IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v429y2015icp35-44.html
   My bibliography  Save this article

Solutions for a q-generalized Schrödinger equation of entangled interacting particles

Author

Listed:
  • Alves, L.G.A.
  • Ribeiro, H.V.
  • Santos, M.A.F.
  • Mendes, R.S.
  • Lenzi, E.K.

Abstract

We report on the time dependent solutions of the q-generalized Schrödinger equation proposed by Nobre et al. (2011). Here we investigate the case of two free particles and also the case where two particles were subjected to a Moshinsky-like potential with time dependent coefficients. We work out analytical and numerical solutions for different values of the parameter q and also show that the usual Schrödinger equation is recovered in the limit of q→1. An intriguing behavior was observed for q=2, where the wave function displays a ring-like shape, indicating a bind behavior of the particles. Differently from the results previously reported for the case of one particle, frozen states appear only for special combinations of the wave function parameters in case of q=3.

Suggested Citation

  • Alves, L.G.A. & Ribeiro, H.V. & Santos, M.A.F. & Mendes, R.S. & Lenzi, E.K., 2015. "Solutions for a q-generalized Schrödinger equation of entangled interacting particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 35-44.
  • Handle: RePEc:eee:phsmap:v:429:y:2015:i:c:p:35-44
    DOI: 10.1016/j.physa.2015.02.063
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115001806
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2015.02.063?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cirto, Leonardo J.L. & Assis, Vladimir R.V. & Tsallis, Constantino, 2014. "Influence of the interaction range on the thermostatistics of a classical many-body system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 286-296.
    2. Pennini, F. & Plastino, A.R. & Plastino, A., 2014. "Pilot wave approach to the NRT nonlinear Schrödinger equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 195-205.
    3. Santos, A.P. & Silva, R. & Alcaniz, J.S. & Anselmo, D.H.A.L., 2012. "Non-Gaussian effects on quantum entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(6), pages 2182-2192.
    4. Majtey, A.P. & Plastino, A.R. & Plastino, A., 2012. "New features of quantum discord uncovered by q-entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2491-2499.
    5. Buiatti, Marco & Grigolini, Paolo & Palatella, Luigi, 1999. "A non extensive approach to the entropy of symbolic sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(1), pages 214-224.
    6. Curilef, S. & Plastino, A.R. & Plastino, A., 2013. "Tsallis’ maximum entropy ansatz leading to exact analytical time dependent wave packet solutions of a nonlinear Schrödinger equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2631-2642.
    7. Vignat, Christophe & Plastino, Angel & Plastino, Angel R. & Dehesa, Jesus Sanchez, 2012. "Quantum potentials with q-Gaussian ground states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1068-1073.
    8. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
    9. Silva, A.T. & Lenzi, E.K. & Evangelista, L.R. & Lenzi, M.K. & da Silva, L.R., 2007. "Fractional nonlinear diffusion equation, solutions and anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 65-71.
    10. Zander, C. & Plastino, A.R., 2006. "Composite systems with extensive Sq (power-law) entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 145-156.
    11. Toranzo, I.V. & Plastino, A.R. & Dehesa, J.S. & Plastino, A., 2013. "Quasi-stationary states of the NRT nonlinear Schrödinger equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3945-3951.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Naif Alotaibi & A. S. Al-Moisheer & Ibrahim Elbatal & Mansour Shrahili & Mohammed Elgarhy & Ehab M. Almetwally, 2023. "Half Logistic Inverted Nadarajah–Haghighi Distribution under Ranked Set Sampling with Applications," Mathematics, MDPI, vol. 11(7), pages 1, April.
    2. da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    3. Masi, Marco, 2007. "On the extended Kolmogorov–Nagumo information-entropy theory, the q→1/q duality and its possible implications for a non-extensive two-dimensional Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 67-78.
    4. Deeb, Omar El, 2023. "Entropic spatial auto-correlation of voter uncertainty and voter transitions in parliamentary elections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    5. Sekania, Michael & Appelt, Wilhelm H. & Benea, Diana & Ebert, Hubert & Vollhardt, Dieter & Chioncel, Liviu, 2018. "Scaling behavior of the Compton profile of alkali metals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 489(C), pages 18-27.
    6. Chapeau-Blondeau, François, 2014. "Tsallis entropy for assessing quantum correlation with Bell-type inequalities in EPR experiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 204-215.
    7. Gayen, Atin & Kumar, M. Ashok, 2021. "Projection theorems and estimating equations for power-law models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    8. Ou, Congjie & Huang, Zhifu & Chen, Jincan & El Kaabouchi, A. & Nivanen, L. & Le Méhauté, A. & Wang, Qiuping A., 2009. "A basic problem in the correlations between statistics and thermodynamics," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2313-2318.
    9. Pintarelli, María B. & Vericat, Fernando, 2003. "Generalized Hausdorff inverse moment problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(3), pages 568-588.
    10. Telesca, Luciano, 2010. "Nonextensive analysis of seismic sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1911-1914.
    11. Suyari, Hiroki & Wada, Tatsuaki, 2008. "Multiplicative duality, q-triplet and (μ,ν,q)-relation derived from the one-to-one correspondence between the (μ,ν)-multinomial coefficient and Tsallis entropy Sq," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 71-83.
    12. Kozaki, M. & Sato, A.-H., 2008. "Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1225-1246.
    13. Ou, Congjie & Chen, Jincan & Wang, Qiuping A., 2006. "Temperature definition and fundamental thermodynamic relations in incomplete statistics," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 518-521.
    14. Deng, Xinyang & Deng, Yong, 2014. "On the axiomatic requirement of range to measure uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 163-168.
    15. Tsallis, Constantino & Borges, Ernesto P., 2023. "Time evolution of nonadditive entropies: The logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    16. Preda, Vasile & Dedu, Silvia & Sheraz, Muhammad, 2014. "New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 350-359.
    17. Zozor, S. & Vignat, C., 2007. "On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 499-517.
    18. Naudts, Jan, 2004. "Generalized thermostatistics and mean-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 279-300.
    19. Liu, Yanxiu & Xu, Cheng & Huang, Zhifu & Lin, Bihong, 2017. "The internal energy expression of a long-range interaction complex system and its statistical physical properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 423-427.
    20. Xie, Rongrong & Deng, Shengfeng & Deng, Weibing & Pato, Mauricio P., 2022. "Generalized Poisson ensemble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:429:y:2015:i:c:p:35-44. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.