Quantum walks as thermalisations, with application to fullerene graphs

Dhamapurkar, Shyam1; Dahlsten, Oscar1,3,4

2024-06-15

10.1016/j.physa.2024.129823

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS   影响因子和分区

0378-4371

1873-2119

We consider to what extent quantum walks can constitute models of thermalisation, analogously to how classical random walks can be models for classical thermalisation. In a quantum walk over a graph, a walker moves in a superposition of node positions via a unitary time evolution. We show a quantum walk can be interpreted as an equilibration of a kind investigated in the literature on thermalisation in unitarily evolving quantum systems. This connection implies that recent results concerning the equilibration of observables can be applied to analyse the node position statistics of quantum walks. We illustrate this in the case of a family of graphs known as fullerenes. We find that a bound from Short et al., implying that certain expectation values will at most times be close to their time -averaged value, applies tightly to the node position probabilities. Nevertheless, the node position statistics do not thermalise in the standard sense. In particular, quantum walks over fullerene graphs constitute a counterexample to the hypothesis that subsystems equilibrate to the Gibbs state. We also exploit the bridge created to show how quantum walks can be used to probe the universality of the eigenstate thermalisation hypothesis relation. We find that whilst in C60 with a single walker, the eigenstate thermalisation hypothesis relation does not hold for node position projectors, it does hold for the average position, enforced by a symmetry of the Hamiltonian. The findings suggest a unified study of quantum walks and quantum self-thermalisations is natural and feasible.

Thermalisation Gibbs state Continuous time quantum walks Eigenstate thermalisation hypothesis

SCI ; EI

英语

第一 ; 通讯

National Natural Science Foundation of China["12050410246","1200509","12050410245"] ; City University of Hong Kong[9610623]

Physics

Physics, Multidisciplinary

WOS:001246487800001

ELSEVIER

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
2.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
3.City Univ Hong Kong, Dept Phys, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China
4.Southern Univ Sci & Technol, Inst Nanosci & Applicat, Shenzhen 518055, Peoples R China

Dhamapurkar, Shyam,Dahlsten, Oscar. Quantum walks as thermalisations, with application to fullerene graphs[J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS,2024,644.

Dhamapurkar, Shyam,&Dahlsten, Oscar.(2024).Quantum walks as thermalisations, with application to fullerene graphs.PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS,644.

Dhamapurkar, Shyam,et al."Quantum walks as thermalisations, with application to fullerene graphs".PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 644(2024).