Geodesics in information geometry: Classical and quantum phase transitions

被引：28

作者：

Kumar, Prashant ^{[1
]}

Mahapatra, Subhash ^{[1
]}

Phukon, Prabwal ^{[1
]}

Sarkar, Tapobrata ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Phys, Kanpur 208016, Uttar Pradesh, India

来源：

PHYSICAL REVIEW E | 2012年 / 86卷 / 05期

关键词：

THERMODYNAMICS;

D O I：

10.1103/PhysRevE.86.051117

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We study geodesics on the parameter manifold for systems exhibiting second order classical and quantum phase transitions. The coupled nonlinear geodesic equations are solved numerically for a variety of models which show such phase transitions in the thermodynamic limit. It is established that both in the classical as well as in the quantum cases, geodesics are confined to a single phase and exhibit turning behavior near critical points. Our results are indicative of a geometric universality in widely different physical systems.

引用

页数：6

共 50 条

[41] Rare region effects at classical, quantum and nonequilibrium phase transitions
Vojta, Thomas
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (22): : R143 - R205
[42] Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
de Sousa, Matheus S. M.
Cruz, Antonio L.
Chen, Wei
[J]. PHYSICAL REVIEW B, 2023, 107 (20)
[43] INFORMATION GEOMETRY IN FUNCTIONAL SPACES OF CLASSICAL AND QUANTUM FINITE STATISTICAL SYSTEMS
INGARDEN, RS
[J]. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1981, 19 (12) : 1609 - 1633
[44] Mechanics of geodesics in information geometry and black hole thermodynamics
Chanda, Sumanto
Wada, Tatsuaki
[J]. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2024, 21 (05)
[45] Quantum information and phase transitions: fidelity and state distinguishability
Vieira, V. R.
[J]. SYMMETRY AND STRUCTURAL PROPERTIES OF CONDENSED MATTER, 2010, 213
[46] Information geometry and asymptotic geodesics on the space of normal distributions
Globke W.
Quiroga-Barranco R.
[J]. Information Geometry, 2021, 4 (1) : 131 - 153
[47] Quantum phase transitions in the LMG model by means of quantum information concepts
Castanos, O.
Lopez-Pena, R.
Nahmad-Achar, E.
Hirsch, J. G.
[J]. XXXV SYMPOSIUM ON NUCLEAR PHYSICS, 2012, 387
[48] QUANTUM JUMPS, GEODESICS, AND THE TOPOLOGICAL PHASE
BENEDICT, MG
FEHER, LG
[J]. PHYSICAL REVIEW D, 1989, 39 (10): : 3194 - 3196
[49] Quantum response to classical transitions
Satija, II
[J]. PHYSICAL REVIEW E, 2002, 66 (01):
[50] Quantum simulation of quantum phase transitions using the convex geometry of reduced density matrices
Warren, Samuel
Sager-Smith, Leeann M.
Mazziotti, David A.
[J]. PHYSICAL REVIEW A, 2022, 106 (01)

← 1 2 3 4 5 →