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arxiv: 2606.10067 · v1 · pith:AEJHOZMMnew · submitted 2026-06-08 · ❄️ cond-mat.dis-nn · cond-mat.mes-hall· cond-mat.stat-mech

Jittery Quantum Boomerang Effect

Pedro Dornelas , Gerson J. Ferreira This is my paper

Pith reviewed 2026-06-27 13:59 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.mes-hallcond-mat.stat-mech
keywords quantum boomerang effectRashba spin-orbit couplingAnderson localizationZitterbewegungspin Hall effectdisordered 2DEGwave packet dynamicsweak antilocalization
0
0 comments X

The pith

In a disordered Rashba 2DEG, wave-packet center returns to origin with transverse motion damped by impurity scattering and longitudinal motion showing partial return at stronger disorder.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies the time evolution of a spin-polarized wave packet launched with finite x-momentum in a disordered Rashba two-dimensional electron gas. It identifies a jittery quantum boomerang in which both longitudinal and transverse displacements return toward the origin, yet through separate mechanisms. Equations of motion from the quantum kinetic equation show that impurity scattering acts as viscous damping, suppressing transient Zitterbewegung and restoring y = 0 at long times. Longitudinal motion saturates in the Drude sense at weak disorder but develops a partial return as disorder grows, marking the crossover from weak antilocalization to Anderson localization. The transverse damping is consistent with the vanishing intrinsic spin Hall conductivity of the disordered Rashba model and with time-domain observations of a transient intrinsic spin Hall effect.

Core claim

The central claim is the identification of a jittery quantum boomerang effect in which the wave-packet center returns to the origin through fundamentally distinct mechanisms: impurity scattering functions as viscous damping that eliminates transient Zitterbewegung and returns the transverse displacement to zero, while longitudinal dynamics evolve from Drude-like saturation at weak disorder to a partial return at stronger disorder that signals the weak-antilocalization to Anderson-localization transition in two dimensions.

What carries the argument

Equations of motion derived from the quantum kinetic equation, which treat impurity scattering as a viscous damping term that suppresses the transverse Zitterbewegung component.

If this is right

  • The transient intrinsic spin Hall effect appears in the time domain because transverse motion is damped while longitudinal motion is not.
  • The disordered Rashba model remains consistent with zero intrinsic spin Hall conductivity at long times.
  • Longitudinal dynamics provide a direct time-domain signature of the crossover from weak antilocalization to Anderson localization in two dimensions.
  • The Chebyshev expansion with disorder averaging confirms the kinetic-equation predictions for weak scattering.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Separate damping of transverse versus longitudinal components may permit independent tuning of spin and charge relaxation in spintronic structures.
  • The same directional distinction could appear in other two-dimensional systems that combine spin-orbit coupling with disorder.
  • Measuring the time at which transverse return saturates would give an experimental estimate of the effective viscous damping rate.

Load-bearing premise

The quantum kinetic equation reproduces the Chebyshev numerical results in the weak-scattering regime, permitting the viscous-damping interpretation for the transverse motion.

What would settle it

Observation that the transverse displacement fails to return to zero at long times in the weak-disorder limit, or that the longitudinal partial return fails to appear as disorder strength is increased.

Figures

Figures reproduced from arXiv: 2606.10067 by Gerson J. Ferreira, Pedro Dornelas.

Figure 1
Figure 1. Figure 1: (a) Band structure of the clean Rashba 2DEG, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Numerical jittery quantum boomerang dynam [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a,b) Ensemble-averaged dynamics of momentum [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

We study the dynamics of a spin-polarized wave packet in a disordered Rashba two-dimensional electron gas and identify a jittery quantum boomerang effect in which longitudinal and transverse motion return to the origin through fundamentally distinct mechanisms. Starting from an initial state with finite momentum along $x$ and spin polarized along $z$, we calculate the time evolution by combining a Chebyshev expansion of the time-evolution operator with a disorder ensemble average. In the weak-scattering regime, equations of motion derived from the quantum kinetic equation reproduce the numerical trends and show that impurity scattering acts as a viscous damping mechanism that suppresses the transient Zitterbewegung and drives the transverse displacement back to $y=0$ at long times. In contrast, the longitudinal dynamics show a Drude-like saturation at weak disorder. These results are consistent with the vanishing intrinsic spin Hall conductivity in the disordered Rashba model and with experimental observations of a transient intrinsic spin Hall effect in the time-domain. As disorder increases, the longitudinal dynamics evolve to a partial return toward the origin, which signals a transition from weak antilocalization to Anderson localization in 2D.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript examines the time evolution of an initially spin-polarized wave packet with finite x-momentum in a disordered Rashba 2DEG. Using Chebyshev polynomial expansion for numerical time evolution (with disorder averaging) combined with a quantum kinetic equation, it identifies a 'jittery quantum boomerang effect' in which transverse (y) displacement returns to the origin via impurity scattering acting as viscous damping that suppresses transient Zitterbewegung, while longitudinal (x) dynamics exhibit Drude-like saturation at weak disorder; stronger disorder induces partial return signaling a weak antilocalization to Anderson localization crossover. Results are stated to be consistent with vanishing intrinsic spin Hall conductivity.

Significance. If the claimed mechanistic distinction and kinetic-equation validation hold, the work supplies a concrete time-domain picture connecting transient spin Hall response, disorder-induced damping, and 2D localization physics in Rashba systems, extending beyond steady-state conductivity calculations.

major comments (1)
  1. [Abstract / kinetic-equation derivation] Abstract and the section deriving equations of motion from the quantum kinetic equation: the assertion that these equations 'reproduce the numerical trends' is load-bearing for the viscous-damping interpretation of transverse motion, yet the provided text supplies no quantitative metrics (overlaid plots, RMS deviations, or parameter-specific comparisons) between the kinetic-equation solution and the Chebyshev ensemble data; without such validation the damping-mechanism claim remains unverified.
minor comments (2)
  1. [Abstract] The abstract mentions consistency with vanishing spin Hall conductivity but does not cite the specific prior result or section where this consistency is demonstrated.
  2. [Numerical methods] No error bars or ensemble-size information is referenced for the Chebyshev numerics, which would strengthen the reported trends.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We appreciate the recognition of the work's potential to connect transient spin Hall dynamics with disorder-induced damping and localization. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract / kinetic-equation derivation] Abstract and the section deriving equations of motion from the quantum kinetic equation: the assertion that these equations 'reproduce the numerical trends' is load-bearing for the viscous-damping interpretation of transverse motion, yet the provided text supplies no quantitative metrics (overlaid plots, RMS deviations, or parameter-specific comparisons) between the kinetic-equation solution and the Chebyshev ensemble data; without such validation the damping-mechanism claim remains unverified.

    Authors: We agree that the current manuscript does not supply quantitative metrics or overlaid comparisons to validate the agreement between the quantum kinetic equation solutions and the Chebyshev ensemble averages. This weakens the support for the viscous-damping interpretation. In the revised version we will add overlaid plots of the transverse and longitudinal displacements obtained from both methods (for representative disorder strengths and times), together with quantitative measures such as root-mean-square deviations or time-integrated differences. These additions will appear in the section deriving the equations of motion and will be referenced from the abstract. revision: yes

Circularity Check

0 steps flagged

No circularity: independent numerical evolution and kinetic-equation derivation

full rationale

The paper computes time evolution via Chebyshev expansion of the time-evolution operator plus disorder ensemble average, then separately derives equations of motion from the quantum kinetic equation. The statement that the kinetic-equation results reproduce numerical trends is presented as an external consistency check in the weak-scattering regime, not as a definitional identity or fitted-parameter renaming. No load-bearing self-citations, ansatz smuggling, or uniqueness theorems imported from prior author work are indicated; the longitudinal/transverse mechanism distinction follows directly from the distinct terms in the derived equations of motion. The consistency note with vanishing spin Hall conductivity is external and does not reduce the central claim to its inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claim rests on standard quantum time evolution in the Rashba Hamiltonian plus ensemble averaging; no new entities are postulated.

free parameters (1)
  • disorder strength
    Varied across regimes to observe the transition from weak antilocalization to Anderson localization.
axioms (2)
  • domain assumption Rashba Hamiltonian for 2DEG with spin-orbit coupling
    Invoked as the underlying model for the disordered two-dimensional electron gas.
  • domain assumption Impurity scattering modeled via ensemble average over random potentials
    Standard treatment in mesoscopic physics for disorder effects.

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discussion (0)

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Reference graph

Works this paper leans on

74 extracted references · 3 linked inside Pith

  1. [1]

    In topological Anderson insula- tors [31–34], disorder renormalizes the Hamiltonian and induces topological phase transitions

    can be made robust against disorder in the persistent spin helix regime [19–30]. In topological Anderson insula- tors [31–34], disorder renormalizes the Hamiltonian and induces topological phase transitions. In the spin Hall effect (SHE) [35, 36], disorder and SOC jointly deter- mine the intrinsic and extrinsic contributions to the spin Hall conductivity....

    Pith/arXiv arXiv 2026

  2. [2]

    P. W. Anderson, Absence of Diffusion in Certain Random Lattices, Phys. Rev.109, 1492 (1958)

    1958

  3. [3]

    D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righ- ini, Localization of Light in a Disordered Medium, Nature 390, 671 (1997)

    1997

  4. [4]

    R. L. Weaver, Anderson Localization of Ultrasound, Wave Motion12, 129 (1990)

    1990

  5. [5]

    Billy, V

    J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Cl´ ement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Direct observation of Anderson localiza- tion of matter waves in a controlled disorder, Nature453, 891 (2008)

    2008

  6. [6]

    Roati, C

    G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. In- guscio, Anderson localization of a non-interacting Bose– Einstein condensate, Nature453, 895 (2008)

    2008

  7. [7]

    Abrahams, P

    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)

    1979

  8. [8]

    Hikami, A

    S. Hikami, A. I. Larkin, and Y. Nagaoka, Spin-Orbit In- teraction and Magnetoresistance in the Two Dimensional Random System, Prog. Theor. Phys.63, 707 (1980)

    1980

  9. [9]

    D. C. Marinescu, P. J. Weigele, D. M. Zumb¨ uhl, and J. C. Egues, Closed-Form Weak Localization Magnetoconduc- tivity in Quantum Wells with Arbitrary Rashba and Dresselhaus Spin-Orbit Interactions, Phys. Rev. Lett. 122, 156601 (2019)

    2019

  10. [10]

    F. V. Tikhonenko, D. W. Horsell, R. V. Gorbachev, and A. K. Savchenko, Weak Localization in Graphene Flakes, Phys. Rev. Lett.100, 056802 (2008)

    2008

  11. [11]

    Yan and H

    H. Yan and H. Liu, Weak Localization and Antilocal- ization in Twisted Bilayer Graphene, Phys. Rev. B107, 224205 (2023)

    2023

  12. [12]

    L. E. Golub, Theory of Weak Localization in Graphene with Spin-Orbit Interaction, Phys. Rev. B109, L121407 (2024)

    2024

  13. [13]

    Lu and S.-Q

    H.-Z. Lu and S.-Q. Shen, Weak Localization and Weak Anti-Localization in Topological Insulators, inSpintron- ics VII, Vol. 9167 (SPIE, 2014) p. 263

    2014

  14. [14]

    D. L. de Queiroz, W. F. Inoch, L. N. Rodrigues, S. O. Fer- reira, B. S. Archanjo, M. L. Peres, and S. de Castro, Weak antilocalization effect on Bi2Te3/CdTe heterostructures grown on glass substrate by molecular beam epitaxy, J. Appl. Phys.139, 035703 (2026)

    2026

  15. [15]

    J. Nag, B. Bandyopadhyay, S. Goswami, A. Bera, Y. Venkateswara, A. Chanda, S. D. Kaushik, H. Srikanth, P. D. Babu, A. Alam, and K. G. Suresh, Weak localization-antilocalization crossover and topological Hall response in the nearly compensated ferrimagnetic metal V2NbAl, Phys. Rev. B113, L020412 (2026)

    2026

  16. [16]

    J. Wang, W. Powers, Z. Zhang, M. Smith, B. J. McIn- tosh, S. K. Bac, L. Riney, M. Zhukovskyi, T. Orlova, L. P. Rokhinson, Y.-T. Hsu, X. Liu, and B. A. Assaf, Ob- servation of Coexisting Weak Localization and Supercon- ducting Fluctuations in Strained Sn1–xInxTe Thin Films, Nano Lett.22, 792 (2022)

    2022

  17. [17]

    A. H. Al-Tawhid, J. Kanter, M. Hatefipour, D. P. Kumah, J. Shabani, and K. Ahadi, Superconductivity and Weak Anti-localization at KTaO3 (111) Interfaces, J. Electron. Mater.51, 6305–6309 (2022)

    2022

  18. [18]

    C.-W. Lin, I. N. Chen, Z. Lei, and L. M. Wang, Two- dimensional-like superconducting properties and weak antilocalization transport in Fese 0.4te0.6 single crystals: Topology-driven magnetotransport, Phys. Rev. B108, 214509 (2023)

    2023

  19. [19]

    Datta and B

    S. Datta and B. Das, Electronic Analog of the Electro- optic Modulator, Appl. Phys. Lett.56, 665 (1990)

    1990

  20. [20]

    Schliemann, J

    J. Schliemann, J. C. Egues, and D. Loss, Nonballistic Spin-Field-Effect Transistor, Phys. Rev. Lett.90, 146801 (2003)

    2003

  21. [21]

    B. A. Bernevig, J. Orenstein, and S.-C. Zhang, Exact SU(2) Symmetry and Persistent Spin Helix in a Spin- Orbit Coupled System, Phys. Rev. Lett.97, 236601 (2006)

    2006

  22. [22]

    J. D. Koralek, C. P. Weber, J. Orenstein, B. A. Bernevig, S.-C. Zhang, S. Mack, and D. D. Awschalom, Emergence of the Persistent Spin Helix in Semiconductor Quantum Wells, Nature458, 610 (2009)

    2009

  23. [23]

    C. P. Weber, J. Orenstein, B. A. Bernevig, S.-C. Zhang, J. Stephens, and D. D. Awschalom, Nondiffusive Spin Dynamics in a Two-Dimensional Electron Gas, Phys. Rev. Lett.98, 076604 (2007)

    2007

  24. [24]

    M. P. Walser, C. Reichl, W. Wegscheider, and G. Salis, Direct Mapping of the Formation of a Persistent Spin Helix, Nat. Phys.8, 757 (2012)

    2012

  25. [25]

    Ishihara, Y

    J. Ishihara, Y. Ohno, and H. Ohno, Direct imag- ing of gate-controlled persistent spin helix state in a modulation-doped GaAs/AlGaAs quantum well, Appl. Phys. Express7, 013001 (2013)

    2013

  26. [26]

    J. Fu, P. H. Penteado, M. O. Hachiya, D. Loss, and J. C. Egues, Persistent Skyrmion Lattice of Noninter- acting Electrons with Spin-Orbit Coupling, Phys. Rev. Lett.117, 226401 (2016)

    2016

  27. [27]

    Altmann, F

    P. Altmann, F. G. G. Hernandez, G. J. Ferreira, M. Ko- hda, C. Reichl, W. Wegscheider, and G. Salis, Current- Controlled Spin Precession of Quasistationary Electrons in a Cubic Spin-Orbit Field, Phys. Rev. Lett.116, 196802 (2016)

    2016

  28. [28]

    Dettwiler, J

    F. Dettwiler, J. Fu, S. Mack, P. J. Weigele, J. C. Egues, D. D. Awschalom, and D. M. Zumb¨ uhl, Stretchable Per- sistent Spin Helices in GaAs Quantum Wells, Phys. Rev. X7, 031010 (2017)

    2017

  29. [29]

    G. J. Ferreira, F. G. G. Hernandez, P. Altmann, and 7 G. Salis, Spin Drift and Diffusion in One- and Two- Subband Helical Systems, Phys. Rev. B95, 125119 (2017)

    2017

  30. [30]

    P. J. Weigele, D. C. Marinescu, F. Dettwiler, J. Fu, S. Mack, J. C. Egues, D. D. Awschalom, and D. M. Zumb¨ uhl, Symmetry Breaking of the Persistent Spin He- lix in Quantum Transport, Phys. Rev. B101, 035414 (2020)

    2020

  31. [31]

    I. R. de Assis, R. Raimondi, and G. J. Ferreira, Spin Drift-Diffusion for Two-Subband Quantum Wells, Phys. Rev. B103, 165304 (2021)

    2021

  32. [32]

    Li, R.-L

    J. Li, R.-L. Chu, J. K. Jain, and S.-Q. Shen, Topological Anderson Insulator, Phys. Rev. Lett.102, 136806 (2009)

    2009

  33. [33]

    C. W. Groth, M. Wimmer, A. R. Akhmerov, J. Tworzyd lo, and C. W. J. Beenakker, Theory of the Topological Anderson Insulator, Phys. Rev. Lett.103, 196805 (2009)

    2009

  34. [34]

    B. D. Assun¸ c˜ ao, G. J. Ferreira, and C. H. Lewenkopf, Phase transitions and scale invariance in topological An- derson insulators, Phys. Rev. B109, L201102 (2024)

    2024

  35. [35]

    E. V. C. Lopes, F. C. de Lima, C. Lewenkopf, and A. Fazzio, Engineering Quantum Phases in Two Di- mensions via Vacancy-Induced Electronic Reconstruc- tion, arXiv:2603.17122 (2026)

    arXiv 2026

  36. [36]

    Nagaosa, J

    N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Anomalous Hall effect, Rev. Mod. Phys.82, 1539 (2010)

    2010

  37. [37]

    Sinova, S

    J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Spin Hall effects, Rev. Mod. Phys.87, 1213 (2015)

    2015

  38. [38]

    E. G. Mishchenko, A. V. Shytov, and B. I. Halperin, Spin Current and Polarization in Impure Two-Dimensional Electron Systems with Spin-Orbit Coupling, Phys. Rev. Lett.93, 226602 (2004)

    2004

  39. [39]

    E. I. Rashba, Sum rules for spin Hall conductivity can- cellation, Phys. Rev. B70, 201309 (2004)

    2004

  40. [40]

    Inoue, G

    J.-i. Inoue, G. E. W. Bauer, and L. W. Molenkamp, Sup- pression of the persistent spin Hall current by defect scat- tering, Phys. Rev. B70, 041303 (2004)

    2004

  41. [41]

    Raimondi and P

    R. Raimondi and P. Schwab, Spin-Hall effect in a disor- dered two-dimensional electron system, Phys. Rev. B71, 033311 (2005)

    2005

  42. [42]

    Raimondi, C

    R. Raimondi, C. Gorini, P. Schwab, and M. Dzierzawa, Quasiclassical approach to the spin Hall effect in the two-dimensional electron gas, Phys. Rev. B74, 035340 (2006)

    2006

  43. [43]

    Engel, E

    H.-A. Engel, E. I. Rashba, and B. I. Halperin, Theory of Spin Hall Effects in Semiconductors, inHandbook of Magnetism and Advanced Magnetic Materials(John Wi- ley & Sons, Ltd, 2007)

    2007

  44. [44]

    W. Yang, K. Chang, and S.-C. Zhang, Intrinsic Spin Hall Effect Induced by Quantum Phase Transition in HgCdTe Quantum Wells, Phys. Rev. Lett.100, 056602 (2008)

    2008

  45. [45]

    L. K. Werake, B. A. Ruzicka, and H. Zhao, Observation of Intrinsic Inverse Spin Hall Effect, Phys. Rev. Lett.106, 107205 (2011)

    2011

  46. [46]

    Schliemann, Ballistic Side-Jump Motion of Electrons and Holes in Semiconductor Quantum Wells, Phys

    J. Schliemann, Ballistic Side-Jump Motion of Electrons and Holes in Semiconductor Quantum Wells, Phys. Rev. B75, 045304 (2007)

    2007

  47. [47]

    Bernardes, J

    E. Bernardes, J. Schliemann, C. Egues, and D. Loss, Spin Orbit Interaction and Zitterbewegung in Symmetric Wells, Phys. Status Solidi C3, 4330 (2006)

    2006

  48. [48]

    Zawadzki and T

    W. Zawadzki and T. M. Rusin, Zitterbewegung (Trem- bling Motion) of Electrons in Semiconductors: A Review, J. Phys. Condens. Matter23, 143201 (2011)

    2011

  49. [49]

    Vignale and I

    G. Vignale and I. V. Tokatly, Theory of the nonlinear Rashba-Edelstein effect: The clean electron gas limit, Phys. Rev. B93, 035310 (2016)

    2016

  50. [50]

    G. J. Ferreira, R. P. Maciel, P. H. Penteado, and J. C. Egues, Zitterbewegung and bulk-edge Landau-Zener tun- neling in topological insulators, Phys. Rev. B98, 165120 (2018)

    2018

  51. [51]

    I. R. Lavor, D. R. da Costa, L. Covaci, M. V. Miloˇ sevi´ c, F. M. Peeters, and A. Chaves, Zitterbewegung of Moir´ e Excitons in Twisted mos 2/wse2 Heterobilayers, Phys. Rev. Lett.127, 106801 (2021)

    2021

  52. [52]

    Y.-M. R. Hu, E. A. Ostrovskaya, and E. Estrecho, Zitterbewegung effect and quantum geometry in non- Hermitian exciton-polariton systems, Appl. Phys. Lett. 127, 253101 (2025)

    2025

  53. [53]

    Predin, Chirality of Zitterbewegung and its relation to Berry curvature in Dirac systems, arXiv:2604.08145 (2026)

    S. Predin, Chirality of Zitterbewegung and its relation to Berry curvature in Dirac systems, arXiv:2604.08145 (2026)

    Pith/arXiv arXiv 2026

  54. [54]

    Culcer, Zitterbewegung velocity in semiclassical elec- tron dynamics, arXiv:2605.15292 (2026)

    D. Culcer, Zitterbewegung velocity in semiclassical elec- tron dynamics, arXiv:2605.15292 (2026)

    Pith/arXiv arXiv 2026

  55. [55]

    T. Prat, D. Delande, and N. Cherroret, Quantum Boomeranglike Effect of Wave Packets in Random Me- dia, Phys. Rev. A99, 023629 (2019)

    2019

  56. [56]

    Sajjad, J

    R. Sajjad, J. L. Tanlimco, H. Mas, A. Cao, E. Nolasco- Martinez, E. Q. Simmons, F. L. N. Santos, P. Vignolo, T. Macr` ı, and D. M. Weld, Observation of the Quantum Boomerang Effect, Phys. Rev. X12, 011035 (2022)

    2022

  57. [57]

    X. Hou, Z. Wu, F. Wang, S. Zhu, B. Yan, and Z. Yang, Quantum Boomerang Effect of Light, Nat. Commun.17, 1579 (2026)

    2026

  58. [58]

    Janarek, B

    J. Janarek, B. Gr´ emaud, J. Zakrzewski, and D. Delande, Quantum Boomerang Effect in Systems without Time- Reversal Symmetry, Phys. Rev. B105, L180202 (2022)

    2022

  59. [59]

    Noronha and T

    F. Noronha and T. Macr` ı, Ubiquity of the quantum boomerang effect in Hermitian Anderson-localized sys- tems, Phys. Rev. B106, L060301 (2022)

    2022

  60. [60]

    Janarek, D

    J. Janarek, D. Delande, N. Cherroret, and J. Zakrzewski, Quantum Boomerang Effect for Interacting Particles, Phys. Rev. A102, 013303 (2020)

    2020

  61. [61]

    Janarek, J

    J. Janarek, J. Zakrzewski, and D. Delande, Many-Body Quantum Boomerang Effect, Phys. Rev. B107, 094204 (2023)

    2023

  62. [62]

    Janarek, N

    J. Janarek, N. Cherroret, and D. Delande, Berezinskii Approach to Disordered Spin Systems with Asymmetric Scattering and Application to the Quantum Boomerang Effect, Acta Phys. Pol. A144, 429 (2023)

    2023

  63. [63]

    Capuzzi, L

    P. Capuzzi, L. Tessieri, Z. Akdeniz, A. Minguzzi, and P. Vignolo, Spin-Charge Separation in the Quantum Boomerang Effect, Phys. Rev. A109, 063315 (2024)

    2024

  64. [64]

    Zamora, L

    S. Zamora, L. M. M. Dur˜ ao, F. Noronha, and T. Macr` ı, Boomerang Effect in Classical Stochastic Models, Phys. Rev. E111, 024104 (2025)

    2025

  65. [65]

    A. R. C. Buarque, W. S. Dias, and E. P. Raposo, Boomerang quantum walks, Quantum Inf. Process.25, 199 (2026)

    2026

  66. [66]

    Noronha, J

    F. Noronha, J. A. S. Louren¸ co, and T. Macr` ı, Robust quantum boomerang effect in non-Hermitian systems, Phys. Rev. B106, 104310 (2022)

    2022

  67. [67]

    Tessieri, Z

    L. Tessieri, Z. Akdeniz, N. Cherroret, D. Delande, and P. Vignolo, Quantum boomerang effect: Beyond the standard Anderson model, Phys. Rev. A103, 063316 (2021)

    2021

  68. [68]

    Tal-Ezer and R

    H. Tal-Ezer and R. Kosloff, An accurate and efficient 8 scheme for propagating the time dependent Schr¨ odinger equation, J. Chem. Phys.81, 3967 (1984)

    1984

  69. [69]

    Fehske, J

    H. Fehske, J. Schleede, G. Schubert, G. Wellein, V. S. Fil- inov, and A. R. Bishop, Numerical Approaches to Time Evolution of Complex Quantum Systems, Phys. Lett. A 373, 2182 (2009)

    2009

  70. [70]

    Rammer and H

    J. Rammer and H. Smith, Quantum Field-Theoretical Methods in Transport Theory of Metals, Rev. Mod. Phys. 58, 323 (1986)

    1986

  71. [71]

    Rammer,Quantum Field Theory of Non-equilibrium States(Cambridge University Press, Cambridge, 2007)

    J. Rammer,Quantum Field Theory of Non-equilibrium States(Cambridge University Press, Cambridge, 2007)

    2007

  72. [72]

    Haug and A.-P

    H. Haug and A.-P. Jauho,Quantum Kinetics in Trans- port and Optics of Semiconductors, Solid-State Sciences, Vol. 123 (Springer, Berlin, Heidelberg, 2008)

    2008

  73. [73]

    K. Shen, R. Raimondi, and G. Vignale, Theory of Cou- pled Spin-Charge Transport Due to Spin-Orbit Interac- tion in Inhomogeneous Two-Dimensional Electron Liq- uids, Phys. Rev. B90, 245302 (2014)

    2014

  74. [74]

    Kakoi and K

    M. Kakoi and K. Slevin, Time Evolution of Coherent Wave Propagation and Spin Relaxation in Spin-Orbit- Coupled Systems, Phys. Rev. A109, 033303 (2024). Appendix A: Numerical implementation The time-evolution operatorU(dt) =e −iHdt/ℏ is implemented using a Chebyshev polynomial expansion [67, 68], whose recurrence relation yields the following recursive exp...

    2024