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

State Space to Transfer Function01:21

State Space to Transfer Function

671
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
671
Transfer Function to State Space01:23

Transfer Function to State Space

936
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
936
State Space Representation01:27

State Space Representation

682
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
682
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

459
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
459
Vector Product (Cross Product)01:17

Vector Product (Cross Product)

28.5K
Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of the angle between both the vectors and the direction perpendicular to both the individual vectors. As there are always two directions perpendicular to a given plane, one on each side, the direction of the vector product is governed by the right-hand thumb rule.
Consider the cross product of two vectors. Imagine rotating the first vector about...
28.5K
Scalar and Vector Triple Products01:06

Scalar and Vector Triple Products

4.7K
Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors....
4.7K

You might also read

Related Articles

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

Sort by
Same author

XYZ Integrability the Easy Way.

Journal of statistical physics·2026
Same author

Entanglement and the density matrix renormalization group in the generalized Landau paradigm.

Nature physics·2025
Same author

Low-Depth Unitary Quantum Circuits for Dualities in One-Dimensional Quantum Lattice Models.

Physical review letters·2025
Same author

Emergent Conformal Boundaries from Finite-Entanglement Scaling in Matrix Product States.

Physical review letters·2024
Same author

Extracting the Speed of Light from Matrix Product States.

Physical review letters·2023
Same author

Evidence for the utility of quantum computing before fault tolerance.

Nature·2023

Related Experiment Video

Updated: Mar 21, 2026

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism
08:44

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism

Published on: October 17, 2025

801

Stochastic matrix product states.

Kristan Temme1, Frank Verstraete

  • 1Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

We introduce stochastic matrix product states for nonequilibrium systems. A new correlation measure, entropy cost, quantifies the resources needed for these states, demonstrated using the asymmetric exclusion process.

More Related Videos

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

9.1K
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

9.8K

Related Experiment Videos

Last Updated: Mar 21, 2026

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism
08:44

Dynamic Clamp Methods to Investigate Impaired Neuronal Excitability Associated with Autism

Published on: October 17, 2025

801
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

9.1K
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

9.8K

Area of Science:

  • Statistical Mechanics
  • Quantum Information Theory
  • Condensed Matter Physics

Background:

  • Matrix product states (MPS) are a powerful tool for studying one-dimensional quantum systems.
  • Nonequilibrium stochastic processes present challenges for traditional MPS methods.
  • Characterizing correlations in open quantum systems is crucial for understanding their behavior.

Purpose of the Study:

  • To introduce and define stochastic matrix product states (Stoch-MPS).
  • To develop an analogue of Schmidt coefficients for steady states of nonequilibrium processes.
  • To introduce a new correlation measure, the entropy cost S(C), analogous to entanglement entropy.

Main Methods:

  • Derivation of a natural form for stochastic matrix product states.
  • Definition of Schmidt coefficient analogues for steady states.
  • Analysis of the asymmetric exclusion process as a test case.

Main Results:

  • Stochastic matrix product states provide a framework for nonequilibrium systems.
  • The entropy cost S(C) is shown to quantify the bond dimension required for Stoch-MPS representation.
  • The asymmetric exclusion process demonstrates the utility of these concepts.

Conclusions:

  • Stoch-MPS offer a new perspective on the structure of nonequilibrium steady states.
  • The entropy cost S(C) serves as a vital measure for correlation and MPS resource quantification.
  • These findings pave the way for analyzing complex correlated systems out of equilibrium.