Exponential Ramp in the Quadratic Sachdev-Ye-Kitaev Model

Michael Winer1, Shao-Kai Jian1, Brian Swingle1

  • 1Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA.

Physical Review Letters
|January 8, 2021
PubMed
Summary

Researchers studied the spectral form factor in disordered integrable many-body models. They discovered an exponential ramp in the Sachdev-Ye-Kitaev model, differing from chaotic systems.

Related Concept Videos

Exponential Equations for Modeling Growth02:33

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is...
71
Introduction to Exponential Functions01:29

Introduction to Exponential Functions

Exponential functions are fundamental in modeling dynamic processes where the rate of change is proportional to the current value. Defined by f(x) = bx, where b is a positive constant not equal to one, they form the basis for describing processes of growth and decay depending on whether the base b is greater than or less than one.Exponential models describe situations where change occurs at a rate proportional to the current amount. These include phenomena such as bacterial proliferation,...
125
Exponential Functions with Base e01:30

Exponential Functions with Base e

Exponential functions with base e are essential for modeling continuous processes of growth and decay. The constant e, approximately 2.718, naturally arises in systems where change occurs proportionally to the current value. A positive exponent represents continuous growth, while a negative exponent represents continuous decay. These functions are especially useful for describing situations where change happens smoothly over time rather than in discrete steps.One clear example of exponential...
62
Quadratic Models01:23

Quadratic Models

Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
64
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...
501
Exponential Equations with Logarithms: Problem Solving01:29

Exponential Equations with Logarithms: Problem Solving

In ecological studies, exponential models are often used to predict how populations grow over time under favorable conditions. These models assume that the growth rate is proportional to the current population, leading to continuous and compounding increases.The model expresses the population as a function of time, combining the initial population with a growth factor raised to an exponent involving the growth rate and time. To estimate how long it takes for a population to reach a specific...
59