Form Of Uncertainty Principle Research Articles

Investigation on the stability and quantum phase transition of the charged rotating Kiselev Black Hole embedded in Quintessence field with quantum fluctuation of entropy

Immediate local impacts of cosmic acceleration upon a rapidly rotating black hole are very interesting in recent studies. In this paper, the stability of a rapidly rotating black hole and the minimum value of the ratio between the black hole’s angular momentum to it’s mass which ensures the stability, are investigated simultaneously. Also, two modern forms of uncertainty relations are proposed by enhancing the usual Heisenberg algebra with superior terms, in order to supervise on thermodynamic properties of the rotating black hole. An asymptotically flat Kiselev black hole solution, cultivated by quintessence field is chosen for this purpose. The local shifts in spacetime geometry next to the rotating black hole can be resolved from a modified metric, occupying the surrounding spacetime of the black hole. The angular momentum of a rotating black hole depends on the rate of change in acquiring mass by it. On the other hand, at the same time, due to the effect of the quintessence field, there exists repulsive gravitational force inside the black hole. So, there is an uncertainty in the position of innermost stable circular orbit as well as radius of the rotating black hole. This uncertainty is also investigated in our work. Relying on two new forms of uncertainty principle, the modified thermodynamic variables like black hole’s Hawking temperature, heat-capacity, entropy at the black hole’s event horizon, etc. are computed under rotation. Quantum corrections of black hole’s Hawking temperature, entropy, free-energy, etc. are also explored. Further, quantum corrected heat capacity of the rotating black hole is studied and also thermal stability is inquired. The existence of transitions of phase in case of a rapidly rotating black hole are also found out. Again, quantum corrected entropy of black hole contains logarithmic terms and their effects on thermal stability of the rotating black hole are also discussed. Modifications in the mass-temperature, specific heat, etc. of a rotating black hole are also presented according to the modified extension parameters.

Discrete Gaussian measures and new bounds of the smoothing parameter for lattices

In this paper, we start with a discussion of discrete Gaussian measures on lattices. Several results of Banaszczyk are analyzed, a simple form of uncertainty principle for discrete Gaussian measure is formulated. In the second part of the paper we prove two new bounds for the smoothing parameter of lattices. Under the natural assumption that $$\varepsilon$$ is suitably small, we obtain two estimations of the smoothing parameter:

Experimental test of fine-grained entropic uncertainty relation in the presence of quantum memory

The uncertainty principle, which gives the constraints on obtaining precise outcomes for incompatible measurements, provides a new vision of the real world that we are not able to realize from the classical knowledge. In recent years, numerous theoretical and experimental developments about the new forms of the uncertainty principle have been achieved. Among these efforts, one attractive goal is to find tighter bounds of the uncertainty relation. Here, using an all optical setup, we experimentally investigate a most recently proposed form of uncertainty principle—the fine-grained uncertainty relation assisted by a quantum memory. The experimental results on the case of two-qubit state with maximally mixed marginal demonstrate that the fine-graining method can help to get a tighter bound of the uncertainty relation. Our results might contribute to further understanding and utilizing of the uncertainty principle.

Uncertainty Principle and Phase–Amplitude Analysis of Signals on the Unit Sphere

This paper is devoted to studying uncertainty principle of Heisenberg type for signals on the unit sphere in the Clifford algebra setting. In the Clifford algebra setting we propose two forms of uncertainty principle for spherical signals, of which both correspond to the strongest form of uncertainty principle for periodic signals. The lower-bounds of the proven uncertainty principles are in terms of a scalar-valued phase derivative.