R Janaswamy 2008 J. Phys. A: Math. Theor. 41 155306 doi:10.1088/1751-8113/41/15/155306
Transitional probabilities for the 4-state random walk on a lattice
R Janaswamy
Show affiliationsThe diffusion and Schrödinger propagators have been known to coexist on a lattice when a particle undergoing random walk is endowed with two states of spin in addition to the two states of direction in a 1+1 spacetime dimension. In this paper we derive explicit expressions for the various transitional probabilities by employing generating functions and transform methods. The transitional probabilities are all expressed in terms of a one-dimensional integral involving trigonometric functions and/or Chebyshev polynomials of the first and second kind from which the spacetime continuum limits of the diffusion equation and Schrödinger equation follow directly.
- PACS
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05.40.Fb Random walks and Levy flights
- MSC
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82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
41A50 Best approximation, Chebyshev systems
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
- Subjects
- Dates
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Issue 15 (18 April 2008)
Received 27 October 2007, in final form 3 March 2008
Published 2 April 2008
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Transitional probabilities for the 4-state random walk on a lattice
R Janaswamy 2008 J. Phys. A: Math. Theor. 41 155306
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