##  [Spectral Gap](/spectral-gap) 

  ##  [Spectral Gap](https://natural.quantumdictionary.io/spectral-gap-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The positive separation in the spectrum of a linear operator (or transition operator) between the dominant spectral value controlling the steady state and the remainder of the spectrum; it quantifies the slowest nontrivial relaxation rate to equilibrium.

 

 

 

 

 





 

 



 ##  [Spectral Gap](https://mathlogic.quantumdictionary.io/spectral-gap-1) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The difference between distinguished parts of the spectrum of a linear operator or matrix, commonly the gap between the dominant spectral value(s) and the remainder (for example, the difference between the largest and second-largest eigenvalues in modulus or real part).

 

 

 

 

 





 

 



 ##  [Spectral Gap](https://puremath.quantumdictionary.io/spectral-gap-2) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A positive lower bound in the spectrum of a linear operator that separates a distinguished part of the spectrum (often the ground state or the eigenvalue 0) from the remainder: there exists ε>0 so that no spectral value lies in (0,ε).