Temperature: The ignored factor in quantum mechanics
Ashkan Shekaari, Mahmoud Jafari
备注：
In fact, according to the comments we received from other researchers of the field, and based on our further investigation, and more importantly by taking into account the arXiv's advice regarding the way to update and make corrections to articles, we manipulated and improved some parts of our previous manuscript in order to be more rigorous in content and more illustrative in presentation
We have developed a theoretical formalism to introduce temperature as a parameter into the framework of non-relativistic quantum mechanics using the laws of classical thermodynamics and the canonical ensemble scheme of statistical mechanics. A self-consistent Hamiltonian has then been constructed for a given quantum many-body system which includes the effect of temperature in the form of correction terms added to the corresponding zero-temperature Hamiltonian of the system. Investigating some quantum mechanical systems with exact zero-temperature solutions including the particle-in-a-box model, the free particle, and the harmonic oscillator within our finite-temperature approach up to the first order of self-consistency has led to temperature-dependent Hamiltonians describing these systems above absolute zero without encountering any physically unacceptable brand of behavior for their wave functions and energy spectra. Results firmly support the view that a quantum mechanical system at a finite temperature behaves as if it is in a zero-temperature excited state.
We present the general ideas on SuperSymmetric Quantum Mechanics (SUSY-QM) using different representations for the operators in question, which are defined by the corresponding bosonic Hamiltonian as part of SUSY Hamiltonian and its supercharges, which are defined as matrix or differential operators. We show that, although most of the SUSY partners of one-dimensional Schrödinger problems have already been found,there are still some unveiled aspects of the factorization procedure which may lead to richer insights of the problem involved.
Constraints play an important role in dynamical systems. However, the subtle effect of constraints in quantum mechanics is not very well studied. In the present work we concentrate on the quantum dynamics of a point particle moving on a non-trivial torus knot. We explicitly take into account the role of curvature and torsion, generated by the constraints that keep the particle on the knot. We exploit the "Geometry Induced Potential (GIP) approach" to construct the Schrodinger equation for the dynamical system, obtaining thereby new results in terms of particle energy eigenvalues and eigenfunct…
The De Broglie-Bohm (DeBB)\cite{DeBB} Causal Quantum Mechanics played a crucial role in Bell's discovery \cite{Bell1964} that quantum mechanics violates EPR local reality \cite{EPR1935}, and also in Bell's search for an exact quantum mechanics. The experiments of Aspect et al \cite{Aspect1981} confirm quantum correlations between plane polarizations of two photons and violation of Bell's inequalities by a factor $\sqrt 2 $. I prove that similar experiments with elliptic polarizers can also show quantum violations of Bell's inequality by the same factor. I summarize our construction of a maxima…
Implementing a quantum algorithm on a NISQ device has several challenges that arise from the fact that such devices are noisy and have limited quantum resources. Thus, various factors contributing to the depth and width as well as to the noise of an implementation of an algorithm must be understood in order to assess whether an implementation will execute successfully on a given NISQ device. In this contribution, we discuss these factors and their impact on algorithm implementations. Especially, we will cover state preparation, oracle expansion, connectivity, circuit rewriting, and readout: th…
It is unusual to find QCD factorization explained in the language of quantum information science. However, we will discuss how the issue of factorization and its breaking in high-energy QCD processes relates to phenomena like decoherence and entanglement. We will elaborate with several examples and explain them in terms familiar from basic quantum mechanics and quantum information science.
目前的量子力学是以哥本哈根学派的解释为基础的。爱因斯坦不属于哥本哈根学派，因为他不相信基本物理定律的概率解释。这就是为什么我们仍然在争论是否有一个更确定性的理论。爱因斯坦和哥本哈根学派分离的原因之一可能是哥本哈根学派的物理学家完全忽略了爱因斯坦的主要关注点：相对性原理。Paul A. M.狄拉克是第一个意识到这个问题的人。事实上，从1927年到1963年，保罗·A. M.狄拉克发表了至少四篇论文，研究问题的不确定性关系符合爱因斯坦的洛伦兹协变性。有趣的是，结合这些文件狄拉克使不确定关系符合相对论。它表明，两个耦合振荡器的数学使我们能够进行这项工作。然后，我们被引导到的问题，是否局部概率分布的概念是一致的洛伦兹协方差。
Factorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics. I: general classification of reducibility and analysis of the third-order algebra
Solution of the discrete Wheeler-DeWitt equation in the vicinity of small scale factors and quantum mechanics in the space of negative constant curvature
An Analysis of States in the Phase Space: From Quantum Mechanics to General Relativity
本文具有启发性。这个概念框架仅基于量子不确定性的假设，以前曾在两篇论文中介绍过[S。Tosto，Il Nuovo Cimento B，第111卷，第2期，1996年和S. Tosto，Il Nuovo Cimento D，vol. 18，n.12，1996]。这些论文没有试图通过一种新的近似来提高现有计算模型的准确性，而是从一开始就承认缺乏关于组成粒子的局部性质的确定性信息，这些粒子被认为是随机的、未知的和不可预测的，因此原则上被忽略了。其主要思想是量子系统的物理性质可以仅仅考虑动力学变量的离域范围而不是它们的局部值来推断。实际上，尽管提出的方法的不可知性，这两篇论文表明，在所有情况下，获得解决相关的波动方程的物理信息达到再现准确。本文将量子不确定性的概念进一步推广到空间和时间坐标上，考虑了时空的唯一离域范围，并从一开始就抛弃了共轭动力学变量的局部值。这篇论文展示了一个意想不到的丰富的信息，可以简单地将空间不确定性的概念扩展到时空不确定性：结果与波动力学的算子形式主义和狭义相对论的基本假设是内在一致的，两者都是推论。此外，甚至引力似乎本质上也是一种量子现象。狭义相对论和广义相对论最相关的结果是通过使用在早期论文中首次引入的简单量子形式，作为粒子时空离域的直接结果而实现的。
Role of dissipation dilution in achieving high mechanical quality factors in van der Waals resonators
Technical University of Munich（慕尼黑工业大学）；Walter Schottky Institute and Physics Department, Technical University of Munich（沃尔特·施科特基研究所与物理系，慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
