Quark-Parton Phase Transitions and the Entropy Problem in Quantum Mechanics
Y. S. Kim
备注：
RevTex 9 pages, 6 epsfigs, presented at International Conference on Quantum Electrodynamics and Statistical Physics, dedicated to the 90th anniversary of Alexander I. Akhiezer (Kharkov, Ukraine, Oct. 30 -- Nov. 3, 2001. One corrupted figure (fig. 6) replaced
发表信息：
Problems of Atomic Science and Technology, Special Issue dedicated to the 90th Birthday Anniversary of A. I. Akhiezer, No. 6 (1), 149--153 (2001)
Since Feynman proposed his parton model in 1969, one of the most pressing problems in high-energy physics has been whether partons are quarks. It is shown that the quark model and the parton model are two different manifestations of one covariant entity. The nature of transition from the confined quarks to plasma-like partons is studied in terms of the entropy and temperature coming from the time-separation variable. According to Einstein, the time-separation variable exists wherever there is a spatial separation, but it is not observed in the present form of quantum mechanics. It belongs to Feynman's rest of the universe.
We investigate the quantum entanglement in rapidity space of the soft gluon wave function of a quarkonium, in theories with non-trivial rapidity evolutions. We found that the rapidity evolution drastically changes the behavior of the entanglement entropy, at any given order in perturbation theory. At large $N_c$, the reduced density matrices that "resum" the leading rapidity-logs can be explicitly constructed, and shown to satisfy Balitsky-Kovchegov (BK)-like evolution equations. We study their entanglement entropy in a simplified $1+1$ toy model, and in 3D QCD. The entanglement entropy in the…
Quantum entanglement between partons in a strongly coupled quantum field theory
University of Science & Technology of China（中国科学技术大学）；Instituto Galego de Física de Altas Enerxías IGFAE, Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学加利西亚高能物理研究所）；Department of Physics, University of Turin（都灵大学物理系）；INFN, Section of Turin（意大利国家核物理研究院都灵分部）；Center for Frontiers in Nuclear Science, Stony Brook University（石溪大学核科学前沿中心）；Anhui Center for Fundamental Sciences in Theoretical Physics（安徽理论物理基础科学中心）；School of Mechanics and Physics, Anhui University of Science and Technology（安徽理工大学力学与物理学院）
High energy hadron interactions are commonly described by using a probabilistic parton model that ignores quantum entanglement present in the light-cone wave functions. Here we argue that since a high energy interaction samples an instant snapshot of the hadron wave function, the phases of different Fock state wave functions cannot be measured - therefore the light-cone density matrix has to be traced over these unobservable phases. Performing this trace with the corresponding $U(1)$ Haar integration measure leads to "Haar scrambling" of the density matrix, and to the emergence of entanglement…
We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while quantum systems can be considered the ones where the internal dynamics cannot be accessed at all. As information entropy can be used to characterize how much the state of the whole system identifies the state of its parts, classical systems can have arbitrarily small information entropy while quantum systems cannot. This provides insights that allow us to und…
University of Science and Technology of China（中国科学技术大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Anhui Center for Fundamental Sciences in Theoretical Physics（安徽理论物理基础科学中心）；School of Mechanics and Physics, Anhui University of Science and Technology（安徽理工大学力学与光电学院）
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^*$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of this approach to the study of entanglement measures for systems of identical particles are outlined. The ambiguities in the definition of entropy within this approach are then related to the action of unitaries in the commutant of the representation and their relation to modular theory explained.
We consider the target space entanglement in quantum mechanics of non-interacting fermions at finite temperature. Unlike pure states investigated in arXiv:2105.13726, the (Rényi) entanglement entropy for thermal states does not follow a simple bound because all states in the infinite-dimensional Hilbert space are involved. We investigate a general formula of the target space Rényi entropy for $N$ fermions at finite temperature, and present numerical results of the entropy in a one-dimensional model. We also argue the large $N$ behaviors with a comparison to the grand canonical ensemble.
Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the statistical mechanical entropy is defined by Gibbs. The relation between these two definitions of entropy is still not fully explored. In this work, we study this problem by employing the phase-space formulation of quantum mechanics. For those quantum states having well-defined classical counterparts, we study the quantum-classical correspondence and quantum cor…
This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with methods of computation are developed in general covariant form for curved phase spaces modelled as cotangent Lorentz bundles. The constructions are based on ideas relating the Grigory Perelman's entropy for geometric flows and associated statistical thermodynamic systems to the quantum von Neumann entropy, classical and quantum relative and conditional entr…
The concept of Logical Entropy, $S_L = 1- \sum_{i=1}^n p_i^2$, where the $p_i$ are normalized probabilities, was introduced by David Ellerman in a series of recent papers. Although the mathematical formula itself is not new, Ellerman provided a sound probabilistic interpretation of $S_L$ as a measure of the distinctions of a partition on a given set. The same formula comes across as a useful definition of entropy in quantum mechanics, where it is linked to the notion of purity of a quantum state. The quadratic form of the logical entropy lends itself to a generalization of the probabilities th…
The information on a quantum process acquired through measurements plays a crucial role in the determination of its non-equilibrium thermodynamic properties. We report on the experimental inference of the stochastic entropy production rate for a continuously monitored mesoscopic quantum system. We consider an optomechanical system subjected to continuous displacement Gaussian measurements and characterise the entropy production rate of the individual trajectories followed by the system in its stochastic dynamics, employing a phase-space description in terms of the Wigner entropy. Owing to the …
