Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Transition State Theory01:25

Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
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.
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...
The Swing Equation01:21

The Swing Equation

The Swing Equation is a fundamental tool in power system dynamics, especially for analyzing the behavior of generating units like three-phase synchronous generators. This equation emerges from applying Newton's second law to the rotor of a generator, encompassing factors such as inertia, angular acceleration, and the interplay between mechanical and electrical torques.
In a steady-state operation, the mechanical torque (Τm) supplied to the generator is balanced by the electrical torque (Τe)...
The Integrated Rate Law: The Dependence of Concentration on Time02:39

The Integrated Rate Law: The Dependence of Concentration on Time

While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Topological nodal i-wave superconductivity in PtBi<sub>2</sub>.

Nature·2025
Same author

Helical Topological Superconducting Pairing at Finite Excitation Energies.

Physical review letters·2024
Same author

Random-matrix theory for the Lindblad master equation.

Chaos (Woodbury, N.Y.)·2021
Same author

Electronic structure, transport, and collective effects in molecular layered systems.

Beilstein journal of nanotechnology·2017
Same author

Spin-dependent transport and functional design in organic ferromagnetic devices.

Beilstein journal of nanotechnology·2017
Same author

Topological Kondo effect in transport through a superconducting wire with multiple Majorana end states.

Physical review letters·2015

Related Experiment Video

Updated: Jun 19, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Random transition-rate matrices for the master equation.

Carsten Timm1

  • 1Institute for Theoretical Physics, Technische Universität Dresden, 01062 Dresden, Germany. carsten.timm@tu-dresden.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 2, 2009
PubMed
Summary
This summary is machine-generated.

Random-matrix theory reveals unique eigenvalue distributions in Pauli master equations. This analysis of transition-rate matrices offers new insights into complex stochastic system dynamics.

More Related Videos

Recombination Dynamics in Thin-film Photovoltaic Materials via Time-resolved Microwave Conductivity
11:30

Recombination Dynamics in Thin-film Photovoltaic Materials via Time-resolved Microwave Conductivity

Published on: March 6, 2017

Related Experiment Videos

Last Updated: Jun 19, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Recombination Dynamics in Thin-film Photovoltaic Materials via Time-resolved Microwave Conductivity
11:30

Recombination Dynamics in Thin-film Photovoltaic Materials via Time-resolved Microwave Conductivity

Published on: March 6, 2017

Area of Science:

  • Statistical Physics
  • Quantum Mechanics
  • Applied Mathematics

Background:

  • Complex stochastic systems are often modeled using the Pauli master equation.
  • The dynamics of these systems are governed by the eigenvalues of transition-rate matrices.
  • Understanding eigenvalue properties is crucial for analyzing system behavior.

Purpose of the Study:

  • To apply random-matrix theory to transition-rate matrices within the Pauli master equation.
  • To investigate the distribution and correlations of eigenvalues for different transition rate scenarios.
  • To compare the resulting matrix ensembles with standard ensembles.

Main Methods:

  • Application of random-matrix theory to Pauli master equation transition-rate matrices.
  • Analysis of eigenvalue distributions and correlations for both symmetric (identical rates) and asymmetric (independent rates) matrices.
  • Comparison of novel matrix ensembles with established random matrix theory ensembles.

Main Results:

  • Identical and independent transition rates lead to distinct symmetric and asymmetric matrix ensembles, respectively.
  • These ensembles exhibit different eigenvalue distributions compared to standard ensembles.
  • An anomalous scaling of the fraction of real eigenvalues with matrix dimension was observed in the asymmetric case.

Conclusions:

  • Random-matrix theory provides a powerful framework for analyzing complex stochastic systems via Pauli master equations.
  • The nature of transition rates (identical vs. independent) significantly impacts matrix properties and eigenvalue behavior.
  • The findings highlight deviations from standard random-matrix theory predictions, particularly for asymmetric matrices.