On entropy and complexity of coherent states and Kähler geometry

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-07-22 DOI:10.1016/j.geomphys.2025.105598

Koushik Ray

引用次数: 0

Abstract

Consanguinity of entropy and complexity is pointed out through the example of coherent states of the group

S L (d + 1, C)

. Both are obtained from the Kähler potential of the underlying geometry of the sphere corresponding to the Fubini-Study metric. Entropy is shown to be equal to the Kähler potential written in terms of dual symplectic variables as the Guillemin potential for toric manifolds. The logarithm of complexity relating two states is shown to be equal to Calabi's diastasis function. Optimality of the Fubini-Study metric is indicated by considering its deformation.

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论相干态的熵和复杂性与Kähler几何

通过群SL（d+1，C）相干态的例子指出了熵与复杂度的亲缘关系。两者都是从对应于Fubini-Study度量的球体基础几何的Kähler势中获得的。熵被证明等于Kähler势，用对偶辛变量的形式写成，作为环流形的吉列明势。有关两种状态的复杂性的对数被证明等于卡拉比的耗散函数。考虑了Fubini-Study度量的变形，说明了其最优性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity