Dynamics of the probability density in the internal region of a double for a Dirac delta potential
Keywords:Quantum transients, Double delta potential, Moshinsky shutter.
AbstractBased on exact analytical solutions of the time-dependent Schrödinger equation, and initial conditions of plane waves cut in x-space by an absorbing or reflecting quantum shutter, the dynamic behavior of the electronic probability density or buildup is analyzed, in the internal region of a double Dirac delta potential double, from very short times (given in half-lives), until reaching the stationary situation. The buildup is compared between both cases, absorbent and reflective quantum shutter, finding that for short times the buildup depends on the initial condition (IC) used, while for long times, it is independent of said IC. Using the reflecting IC, the buildup is analyzed from practically zero time, until the steady-state is reached. The results found may be relevant in the context of rapid response in devices known as resonant tunneling diodes.
Born, M. E. Wolf. “Principles of optics,” Pergamon Press, Inc. Sixty edition. New York, 1959, pp. 808. https://www.iaa.csic.es/~dani/ebooks/Optics/Principles%20of%20Optics%20-%20M.Born,%20E.%20Wolf.pdf
A. S. Gerasimov y M. V. Kazarnovskii, “Possibility of observing nontationary quantum-mechanical effects by means of ultracold neutron,” Sov. Phys. JETP, Vol. 44, pp. 892-987, 1976 http://jetp.ac.ru/cgi-bin/dn/e_044_05_0892.pdf.
R. Gähler, A. G. Klein y A. Zeilinger, “Neutron optical tests of nonlinear wave mechanics”, Phys. Rev. A, Vol. 23, pp. 1611-1617, 1981. https://doi.org/10.1103/PhysRevA.23.1611. DOI: https://doi.org/10.1103/PhysRevA.23.1611
J. Felber, R. Gähler, C. Raush y R. Golub, “Matter waves at a vibrating surface: Transition from quantum-mechanical to classical behavior”, Phys. Rev. A, Vol. 53, pp. 319-328, 1996. https://doi.org/10.1103/PhysRevA.53.319. DOI: https://doi.org/10.1103/PhysRevA.53.319
A. del Campo, G. García-Calderón y J.G. Muga, “Quantum transients” Phys. Rep. vol. 476, pp. 1-50, 2009. https://doi.org/10.1016/j.physrep.2009.03.002. DOI: https://doi.org/10.1016/j.physrep.2009.03.002
J. Villavicencio, R. Romo y A. Hernández-Maldonado, “Absorption dynamics and delay time in complex potentials”, Phys. Scr. Vol. 93, no. 055201, 2018. https://orcid.org/0000-0002-2523-6584. DOI: https://doi.org/10.1088/1402-4896/aab41c
P. Szriftgiser, D. Guërey-Odelin, M. Arndt, y J. Dablibard, “Atomic wave diffraction and interference using temporal slits”, Phys. Rev. Lett., vol. 77, no. 1, pp. 4-7, 1996. https://doi.org/10.1103/PhysRevLett.77.4. DOI: https://doi.org/10.1103/PhysRevLett.77.4
T. Hils, J. Felber, R. Gähler, W. Gläaser, R. Golub, K. Habicht, y P. Wille. “Matter-wave optics in the time domain: Results of a cold-neutron experiment”. Phys. Rev. A, Vol. 58, pp. 4784-4790, 1998. https://doi.org/10.1103/PhysRevA.58.4784. DOI: https://doi.org/10.1103/PhysRevA.58.4784
G. García-Calderón y A. Hernández-Maldonado, “Delay time as a quantum transient interference effect”, Physical Review A, Vol. 86, no. 062118, 2012. https://doi.org/10.1103/PhysRevA.86.062118. DOI: https://doi.org/10.1103/PhysRevA.86.062118
A. Hernández, “Delay time in a single barrier for a movable quantum shutter” Phys. Rev. A, Vol. 81, No. 054101, 2010. https://doi.org/10.1103/PhysRevA.81.054101. DOI: https://doi.org/10.1103/PhysRevA.81.054101
G. García-Calderón y A. Rubio. “Transient effects and delay time in the dynamics of resonant tunneling”. Phys Rev. A, Vol. 56, pp. 3361-3370, 1997. https://doi.org/10.1103/PhysRevA.55.3361. DOI: https://doi.org/10.1103/PhysRevA.55.3361
J. Villavicencio y R. Romo., “Dynamical analysis of the buildup process near resonance”, Appl. Phys. Lett., Vol. 77, no. 3, pp. 379-381, 2000. https://doi.org/10.1063/1.126982. DOI: https://doi.org/10.1063/1.126982
J. Villavicencio y A. Hernández-Maldonado, “Transient quantum beats, Rabi oscillations, and delay time of modulated matter waves”, Phys Rev. A, Vol. 101, no. 042109, 2020. https://doi.org/10.1103/PhysRevA.101.042109. DOI: https://doi.org/10.1103/PhysRevA.101.042109
R. Romo y J. Villavicencio. “Dynamical description of the buildup process in resonant tunneling: evidence of exponential and nonexponential contributions”. Phys. Rev. B Vol. 60: R2142-R2145, 1999. https://doi.org/10.1103/PhysRevB.60.R2142. DOI: https://doi.org/10.1103/PhysRevB.60.R2142
R. Romo y J. Villavicencio. “Role of the buildup oscillations on the speed of resonant tunneling diodes”. Appl. Phys. Lett. Vol. 78, pp. 1769-1771, 2001. https://doi.org/10.1063/1.1354164. DOI: https://doi.org/10.1063/1.1354164
R. Romo, J. Villavicencio y G. García-Calderón. “Transient tunneling effects of resonance doublets in triple barrier systems”. Phys. Rev. B, Vol. 66, no. 033108, 2002. https://doi.org/10.1103/PhysRevB.66.033108. DOI: https://doi.org/10.1103/PhysRevB.66.033108
A. Hernández Maldonado, “Estudio dinámico del retraso temporal en sistemas cuánticos”, Tesis. (CICESE), pp. 119, 2004.
A. Hernández Maldonado, R. Romo y J. Villavicencio, “Convergence of resonance expansions in quantum wave buildup”, Revista Mexicana de Física, Vol. 62, pp 257–266, 2016. http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S0035-001X2016000300257.
How to Cite
Copyright (c) 2020 Alberto Hernández Maldonado
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors who publish in this journal accept the following conditions:
The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution license 4.0, which allows third parties to use what is published as long as they mention the authorship of the work and the first publication in this magazine.
Authors may make other independent and additional contractual agreements for the non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) as long as they clearly indicate that the work it was first published in this magazine.
Authors are allowed and encouraged to share their work online (for example: in institutional repositories or personal web pages) before and during the manuscript submission process, as it can lead to productive exchanges, greater and more quick citation of published work (see The Effect of Open Access).