uncertainty relations
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Author(s):  
Ofir Flom ◽  
Asher Yahalom ◽  
Jacob Levitan ◽  
Haggai Zilberberg

We study the connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. For this we use model of particle in a box. We have shown that the amplitude can be calculated from the phase and vice versa if the log Analytical uncertainty relations are satisfied.


Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 58
Author(s):  
Houri Ziaeepour

In a previous article we proposed a new model for quantum gravity (QGR) and cosmology, dubbed SU(∞)-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent the SU(∞) symmetry group. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the SU(∞) representing Hilbert spaces. Using quantum uncertainty relations, it is shown that the parameter space—the spacetime—has a 3+1 dimensional Lorentzian geometry. Here, after a review of SU(∞)-QGR, including a demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by the holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. The hope is that this exercise provides a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. We identify several common features among the studied models: the importance of 2D structures; the algebraic decomposition to tensor products; the special role of the SU(2) group in their formulation; the necessity of a quantum time as a relational observable. We discuss how these features can be considered as analogous in different models. We also show that they arise in SU(∞)-QGR without fine-tuning, additional assumptions, or restrictions.


2022 ◽  
Vol 824 ◽  
pp. 136818
Author(s):  
Luca Buoninfante ◽  
Giuseppe Gaetano Luciano ◽  
Luciano Petruzziello ◽  
Fabio Scardigli

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 20
Author(s):  
Moise Bonilla-Licea ◽  
Dieter Schuch

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.


Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 504
Author(s):  
Luca Smaldone ◽  
Giuseppe Vitiello

We review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits giving a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula, which in the relativistic limit reproduces the Pontecorvo oscillation formula and illustrates some of the contradictions arising in the quantum mechanics approximation. We show that the gauge theory structure underlies the neutrino mixing phenomenon and that there exists entanglement between mixed neutrinos. The flavor vacuum is found to be an entangled generalized coherent state of SU(2). We also discuss flavor energy uncertainty relations, which impose a lower bound on the precision of neutrino energy measurements, and we show that the flavor vacuum inescapably emerges in certain classes of models with dynamical symmetry breaking.


Author(s):  
ZHANG Fu Gang

Abstract In this paper, we discuss quantum uncertainty relations of Tsallis relative $\alpha$ entropy coherence for a single qubit system based on three mutually unbiased bases. For $\alpha\in[\frac{1}{2},1)\cup(1,2]$, the upper and lower bounds of sums of coherence are obtained. However, the above results cannot be verified directly for any $\alpha\in(0,\frac{1}{2})$. Hence, we only consider the special case of $\alpha=\frac{1}{n+1}$, where $n$ is a positive integer, and we obtain the upper and lower bounds. By comparing the upper and lower bounds, we find that the upper bound is equal to the lower bound for the special $\alpha=\frac{1}{2}$, and the differences between the upper and the lower bounds will increase as $\alpha$ increases. Furthermore, we discuss the tendency of the sum of coherence, and find that it has the same tendency with respect to the different $\theta$ or $\varphi$, which is opposite to the uncertainty relations based on the R\'{e}nyi entropy and Tsallis entropy.


2021 ◽  
Vol 104 (6) ◽  
Author(s):  
Bo-Fu Xie ◽  
Fei Ming ◽  
Dong Wang ◽  
Liu Ye ◽  
Jing-Ling Chen

2021 ◽  
Vol 2021 (12) ◽  
pp. 123302
Author(s):  
Ariane Soret ◽  
Ohad Shpielberg ◽  
Eric Akkermans

Abstract Thermodynamic uncertainty relations unveil useful connections between fluctuations in thermal systems and entropy production. This work extends these ideas to the disparate field of zero temperature quantum mesoscopic physics where fluctuations are due to coherent effects and entropy production is replaced by a cost function. The cost function arises naturally as a bound on fluctuations, induced by coherent effects—a critical resource in quantum mesoscopic physics. Identifying the cost function as an important quantity demonstrates the potential of importing powerful methods from non-equilibrium statistical physics to quantum mesoscopics.


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