Probing Uncertainty Relations in Non-Commutative Space
arXiv:1712.07748 · doi:10.1007/s10773-019-04150-3
Abstract
In this paper, we compute uncertainty relations for non-commutative space and obtain a better lower bound than the standard one obtained from Heisenberg's uncertainty relation. We also derive the reverse uncertainty relation for product and sum of uncertainties of two incompatible variables for one linear and another non-linear model of the harmonic oscillator. The non-linear model in non-commutating space yields two different expressions for Schrödinger and Heisenberg uncertainty relation. This distinction does not arise in commutative space, and even in the linear model of non-commutative space.
References in corpus (13)
- Thermodynamic uncertainty relation for biomolecular processes
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Heisenberg's Uncertainty Principle
- Stronger uncertainty relations for the sum of variances
- Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials
- State-independent Uncertainty Relations and Entanglement Detection in Noisy Systems
- Rényi entropy uncertainty relation for successive projective measurements
- Uncertainty Relations for Quantum Coherence
- Uncertainty relation in Schwarzschild spacetime
- Probing noncommutative theories with quantum optical experiments
- Entropic uncertainty relation in de Sitter space
- Generalized Uncertainty Principle and Self-Adjoint Operators
- States in non-associative quantum mechanics: Uncertainty relations and semiclassical evolution
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