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Mathematical Modeling of Finite Quantum Systems

  • Vladimir V. Kornyak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7125)

Abstract

We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The finite approach makes the problem constructive and more tractable. We argue that quantum behavior is a natural consequence of the dynamical system symmetries. It is a result of fundamental impossibility to trace identity of indistinguishable objects in their evolution — only information about invariant combinations of such objects is available. We demonstrate that any quantum dynamics can be embedded into a simple permutation dynamics. Quantum phenomena, such as interferences, arise in invariant subspaces of permutation representations of the symmetry group of a system. Observable quantities can be expressed in terms of the permutation invariants.

Keywords

quantum behavior finite groups permutation invariants 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Vladimir V. Kornyak
    • 1
  1. 1.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchDubnaRussia

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