Zero-point energies, the uncertainty principle and positivity of the quantum Brownian density operator

Details Zero-point energies, the uncertainty principle and positivity of the quantum Brownian density operator Zero-point energies, the uncertainty principle and positivity of the quantum Brownian density operator

2012-04-09

arxiv.org/abs/1204.1876v1

Phys. Rev. E 85, 042103 (2012)

Physics

Quantum Physics

Scientific paper

High temperature and white noise approximations are frequently invoked when deriving the quantum Brownian equation for an oscillator. Even if this white noise approximation is avoided, it is shown that if the zero point energies of the environment are neglected, as they often are, the resultant equation will violate not only the basic tenet of quantum mechanics that requires the density operator to be positive, but also the uncertainty principle. When the zero-point energies are included, asymptotic results describing the evolution of the oscillator are obtained that preserve positivity and, therefore, the uncertainty principle.

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