Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Journal of Computational Electronics
Erschienen in: Journal of Computational Electronics 4/2023

07.05.2023

Nonlocalization of singular potentials in quantum dynamics

verfasst von: Sihong Shao, Lili Su

Erschienen in: Journal of Computational Electronics | Ausgabe 4/2023

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Nonlocal modeling has drawn more and more attention and becomes steadily more powerful in scientific computing. In this paper, we demonstrate the superiority of a first-principle nonlocal model—Wigner function—in treating singular potentials which are often used to model the interaction between point charges in quantum science. The nonlocal nature of the Wigner equation is fully exploited to convert the singular potential into the Wigner kernel with weak or even no singularity, and thus highly accurate numerical approximations are achievable, which are hardly designed when the singular potential is taken into account in the local Schrödinger equation. The Dirac delta function, the logarithmic, and the inverse power potentials are considered. Numerically converged Wigner functions under all these singular potentials are obtained with a fourth-order accurate operator splitting spectral method, and display many interesting quantum behaviors as well.
Vorheriger Artikel First principles investigation of transition metal hydrides LiXH3 (X = Ti, Mn, and Cu) for hydrogen storage
Nächster Artikel Polycrystalline silicon nanowire FET performance depending on density of states

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Visscher, L., Dyall, K.G.: Dirac-Fock atomic electronic structure calculations using different nuclear charge distributions. At. Data Nuclear Data Tables 67, 207 (1997)CrossRef
2.
Roy, A.K.: Studies on some singular potentials in quantum mechanics. Int. J. Quantum Chem. 104, 861 (2005)CrossRef
3.
4.
Perelomov, A.M., Popov, V.S.: “Fall to the center” in quantum mechanics. Theor. Math. Phys. 4, 664 (1970)
5.
Meetz, K.: Singular potentials in nonrelativistic quantum mechanics. Il Nuovo Cimento (1955–1965), 34, 690 (1964)
6.
7.
8.
Cinal, M.: Highly accurate numerical solution of Hartree-Fock equation with pseudospectral method for closed-shell atoms. J. Math. Chem. 58, 1571 (2020)MathSciNetCrossRefMATH
9.
Wei, G.W.: Discrete singular convolution for the solution of the Fokker-Planck equation. J. Chem. Phys. 110, 8930 (1999)CrossRef
10.
11.
12.
Gusson, M.F., Gonçalves, A.O.O., Francisco, R.O., Furtado, R.G., Fabris, J.C., Nogueira, J.A.: Dirac \(\delta \)-function potential in quasiposition representation of a minimal-length scenario. Eur. Phys. J. C 78, 1 (2018)CrossRef
13.
Ray, M.W., Ruokokoski, E., Kandel, S., Möttönen, M., Hall, D.S.: Observation of Dirac monopoles in a synthetic magnetic field. Nature 505, 657 (2014)CrossRef
14.
Gal, C.G., Giorgini, A., Grasselli, M.: The nonlocal Cahn-Hilliard equation with singular potential: well-posedness, regularity and strict separation property. J. Differ. Eqn. 263, 5253 (2017)MathSciNetCrossRefMATH
15.
Belloni, M., Robinett, R.W.: The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanics. Phys. Rep. 540, 25 (2014)MathSciNetCrossRefMATH
16.
Araya, R., Behrens, E., Rodríguez, R.: A posteriori error estimates for elliptic problems with Dirac delta source terms. Numerische Mathematik 105, 193 (2006)MathSciNetCrossRefMATH
17.
18.
Wigner, E.: On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749 (1932)CrossRefMATH
19.
Curtright, T.L., Fairlie, D.B., Zachos, C.K.: A concise treatise on quantum mechanics in phase space. World Scientific Publishing Company (2013)
20.
D’Elia, M., Du, Q., Glusa, C., Gunzburger, M., Tian, X., Zhou, Z.: Numerical methods for nonlocal and fractional models. Acta Numer. 29, 1–124 (2020)MathSciNetCrossRefMATH
21.
Greengard, L., Jiang, S., Zhang, Y.: The anisotropic truncated kernel method for convolution with free-space Green’s functions. SIAM J. Sci. Comput. 40, A3733 (2018)MathSciNetCrossRefMATH
22.
Vico, F., Greengard, L., Ferrando, M.: Fast convolution with free-space Green’s functions. J. Comput. Phys. 323, 191 (2016)MathSciNetCrossRefMATH
23.
Xiong, Y., Zhang, Y., Shao, S.: A characteristic-spectral-mixed scheme for six-dimensional Wigner-Coulomb dynamics. arXiv:​2205.​02380, (2022)
24.
25.
26.
Chen, Z., Shao, S., Cai, W.: A high order efficient numerical method for 4-D Wigner equation of quantum double-slit interferences. J. Comput. Phys. 396, 54–71 (2019)MathSciNetCrossRefMATH
27.
Chen, Z., Jiang, H., Shao, S.: A higher-order accurate operator splitting spectral method for the Wigner-Poisson system. J. Comput. Electronics 21, 756 (2022)CrossRef
28.
Shao, S., Lu, T., Cai, W.: Adaptive conservative cell average spectral element methods for transient Wigner equation in quantum transport. Commun. Comput. Phys. 9, 711 (2011)MathSciNetCrossRefMATH
29.
Xiong, Y., Chen, Z., Shao, S.: An advective-spectral-mixed method for time-dependent many-body Wigner simulations. SIAM J. Sci. Comput. 38, B491 (2016)MathSciNetCrossRefMATH
30.
Xiao, Y., Liu, W., Cheng, L., Peng, D.: Four-component relativistic theory for nuclear magnetic shielding constants: critical assessments of different approaches. J. Chem. Phys. 126, 214101 (2007)CrossRef
31.
Macleod, A.J.: Algorithm 779: Fermi-Dirac functions of order-1/2, 1/2, 3/2, 5/2. ACM Trans. Math. Softw. (TOMS) 24, 1–12 (1998)CrossRefMATH
32.
Serber, R.: Scaling law for high-energy elastic scattering. Phys. Rev. Lett. 13, 32 (1964)CrossRef
33.
34.
Whittaker, E.T., Watson, G.N.: A course of modern analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions. University Press (1915)
35.
Xia, M., Shao, S., Chou, T.: A frequency-dependent p-adaptive technique for spectral methods. J. Comput. Phys. 446, 110627 (2021)MathSciNetCrossRefMATH
36.
Xia, M., Shao, S., Chou, T.: Efficient scaling and moving techniques for spectral methods in unbounded domains. SIAM J. Sci. Comput. 43, A3244–A3268 (2021)MathSciNetCrossRefMATH
37.
Chou, T., Shao, S., Xia, M.: Adaptive Hermite spectral methods in unbounded domains. Appl. Numer. Math. 183, 201–220 (2023)MathSciNetCrossRefMATH
Metadaten
Titel
Nonlocalization of singular potentials in quantum dynamics
verfasst von
Sihong Shao
Lili Su
Publikationsdatum
07.05.2023
Verlag
Springer US
Erschienen in
Journal of Computational Electronics / Ausgabe 4/2023
Print ISSN: 1569-8025
Elektronische ISSN: 1572-8137
DOI
https://doi.org/10.1007/s10825-023-02042-8

Weitere Artikel der Ausgabe 4/2023

Journal of Computational Electronics 4/2023 Zur Ausgabe

OriginalPaper

Predicting model of I–V characteristics of quantum-confined GaAs nanotube: a machine learning and DFT-based combined framework

OriginalPaper

Theoretical analysis of relative intensity noise in semiconductor QD lasers

OriginalPaper

Numerical analysis of emerging concept of perovskite/silicon heterojunction solar cells

OriginalPaper

Thermally compensated ZnO film bulk acoustic resonator for RF application above 5GHz frequency

OriginalPaper

Ultra-thin double barrier AlGaN/GaN high threshold voltage HEMT with graded AlGaN/Si3N4 gate and p-type buffer layer

OriginalPaper

The impact of SnMnO2 TCO and Cu2O as a hole transport layer on CIGSSe solar cell performance improvement

Neuer Inhalt

    Bildnachweise