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Interacting quantum walk on a graph.

Alberto D Verga¹

¹Aix-Marseille Université, CPT, Campus de Luminy, case 907, 13288 Marseille, France.

Physical Review. E

|February 21, 2019

Summary

This summary is machine-generated.

We developed a novel quantum system with interacting spins and a hopping particle. This system relaxes to paramagnetic or ferromagnetic states, linked to eigenvector thermalization and random matrix theory.

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Area of Science:

Quantum mechanics
Condensed matter physics
Statistical mechanics

Background:

Understanding quantum system dynamics is crucial.
Investigating spin-particle interactions provides insights into complex quantum behaviors.
Exploring thermalization and entanglement in novel quantum systems is an active research area.

Purpose of the Study:

To introduce and analyze an elementary quantum system composed of spins on a graph and a hopping particle.
To investigate the relaxation dynamics and stationary states of this quantum system.
To explore the relationship between macroscopic properties (paramagnetism/ferromagnetism), eigenvector thermalization, random matrix statistics, and entanglement.

Main Methods:

Sequential construction of the quantum state using unitary transformations.
Coupling of neighboring spins and particle-spin interactions at each node.
Analysis of system relaxation towards stationary states.
Examination of eigenvector thermalization and random matrix statistics.
Investigation of interaction-generated entanglement.

Main Results:

The quantum system relaxes to either a paramagnetic or ferromagnetic stationary state.
This relaxation behavior is demonstrably linked to eigenvector thermalization.
The observed statistics align with predictions from random matrix theory.
A connection is established between macroscopic properties and entanglement generated by interactions.

Conclusions:

The introduced quantum system serves as a model for studying fundamental quantum phenomena.
Eigenvector thermalization and random matrix statistics play a key role in the system's macroscopic behavior.
Interaction-generated entanglement is intrinsically related to the observed relaxation and stationary states.