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Short distance modification of a gravitational system and its optical analog

  • Qin Zhao
  • Mir FaizalEmail author
  • Chenguang Hou
  • Zaid Zaz
Regular Article
  • 22 Downloads

Abstract

Motivated by developments in string theory, such as T-duality, it has been proposed that the geometry of spacetime should have an intrinsic minimal length associated with it. This would modify the short distance behavior of quantum systems studied on such a geometry, and an optical analog for such a short distance modification of quantum system has also been realized by using non-paraxial nonlinear optics. As general relativity can be viewed as an effective field theory obtained from string theory, it is expected that this would also modify the short distance behavior of general relativity. Now the Newtonian approximation is a valid short distance approximation to general relativity, and Schrodinger–Newton equation can be obtained as a non-relativistic semi-classical limit of such a theory, we will analyze the short distance modification of Schrodinger–Newton equation from an intrinsic minimal length in the geometry of spacetime. As an optical analog of the Schrodinger–Newton equation has been constructed, it is possible to optically realize this system. So, this system is important, and we will numerically analyze the solutions for this system. It will be observed that the usual Runge–Kutta method cannot be used to analyze this system. However, we will use a propose and use a new numerical method, which we will call as the two step Runge–Kutta method, for analyzing this system.

Graphical abstract

Keywords

Quantum Optics 

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Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Qin Zhao
    • 1
    • 2
  • Mir Faizal
    • 3
    • 4
    Email author
  • Chenguang Hou
    • 1
  • Zaid Zaz
    • 5
    • 6
  1. 1.Department of PhysicsNational University of SingaporeSingaporeSingapore
  2. 2.Department of Computer ScienceHarbin Institute of Technology ShenzhenP.R. China
  3. 3.Irving K. Barber School of Arts and Sciences, University of British Columbia – OkanaganKelownaCanada
  4. 4.Department of Physics and AstronomyUniversity of LethbridgeLethbridgeCanada
  5. 5.Theoretical Physics Division, Department of Physics, National Institute of TechnologySrinagarIndia
  6. 6.Department of Electronics and Communication EngineeringUniversity of KashmirSrinagarIndia

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