4.7 Article

Complexity of energy eigenstates as a mechanism for equilibration

Journal

PHYSICAL REVIEW E
Volume 87, Issue 3, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.87.032137

Keywords

-

Funding

  1. ERC Starting Grant PERCENT
  2. EUFP7 Q-Essence Project
  3. Spanish Project [FIS2010-14830]
  4. CatalunyaCaixa
  5. Generalitat de Catalunya
  6. CONICET
  7. ICREA Funding Source: Custom

Ask authors/readers for more resources

Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and the complexity of their eigenvectors, provided that a conjecture about the incompressibility of quantum circuits holds. We quantify the complexity by the size of the smallest quantum circuit mapping the local basis onto the energy eigenbasis. Specifically, we consider the set of all Hamiltonians having complexity C, and show that almost all such Hamiltonians equilibrate if C is superquadratic in the system size, which includes the fully random Hamiltonian case in the limit C -> infinity, and do not equilibrate if C is sublinear. We also provide a simple formula for the equilibration time scale in terms of the Fourier transform of the level density. Our results are statistical and, therefore, do not apply to specific Hamiltonians. Yet they establish a fundamental link between equilibration and complexity theory. DOI:10.1103/PhysRevE.87.032137

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.7
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available