Harmonic Oscillator Chain in Noncommutative Phase Space with Rotational Symmetry

  • Kh. P. Gnatenko Ivan Franko National University of Lviv, Department for Theoretical Physics, Laboratory for Statistical Physics of Complex Systems, Institute for Condensed Matter Physics, Nat. Acad. of Sci. of Ukraine
Keywords: harmonic oscillator, composite system, tensors of noncommutativity

Abstract

We consider a quantum space with a rotationally invariant noncommutative algebra of coordinates and momenta. The algebra contains the constructed tensors of noncommutativity involving additional coordinates and momenta. In the rotationally invariant noncommutative phase space, the harmonic oscillator chain is studied. We obtain that the noncommutativity affects the frequencies of the system. In the case of a chain of particles with harmonic oscillator interaction, we conclude that, due to the noncommutativity of momenta, the spectrum of the center-of-mass of the system is discrete and corresponds to the spectrum of a harmonic oscillator.

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Published
2019-02-21
How to Cite
Gnatenko, K. (2019). Harmonic Oscillator Chain in Noncommutative Phase Space with Rotational Symmetry. Ukrainian Journal of Physics, 64(2), 131. https://doi.org/10.15407/ujpe64.2.131
Section
General physics