Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Dot Product: Problem Solving

Dot Product: Problem Solving

The dot product is a powerful tool in problem-solving involving vectors, given that the dot product of two vectors is the product of their magnitudes and the cosine of the angle between them measured anti-clockwise. Solving problems involving the dot product requires understanding its properties and developing a step-by-step process to solve them. Here are the main steps to follow when solving any general problem involving the dot product:
Identify the problem: Start by reading the problem and...

The Chain Rule

The Chain Rule

A system of interconnected gears provides a concrete physical interpretation of the Chain Rule in calculus. Consider three gears arranged in sequence, where the rotational speeds of the first, second, and third gears are represented by the variables x, z, and y, respectively. The first gear drives the second, and the second drives the third, so the motion of each gear depends on the one preceding it. This structure naturally leads to a two-stage variable relationship that can be analyzed using...

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...

Vector Product (Cross Product)

Vector Product (Cross Product)

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...

Cartesian Form for Vector Formulation

Cartesian Form for Vector Formulation

The Cartesian form for vector formulation is a process to calculate the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...

You might also read

Related Articles

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

Sort by

Same author

Quest for the golden ratio universality class.

Physical review. E·2024

Same author

Molecular motor traffic with a slow binding site.

Journal of theoretical biology·2021

Same author

Stationary RNA polymerase fluctuations during transcription elongation.

Physical review. E·2019

Same author

RNA Polymerase interactions and elongation rate.

Journal of theoretical biology·2018

Same author

Kardar-Parisi-Zhang modes in d-dimensional directed polymers.

Physical review. E·2018

Same author

Solution of the Lindblad equation for spin helix states.

Physical review. E·2017

Search research articles

Related Experiment Video

Updated: Apr 25, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Exact matrix product solution for the boundary-driven Lindblad XXZ chain.

D Karevski¹, V Popkov², G M Schütz³

¹Institut Jean Lamour, Department P2M, Groupe de Physique Statistique, Université de Lorraine, CNRS, B.P. 70239, F-54506 Vandoeuvre les Nancy Cedex, France.

Physical Review Letters

|August 29, 2014

Summary

Researchers constructed the exact nonequilibrium steady state for a quantum spin chain using a matrix product ansatz. This method, related to quantum algebra, revealed nonvanishing spin currents and suggests broader applications for driven quantum systems.

More Related Videos

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

Published on: June 2, 2017

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

Related Experiment Videos

Last Updated: Apr 25, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

2D and 3D Matrices to Study Linear Invadosome Formation and Activity

Published on: June 2, 2017

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

Area of Science:

Quantum mechanics
Condensed matter physics
Statistical mechanics

Background:

Understanding nonequilibrium steady states in quantum systems is crucial.
The one-dimensional Heisenberg XXZ spin chain is a key model in quantum many-body physics.
Boundary-driven systems present unique challenges for theoretical analysis.

Purpose of the Study:

To explicitly construct the exact nonequilibrium steady state of the 1D Heisenberg XXZ spin chain.
To explore the connection between the matrix product ansatz and quantum algebras.
To investigate the emergence of stationary currents in driven quantum spin chains.

Main Methods:

Utilizing a matrix product ansatz for the nonequilibrium density matrix.
Identifying and analyzing the underlying quadratic algebra satisfied by the matrices.
Applying coherent state techniques for exact solutions.
Introducing Lindblad operators to model boundary driving.

Main Results:

The exact nonequilibrium steady state was constructed explicitly.
The associated algebra was shown to be related to the quantum algebra U(q)[SU(2)].
Nonvanishing stationary currents for all spin components were demonstrated.
The matrix product ansatz was shown to be applicable to driven quantum systems.

Conclusions:

The matrix product ansatz provides an effective tool for studying driven quantum systems.
The identified quantum algebra offers insights into the system's dynamics.
The findings suggest a generalizable approach for analyzing far-from-equilibrium quantum phenomena.