Related Experiment Video
Updated: Sep 11, 2025

Gradient Echo Quantum Memory in Warm Atomic Vapor
Published on: November 11, 2013
Non-Markov random telegraph processes with arbitrary nonlocal memory
S S Melnyk1, O V Usatenko1,2,3, V A Yampol'skii1,4
1O. Ya. Usikov Institute for Radiophysics and Electronics NASU, 61085 Kharkiv, Ukraine.
None:
We study random dichotomous stationary ergodic processes with nonlocal in-time memory. These processes are characterized by a conditional transition probabilities distribution containing an integral term involving the memory function, which takes into account the past of the process. For the first time, we present a method for solving the integro-differential equation, which connects the arbitrary memory and pair correlation functions in an analytical closed form. Conditions of stationarity for the telegraph process with exponential memory are found. It is shown that the pair correlation function of this process can be of two types: either exponentially decreasing with two different decrements or oscillating with exponentially decreasing amplitude.
Related Concept Videos
Propagation of Uncertainty from Random Error
Random Variables
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
Reversible and Irreversible Processes
Understanding Memory
Interference and Decay
Interference occurs when competing memories hinder the retrieval of particular information. It can be classified into two types: proactive and retroactive interference. Proactive...
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

