Mathematical Modeling of Finite Quantum Systems

Details Mathematical Modeling of Finite Quantum Systems Mathematical Modeling of Finite Quantum Systems

2011-07-28

arxiv.org/abs/1107.5675v2

LNCS 7125, pp. 79-93, 2012

Physics

Quantum Physics

15 pages, talk at the conference "Mathematical Modeling and Computational Physics" Stara Lesna, High Tatra Mountains, Slovakia

Scientific paper

10.1088/1742-6596/343/1/012059

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 symmetries of dynamical systems. 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.

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