. 79, 829 (2007).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/mwxh-g9d5 for more detailed derivations and pseudocode for implementing simulations.
  31. E. P. Hsu, Stochastic Analysis on Manifolds (American Mathematical Society, Providence, 2002), Vol. 38.
  32. A. Greenleaf, M. Lassas, and G. Uhlmann, Anisotropic conductivities that cannot be detected by EIT, Physiol. Meas. 24, 413 (2003).
  33. A. Greenleaf, M. Lassas, and G. Uhlmann, On nonuniqueness for Calderón's inverse problem, Math. Res. Lett. 10, 685 (2003).
  34. C.-W. Qiu, L. Hu, B. Zhang, B.-I. Wu, S. G. Johnson, and J. D. Joannopoulos, Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings, Opt. Express 17, 13467 (2009).
  35. S. Guenneau, A. Diatta, T. M. Puvirajesinghe, and M. Farhat, Cloaking and anamorphism for light and mass diffusion, J. Opt. 19, 103002 (2017).
  36. R. V. Craster, S. Guenneau, H. Hutridurga, and G. A. Pavliotis, Cloaking via mapping for the heat equation, Multiscale Model. Simul. 16, 1146 (2018).
  37. W. Li, J. Guan, Z. Sun, W. Wang, and Q. Zhang, A near-perfect invisibility cloak constructed with homogeneous materials, Opt. Express 17, 23410 (2009).

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Phys. Rev. Research 7, L032025– Published 4 August, 2025
  • Received 19 October 2024
  • Accepted 2 July 2025
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