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Excess energy and countercurrents after a quantum kick

Nuria Santervás-Arranz1,2,*, Massimiliano Stengel3,4, and Emilio Artacho1,5,6,7

  • *Contact author: n.santervas@nanogune.eu
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Phys. Rev. Research 7, 033292 – Published 29 September, 2025

DOI: https://doi.org/10.1103/z497-65ks

Abstract

A quantum system of interacting particles under the effect of a static external potential is hereby described as kicked when that potential suddenly starts moving with a constant velocity v. If initially in a stationary state, the excess energy at any time after the kick equals v·〈P〉(t), with P being the total momentum of the system. If the system is finite and remains bound, the long-time average of the excess energy tends to Mv2, with M the system’s total mass, or a related expression if there is particle emission. Mv2 is twice what expected from an infinitely smooth onset of motion, and any monotonic onset is expected to increase the average energy to a value within both limits. In a macroscopic system, a particle flow emerges countering the potential’s motion when the particles stay partially behind. For charged particles, the described kinetic kick is equivalent to the kick given by the infinitely short electric-field pulse E=mqvδ(t) to the system at rest, useful as a formal limit in ultrafast phenomena. A linear-response analysis of low-v countercurrents in kicked metals shows that the coefficient of the linear term in v is the Drude weight. Nonlinear in v countercurrents are expected for insulators through the electron-hole excitations induced by the kick, going as v3 at low v for centrosymmetric ones. First-principles calculations for simple solids are used to ratify those predictions, although the findings apply more generally to systems such as Mott insulators or cold lattices of bosons or fermions.

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References (45)

  1. A. B. Migdal, Ionizatsiya atomov pri yadernykh reaktsiyakh, Sov. Phys. JETP 9, 1163 (1939).
  2. M. Ibe, W. Nakano, Y. Shoji, and K. Suzuki, Migdal effect in dark matter direct detection experiments, J. High Energy Phys. 03 (2018) 194.
  3. J. M. Pruneda, D. Sánchez-Portal, A. Arnau, J. I. Juaristi, and E. Artacho, Electronic stopping power in LiF from first principles, Phys. Rev. Lett. 99, 235501 (2007).
  4. M. A. Zeb, J. Kohanoff, D. Sánchez-Portal, A. Arnau, J. I. Juaristi, and E. Artacho, Electronic stopping power in gold: The role of d electrons and the H/He anomaly, Phys. Rev. Lett. 108, 225504 (2012).
  5. R. Ullah, F. Corsetti, D. Sánchez-Portal, and E. Artacho, Electronic stopping power in a narrow band gap semiconductor from first principles, Phys. Rev. B 91, 125203 (2015).
  6. A. Schleife, Y. Kanai, and A. A. Correa, Accurate atomistic first-principles calculations of electronic stopping, Phys. Rev. B 91, 014306 (2015).
  7. R. Ullah, E. Artacho, and A. A. Correa, Core electrons in the electronic stopping of heavy ions, Phys. Rev. Lett. 121, 116401 (2018).
  8. A. A. Correa, Calculating electronic stopping power in materials from first principles, Comput. Mater. Sci. 150, 291 (2018).
  9. J. F. Halliday, M. Famili, N. Forcellini, and E. Artacho, Ab initio electronic stationary states for nuclear projectiles in solids, Phys. Rev. Res. 4, 043077 (2022).
  10. C. E. Dreyer, S. Coh, and M. Stengel, Nonadiabatic Born effective charges in metals and the Drude weight, Phys. Rev. Lett. 128, 095901 (2022).
  11. M. Nisoli, P. Decleva, F. Calegari, A. Palacios, and F. Martín, Attosecond electron dynamics in molecules, Chem. Rev. 117, 10760 (2017).
  12. D. Hui, H. Alqattan, M. Sennary, N. V. Golubev, and M. T. Hassan, Attosecond electron microscopy and diffraction, Sci. Adv. 10, eadp5805 (2024).
  13. C. Eigen, J. A. Glidden, R. Lopes, E. A. Cornell, R. P. Smith, and Z. Hadzibabic, Universal prethermal dynamics of Bose gases quenched to unitarity, Nature (London) 563, 221 (2018).
  14. B. Song, S. Dutta, S. Bhave, J.-C. Yu, E. Carter, N. Cooper, and U. Schneider, Realizing discontinuous quantum phase transitions in a strongly correlated driven optical lattice, Nat. Phys. 18, 259 (2022).
  15. R. Resta, Drude weight and superconducting weight, J. Phys.: Condens. Matter 30, 414001 (2018).
  16. P. B. Allen, Electron transport, Contemp. Concepts Condens. Matter Sci. 2, 165 (2006).
  17. In the presence of a stationary current for t<0 in an extended or periodic system, the relation generalizes to 〈H〉(t)=E0+v·Δ〈P〉(t), where Δ〈P〉(t)≡〈P〉(t)−〈P〉0, and where 〈P〉0 is the net momentum associated with the mentioned stationary current.
  18. G. Baym, Lectures on Quantum Mechanics (CRC Press, Boca Raton, Florida, 2018).
  19. P. M. Echenique, R. M. Nieminen, and R. H. Ritchie, Density functional calculation of stopping power of an electron gas for slow ions, Solid State Commun. 37, 779 (1981).
  20. K. Yabana and G. Bertsch, Time-dependent local-density approximation in real time, Phys. Rev. B 54, 4484 (1996).
  21. G. F. Bertsch, J.-I. Iwata, A. Rubio, and K. Yabana, Real-space, real-time method for the dielectric function, Phys. Rev. B 62, 7998 (2000).
  22. M. Schultze, K. Ramasesha, C. Pemmaraju, S. Sato, D. Whitmore, A. Gandman, J. S. Prell, L. Borja, D. Prendergast, K. Yabana et al., Attosecond band-gap dynamics in silicon, Science 346, 1348 (2014).
  23. Z. Dai and A. M. Rappe, Recent progress in the theory of bulk photovoltaic effect, Chem. Phys. Rev. 4, 011303 (2023).
  24. E. Runge and E. K. U. Gross, Density-functional theory for time-dependent systems, Phys. Rev. Lett. 52, 997 (1984).
  25. A. Tsolakidis, D. Sánchez-Portal, and R. M. Martin, Calculation of the optical response of atomic clusters using time-dependent density functional theory and local orbitals, Phys. Rev. B 66, 235416 (2002).
  26. J. M. Soler, E. Artacho, J. D. Gale, A. García, J. Junquera, P. Ordejón, and D. Sánchez-Portal, The SIESTA method for ab initio order-N materials simulation, J. Phys.: Condens. Matter 14, 2745 (2002).
  27. A. García, N. Papior, A. Akhtar, E. Artacho, V. Blum, E. Bosoni, P. Brandimarte, M. Brandbyge, J. I. Cerdá, F. Corsetti et al., SIESTA: Recent developments and applications, J. Chem. Phys. 152, 204108 (2020).
  28. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  29. J. Moreno and J. M. Soler, Optimal meshes for integrals in real-and reciprocal-space unit cells, Phys. Rev. B 45, 13891 (1992).
  30. N. Troullier and J. L. Martins, Efficient pseudopotentials for plane-wave calculations, Phys. Rev. B 43, 1993 (1991).
  31. C. E. Dreyer, M. Stengel, and D. Vanderbilt, Current-density implementation for calculating flexoelectric coefficients, Phys. Rev. B 98, 075153 (2018).
  32. M. Stengel and D. Vanderbilt, Quantum theory of mechanical deformations, Phys. Rev. B 98, 125133 (2018).
  33. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
  34. N. Tancogne-Dejean, M. J. Oliveira, X. Andrade, H. Appel, C. H. Borca, G. Le Breton, F. Buchholz, A. Castro, S. Corni, A. A. Correa et al., Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems, J. Chem. Phys. 152, 124119 (2020).
  35. M. Noda, S. A. Sato, Y. Hirokawa, M. Uemoto, T. Takeuchi, S. Yamada, A. Yamada, Y. Shinohara, M. Yamaguchi, K. Iida et al., Salmon: Scalable ab-initio light–matter simulator for optics and nanoscience, Comput. Phys. Commun. 235, 356 (2019).
  36. C. D. Pemmaraju, F. D. Vila, J. J. Kas, S. A. Sato, J. J. Rehr, K. Yabana, and D. Prendergast, Velocity-gauge real-time TDDFT within a numerical atomic orbital basis set, Comput. Phys. Commun. 226, 30 (2018).
  37. X. Andrade, S. Hamel, and A. A. Correa, Negative differential conductivity in liquid aluminum from real-time quantum simulations, Eur. Phys. J. B 91, 229 (2018).
  38. M. Stengel, M. Royo, and E. Artacho, Pseudopotentials that move: From inertia to electromagnetism, arXiv:2503.18811.
  39. E. Artacho and D. D. O'Regan, Quantum mechanics in an evolving Hilbert space, Phys. Rev. B 95, 115155 (2017).
  40. J. F. Halliday and E. Artacho, Numerical integration of quantum time evolution in a curved manifold, Phys. Rev. Res. 3, 043134 (2021).
  41. Qb@ll Software, https://github.com/LLNL/qball, accessed 5 July 2024.
  42. D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013).
  43. M. Schlipf and F. Gygi, Optimization algorithm for the generation of ONCV pseudopotentials, Comput. Phys. Commun. 196, 36 (2015).
  44. H. Ehrenreich, H. Philipp, and B. Segall, Optical properties of aluminum, Phys. Rev. 132, 1918 (1963).
  45. M. Kimura and N. Lane, Traveling-molecular-orbital-expansion studies of electron capture in collisions of fully stripped ions (Z = 6–9) with H and H2, Phys. Rev. A 35, 70 (1987).

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Phys. Rev. Research 7, 033292– Published 29 September, 2025
  • Received 3 March 2025
  • Accepted 13 August 2025
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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.

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