Adomian Decomposition Approach to Solve the Quantum Mesoscopic Nonlinear LC-circuits with Charge Discreetness

Document Type : Original Research Articles

Authors
Hasan Pahlavani
amenh zamani
Department of Physics, University of Qom, Qom, Islamic Republic of Iran
10.22059/jsciences.2024.358905.1007800
Abstract
The quantum Hamitonian of a nonlinear mesoscopic LC-circuit include a nonlinear inductor and a linear capacitor with charge discreetness is introduced. An analytical function for quantum persistent current due to  the magnetic flux of such nonlinear electrical circuit is obtained by Adomian Decomposition Method (ADM). The nonlinear quantum ring is introduced and the quantum persistent current and the eigenvalues energy are found analytically. It is shown by numerical solution that the persistent current and eigenvalues energy are periodic functions of the magnetic flux with the fundamental parameter ( ),  which is a pure quantum characteristic.  In this paper, we proved for the first time that in a mesoscopic nonlinear quantum ring, similar a linear quantum ring, there is a quantized and periodic persistent current in terms of magnetic flux, which will attract attention in experience and technology.
Keywords
Charge discreteness
Duffing equation
Analytic solution
Mesoscopic circuits
Nonlinear inductor
Subjects
  1. Kumar M  Umesh.  Recent development of Adomian decomposition method for ordinary and partial differential equations. International Journal of Applied and Computational Mathematics, 2022; 8(2): 81.‏
  2. Jaradat A. K, Obeidat A. A, Gharaibeh  M. A,  Qaseer  M. H. Adomian decomposition approach to solve the simple harmonic quantum oscillator. International Journal of Applied Engineering Research, 2018; 13(2): 1056-1059.
  3. Adomian G. Solving frontier problems of physics: the decomposition method . Springer Science & Business Media 2013;  60).‏
  4. Mohammed A. S. H. F,  Bakodah  H. O.  Numerical investigation of the Adomian-based methods with w-shaped optical solitons of Chen-Lee-Liu equation. Physica Scripta, 2020; 96(3): 035206.‏
  5. Ghoreishi M, Ismail  A. M,  Ali N. H. M.  Adomian decomposition method (ADM) for nonlinear wave-like equations with variable coefficient. Applied Mathematical Sciences, 2010; 4(49): 2431-2444.‏
  6. Babolian E,  Biazar J. On the order of convergence of Adomian method. Applied Mathematics and Computation, 2002; 130(2-3):  383-387.‏
  7. Sweilam N. H,  Khader M. M. Approximate solutions to the nonlinear vibrations of multiwalled carbon nanotubes using Adomian decomposition method. Applied Mathematics and Computation, 2010; 217(2): 495-505.
  8. Wazwaz A. M,  El-Sayed S. M.  A new modification of the Adomian decomposition method for linear and nonlinear operators. Applied Mathematics and computation, 2001; 122(3): 393-405.
  9. Siddiqui A. M, Hameed M, Siddiqui B. M, Ghori Q. K. Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid. Communications in Nonlinear Science and Numerical Simulation, 2010; 15(9): 2388-2399.‏
  10. Biermanns J. Der Schwingungskreis mit eisenhaltiger Induktivität. Archiv für Elektrotechnik, 1915; 3(12): 345-353.
  11. Li Y. Q,  Chen  B. Quantum theory for mesoscopic electric circuits. Physical Review B, 1996; 53(7):  4027.‏
  12. Chen B, Li  Y. Q, Fang  H, Jiao  Z. K, Zhang  Q. R.  Quantum effects in a mesoscopic circuit. Physics Letters A, 1995; 205(1): 121-124.
  13. Waffenschmidt E, Ackermann  B,  Ferreira  J. A. Design method and material technologies for passives in printed circuit board embedded circuits. IEEE Transactions on Power Electronics, 2005; 20(3): 576-584.‏
  14. Yokouchi T,  Kagawa  F,  Hirschberger  M, Otani Y, Nagaosa N, Tokura Y. Emergent electromagnetic induction in a helical-spin magnet. Nature, 2020; 586(7828): 232-236.
  15. Guevel L. L, Billiot  G,  De Franceschi  S,  Morel  A,  Jehl  X,  Jansen  A. G. M,  Pillonnet  G. Compact gate-based read-out of multiplexed quantum devices with a cryogenic CMOS active inductor. arXiv preprint arXiv, 2021; 2102 :04364.
  16. Chakraborty T,  Manaselyan  A,  Barseghyan  M,  Laroze, D.  Controllable continuous evolution of electronic states in a single quantum ring. Physical Review B, 2018; 97(4): 041304.‏
  17. Oliveira R. R, Araújo Filho  A. A,  Lima  F. C,  Maluf  R. V,  Almeida  C. A.  Thermodynamic properties of an Aharonov-Bohm quantum ring. The European Physical Journal Plus, 2019; 134(10): 495.‏

 
  1. Neill C,  McCourt T, Mi  X, Jiang  Z, Niu  M. Y, Mruczkiewicz  W, at, al. Accurately computing the electronic properties of a quantum ring. Nature, 2021; 594(7864): 508-512.‏
  2. Zamani A,  Pahlavani  H.   The quantum dynamics of a mesoscopic driven RLC circuit consisting of a linear inductor, a linear resistor and a nonlinear capacitor. International Journal of Modern Physics B 2022; 36: 2250014 .
  3. Zamani A,   Pahlavani  H. The quantum fluctuations of charge and current in a driven nonlinear LC-circuit with a linear capacitor and a nonlinear inductor. Journal of Theoretical and Applied Physics.2023; ‏17(4): 172336(1-8).
  4. Zamani A, Pahlavani  H. Investigation of synchronization for coupled quantum nonlinear electrical LC circuits with mutual inductance. Indian Journal of Physics, 2023; 1-9.‏
  5. Mailly D, Chapelier C, Benoit  A.  Experimental observation of persistent currents in GaAs-AlGaAs single loop. Physical Review Letters, 1993; 70(13): 2020.
  6. Mühle A, Wegscheider  W,  Haug  R. J. Coupling in concentric double quantum rings. Applied Physics Letters. 2007;  91(13).‏
  7. Fornieri A,  Amado  M, Carillo  F,  Dolcini  F,  Biasiol G, Sorbam  L, at al. A ballistic quantum ring Josephson interferometer. Nanotechnology, 2013; 24(24): 245201.‏
  8. Hayashi C.  Nonlinear oscillations in physical systems. 2014 Princeton University Press.
  9. Ueda Y.  Random phenomena resulting from non-linearity in the system described by Duffing's equation. International Journal of Non-Linear Mechanics. 1985; 20(5-6): 481-491.
  10. Louisell W. H. Quantum statistical properties of radiation. 1973 John Wiley.
  11. Kheirandish F,  Pahlavani  H. Driven mesoscopic electric circuits. Modern Physics Letters B, 2008; 22(01): 51-60.
  12. Pahlavani H. The Persistent Current on a Driven Mesoscopic RLC Circuit. International Journal of Modern Physics B, 2011; 25(23n24): 3225-3236.
Journal of Sciences, Islamic Republic of Iran
Volume 34, Issue 4
Autumn 2023
Pages 371-377