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Uncertainty Relation and the Thermal Properties of an Isotropic Harmonic Oscillator (IHO) with the Inverse Quadratic (IQ) Potentials and the Pseudo-Harmonic (PH) with the Inverse Quadratic (IQ) Potentials 具有逆二次（IQ）势的各向同性谐振子（IHO）和具有逆二次元（IQ）电位的伪谐波（PH）的不确定度关系和热性质

Quantum Reports Pub Date : 2023-01-12 DOI: 10.3390/quantum5010004

C. Onate, I. Okon, G. O. Jude, M. Onyeaju, A. Antia

{"title":"Uncertainty Relation and the Thermal Properties of an Isotropic Harmonic Oscillator (IHO) with the Inverse Quadratic (IQ) Potentials and the Pseudo-Harmonic (PH) with the Inverse Quadratic (IQ) Potentials","authors":"C. Onate, I. Okon, G. O. Jude, M. Onyeaju, A. Antia","doi":"10.3390/quantum5010004","DOIUrl":"https://doi.org/10.3390/quantum5010004","url":null,"abstract":"The solutions for a combination of the isotropic harmonic oscillator plus the inversely quadratic potentials and a combination of the pseudo-harmonic with inversely quadratic potentials has not been reported, though the individual potentials have been given attention. This study focuses on the solutions of the combination of the potentials, as stated above using the parametric Nikiforov–Uvarov (PNV) as the traditional technique to obtain the energy equations and their corresponding unnormalized radial wave functions. To deduce the application of these potentials, the expectation values, the uncertainty in the position and momentum, and the thermodynamic properties, such as the mean energy, entropy, heat capacity, and the free mean energy, are also calculated via the partition function. The result shows that the spectra for the PHIQ are higher than the spectra for the IHOIQ. It is also shown that the product of the uncertainties obeyed the Heisenberg uncertainty relation/principle. Finally, the thermal properties of the two potentials exhibit similar behaviours.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43706527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Blocky Diagonalized Scattering Matrices in Chaotic Scattering with Direct Processes 直接过程混沌散射中的块状对角化散射矩阵

Quantum Reports Pub Date : 2022-12-21 DOI: 10.3390/quantum5010002

F. Castañeda-Ramírez, M. Martínez-Mares

引用次数: 0

Entropic DDoS Detection for Quantum Networks 量子网络的熵DDoS检测

Quantum Reports Pub Date : 2022-12-13 DOI: 10.3390/quantum4040044

Del Rajan

引用次数: 0

Quantum Work from a Pseudo-Hermitian Hamiltonian 伪厄米哈密顿量的量子功

Quantum Reports Pub Date : 2022-12-13 DOI: 10.3390/quantum4040043

M. Reboiro, D. Tielas

引用次数: 1

Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver 利用变分量子特征解算器的数据用量子卷积神经网络检测相关系统的量子临界点

Quantum Reports Pub Date : 2022-12-08 DOI: 10.3390/quantum4040042

Nathaniel Wrobel, A. Baul, Ka-Ming Tam, Juana Moreno

引用次数: 0

Energy Transition Density of Driven Chaotic Systems: A Compound Trace Formula 驱动混沌系统的能量跃迁密度:一个复合示踪公式

Quantum Reports Pub Date : 2022-11-30 DOI: 10.3390/quantum4040040

A. M. Ozorio de Almeida

引用次数: 0

A Study of Strong Confinement Regions Using Informational Entropy 利用信息熵研究强约束域

Quantum Reports Pub Date : 2022-11-23 DOI: 10.3390/quantum4040039

Ademir de J. Santos, F. V. Prudente, M. N. Guimarães, Wallas S. Nascimento

引用次数: 3

Field Form of the Dynamics of Classical Many-And Few-Body Systems: From Microscopic Dynamics to Kinetics, Thermodynamics and Synergetics 经典多体和少体系统动力学的场形式:从微观动力学到动力学、热力学和协同学

Quantum Reports Pub Date : 2022-11-20 DOI: 10.3390/quantum4040038

A. Zakharov

引用次数: 0

Fricke Topological Qubits Fricke拓扑量子位

Quantum Reports Pub Date : 2022-11-14 DOI: 10.3390/quantum4040037

M. Planat, David Chester, M. Amaral, K. Irwin

{"title":"Fricke Topological Qubits","authors":"M. Planat, David Chester, M. Amaral, K. Irwin","doi":"10.3390/quantum4040037","DOIUrl":"https://doi.org/10.3390/quantum4040037","url":null,"abstract":"We recently proposed that topological quantum computing might be based on SL(2,C) representations of the fundamental group π1(S3K) for the complement of a link K in the three-sphere. The restriction to links whose associated SL(2,C) character variety V contains a Fricke surface κd=xyz−x2−y2−z2+d is desirable due to the connection of Fricke spaces to elementary topology. Taking K as the Hopf link L2a1, one of the three arithmetic two-bridge links (the Whitehead link 512, the Berge link 622 or the double-eight link 632) or the link 732, the V for those links contains the reducible component κ4, the so-called Cayley cubic. In addition, the V for the latter two links contains the irreducible component κ3, or κ2, respectively. Taking ρ to be a representation with character κd (d<4), with |x|,|y|,|z|≤2, then ρ(π1) fixes a unique point in the hyperbolic space H3 and is a conjugate to a SU(2) representation (a qubit). Even though details on the physical implementation remain open, more generally, we show that topological quantum computing may be developed from the point of view of three-bridge links, the topology of the four-punctured sphere and Painlevé VI equation. The 0-surgery on the three circles of the Borromean rings L6a4 is taken as an example.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43813539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Algebraic Properties of Quantum Reference Frames: Does Time Fluctuate? 量子参考系的代数性质：时间会波动吗？

Quantum Reports Pub Date : 2022-11-08 DOI: 10.3390/quantum5010003

M. Bojowald, Artur Tsobanjan

{"title":"Algebraic Properties of Quantum Reference Frames: Does Time Fluctuate?","authors":"M. Bojowald, Artur Tsobanjan","doi":"10.3390/quantum5010003","DOIUrl":"https://doi.org/10.3390/quantum5010003","url":null,"abstract":"Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference variables, in particular of time, are restricted by their very nature of being used for reference. Mathematically, this property is implemented by imposing constraints on the system to make sure that reference variables are not physical degrees of freedom. These constraints not only relate physical degrees of freedom to reference variables in order to describe their behavior, they also restrict quantum fluctuations of reference variables and their correlations with system degrees of freedom. We introduce the notion of “almost-positive” states as a suitable mathematical method. An explicit application of their properties to examples of recent interest in quantum reference frames reveals previously unrecognized restrictions on possible frame–system interactions. While currently discussed clock models rely on assumptions that, as shown here, make them consistent as quantum reference frames, relaxing these assumptions will expose the models to new restrictions that appear to be rather strong. Almost-positive states also shed some light on a recent debate about the consistency of relational quantum mechanics.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46015134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0