Uncertainty Relation: From Inequality to Equality

Abstract

The uncertainty area (5 (p, q): -[J W(p, q) 2 dp dq] ~1 is proposed in place of äp • Öq, and it is shown that each pure quantum state is a minimum uncertainty state in this sense: S (p, q) = 2 n h. For mixed states, on the other hand, d(p, q) > 2nh. In a phase space of 2F(=6N) dimensions, S: = k B • log[<5 f (p, q)/(2nh) F ]with S F (p, q):= [J W(p, q) 2 d pd F q]' 1 is considered as an alternative to von Neumann's entropy S:=k B • trclog~1)].

Microtubule instability driven by longitudinal and lateral strain propagation

“…Uncertainties were obtained by first sampling distribution realizations with the Metropolis-Hastings algorithm around the reconstructed distributions (see [6] for the algorithm). Then, for every point G l in the free energy distribution, Süssmann's uncertainty estimate δG l = 1/ p l (G) 2 dG was used [7,8], where p l (G) is the distribution of free energies in bin l obtained through Metropolis-Hastings sampling.…”

Stochastic Simulation of Emission Spectra and Classical Photon Statistics of Quantum Dot Superluminescent Diodes

“…The result of the simulation (see Figure 4) shows good agreement with the experimental optical power spectrum [3]. We define the width of the spectral power density [41] [42] ( ) By extracting appropriate simulation parameters from an experimental spectrum, the electric field emitted by the diode can be simulated numerically and can be used to calculate the stationary first-order temporal correlation function and optical power spectrum of the emission.…”

Quantum phase space functions and relations of entropic localisation measures

“…Another measure of localisation of a quantum state in phase space is Süßmann's uncertainty area with dimension of an action, which is defined by ¶ [8,1]…”