- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Statistical mechanics of a discrete Schrödinger equation with saturable nonlinearity

Mogens R. Samuelsen1, Avinash Khare2, Avadh Saxena3, and Kim Ø. Rasmussen3

  • 1Department of Physics, The Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
  • 2Indian Institute of Science Education and Research (IISER), Pune 411021, India
  • 3Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

PDF

Phys. Rev. E 87, 044901 – Published 17 April, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.044901

Abstract

We study the statistical mechanics of the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. 84, 3740 (2000)] regarding the statistical mechanics of the one-dimensional DNLS equation with a cubic nonlinearity. As in this earlier study, we identify the spontaneous creation of localized excitations with a discontinuity in the partition function. The fact that this phenomenon is retained in the saturable DNLS is nontrivial, since in contrast to the cubic DNLS whose nonlinear character is enhanced as the excitation amplitude increases, the saturable DNLS, in fact, becomes increasingly linear as the excitation amplitude increases. We explore the nonlinear dynamics of this phenomenon by direct numerical simulations.

View figure in article

Article Text

References (17)

  1. P. G. Kevrekidis, K. Ø. Rasmussen, and A. R. Bishop, Int. J. Mod. Phys. B 15, 2833 (2001).
  2. The Discrete Nonlinear Schrödinger Equation. Mathematical Analysis, Numerical Computations and Physical Perspectives, edited by P. G. Kevrekidis (Springer, Berlin, 2009).
  3. S. Flach and A. V. Gorbach, Phys. Rep. 467, 1 (2008).
  4. R. S. MacKay and S. Aubry, Nonlinearity 7, 1623 (1994).
  5. E. Fermi, J. Pasta, and S. Ulam, Lect. Appl. Math 15, 143 (1974); “Studies of non linear problems,” Los Alamos Report No. LA-1940 (1955).
  6. K. Ø. Rasmussen, T. Cretegny, P. G. Kevrekidis, and Niels Grønbech-Jensen, Phys. Rev. Lett. 84, 3740 (2000).
  7. M. Johansson and K. Ø. Rasmussen, Phys. Rev. E 70, 066610 (2004).
  8. B. Rumpf, Phys. Rev. E 69, 016618 (2004).
  9. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
  10. A. Trombettoni and A. Smerzi, Phys. Rev. Lett. 86, 2353 (2001).
  11. A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A 38, 807 (2005).
  12. A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A 42, 085002 (2009).
  13. T. R. O. Melvin, A. R. Champneys, P. G. Kevrekidis, and J. Cuevas, Phys. Rev. Lett. 97, 124101 (2006).
  14. M. Syafwan, H. Susanto, S. M. Cox, and B. A. Malomed, J. Phys. A: Math. Theor. 45, 075207 (2012).
  15. When comparing these results to the results for the cubic DNLS presented in Ref. [6], it is important to note that Eq. (2) contains the additional −νψ term in the small amplitude limit compared to the corresponding equation in Ref. [6]. This term accounts for the −νa term in Eq. (15).
  16. S. Lubini, R. Franzosi, R. Livi, G.-L. Oppo, and A. Politi, New J. Phys. 15, 023032 (2013).
  17. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by M. Abramowitz and I. A. Stegun (US GPO, Washington, DC, 1964).

Outline

Information

Phys. Rev. E 87, 044901– Published 17 April, 2013
  • Received 12 February 2013
Article part of CHORUS

©2013 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation