- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Evolving disorder in non-Hermitian lattices

I. Komis, E. T. Kokkinakis, K. G. Makris*, and E. N. Economou

  • *Contact author: makris@physics.uoc.gr
PDF

Phys. Rev. Research 8, 023227 – Published 29 May, 2026

DOI: https://doi.org/10.1103/4z9l-63lr

Abstract

The impact of disorder on wave transport has been extensively studied in Hermitian systems, where static randomness gives rise to Anderson localization. In non-Hermitian lattices, static disorder can lead to peculiar transport features, including jumpy wave evolution. In contrast, much less is known about how transport is modified when the on-site disorder evolves during propagation. Here, we address this problem by investigating two pertinent non-Hermitian lattice models with disorder altered at regular intervals, characterized by a finite disorder period. In lattices with symmetric couplings and complex on-site disorder, short disorder periods suppress localization and give rise to diffusionlike spreading, while longer periods allow the emergence of jumps. In Hatano-Nelson lattices with real on-site disorder, the non-Hermitian skin effect asymptotically dominates regardless of the disorder strength, while the disorder period reshapes the drift velocity and modulates its competition with Anderson localization. These results establish evolving disorder as a way of tuning non-Hermitian transport.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (124)

  1. P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109, 1492 (1958).
  2. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Scaling theory of localization: Absence of quantum diffusion in two dimensions, Phys. Rev. Lett. 42, 673 (1979).
  3. P. A. Lee and T. V. Ramakrishnan, Disordered electronic systems, Rev. Mod. Phys. 57, 287 (1985).
  4. F. Evers and A. D. Mirlin, Anderson transitions, Rev. Mod. Phys. 80, 1355 (2008).
  5. C. A. Condat and T. R. Kirkpatrick, Observability of acoustical and optical localization, Phys. Rev. Lett. 58, 226 (1987).
  6. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Direct observation of Anderson localization of matter waves in a controlled disorder, Nature (London) 453, 891 (2008).
  7. G. Roati, C. D’ Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Anderson localization of a non-interacting Bose–Einstein condensate, Nature (London) 453, 895 (2008).
  8. J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J.-C. Garreau, Experimental observation of the Anderson metal–insulator transition with the atomic kicked rotor, Phys. Rev. Lett. 101, 255702 (2008).
  9. H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. van Tiggelen, Localization of ultrasound in a three-dimensional elastic network, Nat. Phys. 4, 945 (2008).
  10. S. John, Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett. 58, 2486 (1987).
  11. K. Busch and C. M. Soukoulis, Transport properties of random media: A new effective medium theory, Phys. Rev. Lett. 75, 3442 (1995).
  12. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Localization of light in a disordered medium, Nature (London) 390, 671 (1997).
  13. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Transport and Anderson localization in disordered two-dimensional photonic lattices, Nature (London) 446, 52 (2007).
  14. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Anderson localization and nonlinearity in one-dimensional disordered photonic lattices, Phys. Rev. Lett. 100, 013906 (2008).
  15. S. Stützer, U. Peschel, C. R. Rosberg, F. Lederer, R. Morandotti, D. N. Christodoulides, and A. Szameit, Anderson cross-localization, Opt. Lett. 37, 1715 (2012).
  16. S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, Observation of transverse Anderson localization in an optical fiber, Opt. Lett. 37, 2304 (2012).
  17. G. Pelc, S. Guterman, R. Gutiérrez-Cuevas, A. Goetschy, S. M. Popoff, and Y. Bromberg, Open transmission channels in multimode fiber cavities with random mode mixing, Phys. Rev. Lett. 135, 173801 (2025).
  18. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Discretizing light behaviour in linear and nonlinear waveguide lattices, Nature (London) 424, 817 (2003).
  19. J. Wang and A. Z. Genack, Transport through modes in random media, Nature (London) 471, 345 (2011).
  20. M. Segev, Y. Silberberg, and D. N. Christodoulides, Anderson localization of light, Nat. Photonics 7, 197 (2013).
  21. H. H. Sheinfux, Y. Lumer, G. Ankonina, A. Z. Genack, G. Bartal, and M. Segev, Observation of Anderson localization in disordered nanophotonic structures, Science 356, 953 (2017).
  22. A. Dikopoltsev, S. Weidemann, M. Kremer, A. Steinfurth, H. H. Sheinfux, A. Szameit, and M. Segev, Observation of Anderson localization beyond the spectrum of the disorder, Sci. Adv. 8, eabn7769 (2022).
  23. Z. Cherpakova, F. Bleckmann, T. Vogler, and S. Linden, Transverse Anderson localization of surface plasmon polaritons, Opt. Lett. 42, 2165 (2017).
  24. S. Pandey, B. Gupta, S. Mujumdar, and A. Nahata, Direct observation of Anderson localization in plasmonic terahertz devices, Light: Sci. Appl. 6, e16232 (2017).
  25. J. Duan, S. Xiao, and J. Chen, Anderson localized plasmon in graphene with random tensile-strain distribution, Adv. Sci. 6, 1801974 (2019).
  26. E. T. Kokkinakis, I. Komis, K. G. Makris, and E. N. Economou, Non-Hermitian off-diagonal disordered optical lattices, Phys. Rev. B 113, 174210 (2026).
  27. Y. Zhu, H. Jing, R.-W. Peng, C.-Y. Li, J. He, B. Xiong, and M. Wang, Realizing Anderson localization of surface plasmon polaritons and enhancing their interactions with excitons in 2D disordered nanostructures, Appl. Phys. Lett. 116, 201106 (2020).
  28. C. M. Bender and S. Boettcher, Real spectra in non-Hermitian Hamiltonians having PT symmetry, Phys. Rev. Lett. 80, 5243 (1998).
  29. R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, Theory of coupled optical PT-symmetric structures, Opt. Lett. 32, 2632 (2007).
  30. K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, Beam dynamics in PT symmetric optical lattices, Phys. Rev. Lett. 100, 103904 (2008).
  31. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, Optical solitons in PT periodic potentials, Phys. Rev. Lett. 100, 030402 (2008).
  32. A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Observation of PT-symmetry breaking in complex optical potentials, Phys. Rev. Lett. 103, 093902 (2009).
  33. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, Observation of parity–time symmetry in optics, Nat. Phys. 6, 192 (2010).
  34. A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, Parity–time synthetic photonic lattices, Nature (London) 488, 167 (2012).
  35. H. Hodaei, M.-A. Miri, M. Heinrich, D. N. Christodoulides, and M. Khajavikhan, Parity-time–symmetric microring lasers, Science 346, 975 (2014).
  36. L. Feng, R. El-Ganainy, and L. Ge, Non-Hermitian photonics based on parity–time symmetry, Nat. Photonics 11, 752 (2017).
  37. R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Non-Hermitian physics and PT symmetry, Nat. Phys. 14, 11 (2018).
  38. S. K. Özdemir, S. Rotter, F. Nori, and L. Yang, Parity–time symmetry and exceptional points in photonics, Nat. Mater. 18, 783 (2019).
  39. V. V. Konotop, J. Yang, and D. A. Zezyulin, Nonlinear waves in PT-symmetric systems, Rev. Mod. Phys. 88, 035002 (2016).
  40. M. A. Miri and A. Alu, Exceptional points in optics and photonics, Science 363, eaar7709 (2019).
  41. Y. D. Chong, L. Ge, and A. D. Stone, PT-Symmetry breaking and laser-absorber modes in optical scattering systems, Phys. Rev. Lett. 106, 093902 (2011).
  42. L. Ge, Y. D. Chong, and A. D. Stone, Conservation relations and anisotropic transmission resonances in one-dimensional PT-symmetric photonic heterostructures, Phys. Rev. A 85, 023802 (2012).
  43. L. Feng, Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies, Nat. Mater. 12, 108 (2013).
  44. B. Peng, S. K. Ozdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Parity–time-symmetric whispering-gallery microcavities, Nat. Phys. 10, 394 (2014).
  45. L. Feng, Z. Jing Wong, R.-M. Ma, Y. Wang, and X. Zhang, Single-mode laser by parity-time symmetry breaking, Science 346, 972 (2014).
  46. B. Peng, S. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, Loss-induced suppression and revival of lasing, Science 346, 328 (2014).
  47. S. Assawaworrarit, X. Yu, and S. Fan, Robust wireless power transfer using a nonlinear parity–time-symmetric circuit, Nature (London) 546, 387 (2017).
  48. J. Zhang, B. Peng, S. K. Özdemir, K. Pichler, D. O. Krimer, G. Zhao, F. Nori, Y. Liu, S. Rotter, and L. Yang, A phonon laser operating at an exceptional point, Nat. Photonics 12, 479 (2018).
  49. H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, Enhanced sensitivity at higher-order exceptional points, Nature (London) 548, 187 (2017).
  50. M. P. Hokmabadi, A. Schumer, D. N. Christodoulides, and M. Khajavikhan, Non-Hermitian ring laser gyroscopes with enhanced Sagnac sensitivity, Nature (London) 576, 70 (2019).
  51. S. Xia, D. Kaltsas, D. Song, I. Komis, J. Xu, A. Szameit, H. Buljan, K. G. Makris, and Z. Chen, Nonlinear tuning of PT symmetry and non-Hermitian topological states, Science 372, 72 (2021).
  52. I. Komis, D. Kaltsas, S. Xia, H. Buljan, Z. Chen, and K. G. Makris, Robustness versus sensitivity in non-Hermitian topological lattices probed by pseudospectra, Phys. Rev. Res. 4, 043219 (2022).
  53. I. Komis and K. G. Makris, Angular excitation of exceptional points and pseudospectra of photonic lattices, J. Phys. Photonics 6, 045011 (2024).
  54. E. T. Kokkinakis, I. Komis, K. G. Makris, and E. N. Economou, Non-Hermitian impurity problem, Commun. Phys. 9, 152 (2026).
  55. N. Hatano and D. R. Nelson, Localization transitions in non-Hermitian quantum mechanics, Phys. Rev. Lett. 77, 570 (1996).
  56. T. E. Lee, Anomalous edge state in a non-Hermitian lattice, Phys. Rev. Lett. 116, 133903 (2016).
  57. S. Yao and Z. Wang, Edge states and topological invariants of non-Hermitian systems, Phys. Rev. Lett. 121, 086803 (2018).
  58. D. A. Dobrykh, A. V. Yulin, A. P. Slobozhanyuk, A. N. Poddubny, and Y. S. Kivshar, Nonlinear control of electromagnetic topological edge states, Phys. Rev. Lett. 121, 163901 (2018).
  59. C. Hang, D. A. Zezyulin, G. Huang, and V. V. Konotop, Nonlinear topological edge states in a non-Hermitian array of optical waveguides embedded in an atomic gas, Phys. Rev. A 103, L040202 (2021).
  60. M. Ezawa, Dynamical nonlinear higher-order non-Hermitian skin effects and topological trap-skin phase, Phys. Rev. B 105, 125421 (2022).
  61. B. Zhu, Q. Wang, D. Leykam, H. Xue, Q. J. Wang, and Y. D. Chong, Anomalous single-mode lasing induced by nonlinearity and the non-Hermitian skin effect, Phys. Rev. Lett. 129, 013903 (2022).
  62. Y. G. N. Liu et al., Complex skin modes in non-Hermitian coupled laser arrays, Light: Sci. Appl. 11, 336 (2022).
  63. I. Komis, Z. H. Musslimani, and K. G. Makris, Skin solitons, Opt. Lett. 48, 6525 (2023).
  64. S. Wang, B. Wang, C. Liu, C. Qin, L. Zhao, W. Liu, S. Longhi, and P. Lu, Nonlinear non-Hermitian skin effect and skin solitons in temporal photonic feedforward lattices, Phys. Rev. Lett. 134, 243805 (2025).
  65. E. T. Kokkinakis, I. Komis, and K. G. Makris, Self-trapping and skin solitons in two-dimensional non-Hermitian lattices, Commun. Phys. 9, 22 (2026).
  66. S. Li, M. Hu, J. Lin, C. Fang, Z. Tao, and K. Ding, Soliton transitions mediated by skin-mode localization and band nonreciprocity, arXiv:2508.02311.
  67. B. Many Manda and V. Achilleos, Insensitive edge solitons in a non-Hermitian topological lattice, Phys. Rev. B 110, L180302 (2024).
  68. S. Longhi, Modulational instability and dynamical growth blockade in the nonlinear Hatano–Nelson model, Adv. Phys. Res. 4, 2400154 (2025).
  69. H. Ghaemi-Dizicheh, A class of stable nonlinear non-Hermitian skin modes, Phys. Scr. 99, 125411 (2024).
  70. C. Yuce, Nonlinear skin modes and fixed points, Phys. Rev. B 111, 054201 (2025).
  71. A. F. Tzortzakakis, K. G. Makris, and E. N. Economou, Non-Hermitian disorder in two-dimensional optical lattices, Phys. Rev. B 101, 014202 (2020).
  72. Y. Huang and B. I. Shklovskii, Anderson transition in three-dimensional systems with non-Hermitian disorder, Phys. Rev. B 101, 014204 (2020).
  73. P. O. Sukhachov and A. V. Balatsky, Non-Hermitian impurities in Dirac systems, Phys. Rev. Res. 2, 013325 (2020).
  74. H. Liu, Z. Su, Z.-Q. Zhang, and H. Jiang, Topological Anderson insulator in two-dimensional non-Hermitian systems, Chin. Phys. B 29, 050502 (2020).
  75. E. T. Kokkinakis, K. G. Makris, and E. N. Economou, Anderson localization versus hopping asymmetry in a disordered lattice, Phys. Rev. A 110, 053517 (2024).
  76. A. F. Tzortzakakis, K. G. Makris, A. Szameit, and E. N. Economou, Transport and spectral features in non-Hermitian open systems, Phys. Rev. Res. 3, 013208 (2021).
  77. A. Leventis, K. G. Makris, and E. N. Economou, Non-Hermitian jumps in disordered lattices, Phys. Rev. B 106, 064205 (2022).
  78. S. Weidemann, M. Kremer, S. Longhi, and A. Szameit, Coexistence of dynamical delocalization and spectral localization through stochastic dissipation, Nat. Photonics 15, 576 (2021).
  79. Y. He and T. Ozawa, Anomalous wave-packet dynamics in one-dimensional non-Hermitian lattices, arXiv:2512.07484.
  80. X. Luo, T. Ohtsuki, and R. Shindou, Universality classes of the Anderson transitions driven by non-Hermitian disorder, Phys. Rev. Lett. 126, 090402 (2021).
  81. K. Kawabata and S. Ryu, Nonunitary scaling theory of non-Hermitian localization, Phys. Rev. Lett. 126, 166801 (2021).
  82. X. Luo, Z. Xiao, K. Kawabata, T. Ohtsuki, and R. Shindou, Unifying the Anderson transitions in Hermitian and non-Hermitian systems, Phys. Rev. Res. 4, L022035 (2022).
  83. S. Longhi, Anderson localization in dissipative lattices, Ann. Phys. (Berlin) 535, 2200658 (2023).
  84. B. P. Nguyen and K. Kim, Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations, J. Phys. A: Math. Theor. 56, 475701 (2023).
  85. J.-R. Li, S.-F. Zhang, L.-L. Zhang, and W.-J. Gong, Localization in the one-dimensional quantum chain with nonreciprocal disorder, Phys. Rev. B 110, 085409 (2024).
  86. I. Komis, K. G. Makris, K. Busch, and R. El-Ganainy, Effect of imaginary gauge on wave transport in driven-dissipative systems, Phys. Rev. A 112, 043524 (2025).
  87. W.-W. Jin, J. Liu, X. Wang, Y.-R. Zhang, X. Huang, X. Wei, W. Ju, Z. Yang, T. Liu, and F. Nori, Anderson delocalization in strongly coupled disordered non-Hermitian chains, Phys. Rev. Lett. 135, 076602 (2025).
  88. W. Wang, X. Wang, and G. Ma, Anderson Transition at Complex Energies in One-Dimensional Parity-Time-Symmetric Disordered Systems, Phys. Rev. Lett. 134, 066301 (2025).
  89. K. G. Makris, A. Brandstotter, P. Ambichl, Z. H. Musslimani, and S. Rotter, Wave propagation through disordered media without backscattering and intensity variations, Light: Sci. Appl. 6, e17035 (2017).
  90. K. G. Makris, I. Kresic, A. Brandstotter, and S. Rotter, Scattering-free channels of invisibility across non-Hermitian media, Optica 7, 619 (2020).
  91. I. Komis, S. Sardelis, Z. H. Musslimani, and K. G. Makris, Equal-intensity waves in non-Hermitian media, Phys. Rev. E 102, 032203 (2020).
  92. C. E. Rivet, A. Brandstötter, K. G. Makris, H. Lissek, S. Rotter, and R. Fleury, Constant-pressure sound waves in non-Hermitian disordered media, Nat. Phys. 14, 942 (2018).
  93. A. Steinfurth, I. Krešić, S. Weidemann, M. Kremer, K. G. Makris, M. Heinrich, S. Rotter, and A. Szameit, Observation of photonic constant-intensity waves and induced transparency in tailored non-Hermitian lattices, Sci. Adv. 8, eabl7412 (2022).
  94. L. Li, C. H. Lee, and J. Gong, Impurity induced scale-free localization, Commun. Phys. 4, 42 (2021).
  95. C.-X. Guo, X. Wang, H. Hu, and S. Chen, Accumulation of scale-free localized states induced by local non-Hermiticity, Phys. Rev. B 107, 134121 (2023).
  96. B. Li, H.-R. Wang, F. Song, and Z. Wang, Scale-free localization and PT symmetry breaking from local non-Hermiticity, Phys. Rev. B 108, L161409 (2023).
  97. P. Molignini, O. Arandes, and E. J. Bergholtz, Anomalous skin effects in disordered systems with a single non-Hermitian impurity, Phys. Rev. Res. 5, 033058 (2023).
  98. G.-J. Liu, J.-M. Zhang, S.-Z. Li, and Z. Li, Emergent strength-dependent scale-free mobility edge in a nonreciprocal long-range Aubry-André-Harper model, Phys. Rev. A 110, 012222 (2024).
  99. W. Li, Z. Sun, Z. Yang, and F. Li, Universal scale-free non-Hermitian skin effect near the Bloch point, Phys. Rev. B 109, 035119 (2024).
  100. B. Yılmaz, C. Yuce, and C. Bulutay, From scale-free to Anderson localization: A size-dependent transition, Phys. Rev. B 110, 214206 (2024).
  101. C. Yuce, Scale-free localization: The role of semi-edges, Phys. Scr. 100, 035009 (2025).
  102. Y. Zhang, L. Su, and S. Chen, Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices, Phys. Rev. B 111, L140201 (2025).
  103. D. E. Logan and P. G. Wolynes, Dephasing and Anderson localization in topologically disordered systems, Phys. Rev. B 36, 4135 (1987).
  104. D. A. Evensky, R. T. Scalettar, and P. G. Wolynes, Localization and dephasing effects in a time-dependent Anderson Hamiltonian, J. Phys. Chem. 94, 1149 (1990).
  105. J. C. Flores, Diffusion in disordered systems under iterative measurement, Phys. Rev. B 60, 30 (1999).
  106. H. Yamada and K. S. Ikeda, Dynamical delocalization in one-dimensional disordered systems with oscillatory perturbation, Phys. Rev. E 59, 5214 (1999).
  107. S. A. Gurvitz, Delocalization in the Anderson model due to a local measurement, Phys. Rev. Lett. 85, 812 (2000).
  108. J. Košík, V. Bužek, and M. Hillery, Quantum walks with random phase shifts, Phys. Rev. A 74, 022310 (2006).
  109. A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, I. Jex, and C. Silberhorn, Decoherence and disorder in quantum walks: From ballistic spread to localization, Phys. Rev. Lett. 106, 180403 (2011).
  110. I. L. Garanovich, S. Longhi, A. A. Sukhorukov, and Y. S. Kivshar, Light propagation and localization in modulated photonic lattices and waveguides, Phys. Rep. 518, 1 (2012).
  111. J. M. Moix, M. Khasin, and J. Cao, Coherent quantum transport in disordered systems: I. The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems, New J. Phys. 15, 085010 (2013).
  112. M. Žnidarič and M. Horvat, Transport in a disordered tight-binding chain with dephasing, Eur. Phys. J. B 86, 67 (2013).
  113. P. L. Krapivsky, J. M. Luck, and K. Mallick, Survival of classical and quantum particles in the presence of traps, J. Stat. Phys. 154, 1430 (2014).
  114. N. Kamiya, Quantum-to-classical reduction of quantum master equations, Prog. Theor. Exp. Phys. 2015, 043A02 (2015).
  115. L. Levi, Y. Krivolapov, S. Fishman, and M. Segev, Hyper-transport of light and stochastic acceleration by evolving disorder, Nat. Phys. 8, 912 (2012).
  116. A. Dikopoltsev, H. Herzig Sheinfux, and M. Segev, Localization by virtual transitions in correlated disorder, Phys. Rev. B 100, 140202(R) (2019).
  117. S. Longhi, Dephasing-induced mobility edges in quasicrystals, Phys. Rev. Lett. 132, 236301 (2024).
  118. E. T. Kokkinakis, K. G. Makris, and E. N. Economou, Dephasing-induced jumps in non-Hermitian disordered lattices, Phys. Rev. B 111, 214204 (2025).
  119. E. T. Kokkinakis, K. G. Makris, and E. N. Economou, Defect-driven incoherent skin localization, Phys. Rev. Res. 8, L012024 (2026).
  120. S. Wang, C. Qin, W. Liu, B. Wang, F. Zhou, H. Ye, L. Zhao, J. Dong, X. Zhang, S. Longhi, and P. Lu, High-order dynamic localization and tunable temporal cloaking in ac-electric-field driven synthetic lattices, Nat. Commun. 13, 7653 (2022).
  121. S. Longhi, Delocalization of light in photonic lattices with unbounded potentials, Opt. Lett. 48, 5293 (2023).
  122. S. Longhi, Algebraic localization–delocalization phase transition in moving potential wells on a lattice, Ann. Phys. (Berlin) 536, 2300488 (2024).
  123. L. Yu and B. Zhang, Energy variation in stochastically driven light walks [Invited], Opt. Mater. Express 15, 555 (2025).
  124. Let us note that the velocity definition used in Ref. [75], where the disorder-induced enhancement of velocity in the skin-effect-dominated regime was first reported, differs from the one employed here, leading to minor quantitative discrepancies.

Outline

Information

Phys. Rev. Research 8, 023227– Published 29 May, 2026
  • Received 1 December 2025
  • Accepted 30 March 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation