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

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

447
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
447
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

424
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
424
Linear time-invariant Systems01:23

Linear time-invariant Systems

1.1K
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
1.1K
Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

2.7K
A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.
2.7K
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

1.2K
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
1.2K
First Order Systems01:21

First Order Systems

524
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
524

You might also read

Related Articles

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

Sort by
Same author

Why projection-based WF-in-DFT cannot be exact, even with the exact exchange-correlation functional. Formal and practical sources of errors.

The Journal of chemical physics·2026
Same author

Optimally Tuned Multiconfigurational Short-Range DFT for Linear Response Properties.

The journal of physical chemistry. A·2026
Same author

Accurate Chemistry Collection: Coupled cluster atomization energies for broad chemical space.

Scientific data·2026
Same author

Projection-Based DMRG-in-DFT Embedding Corrected by Nonadditive Exchange-Correlation.

Journal of chemical theory and computation·2026
Same author

Multireference Dynamic Correlation Energy from the Combined Particle-Hole and Particle-Particle Adiabatic Connection with Random Phase Approximation.

Journal of chemical theory and computation·2026
Same author

Correcting Basis Set Incompleteness in Wave Function Correlation Energy by Dressing Electronic Hamiltonian with an Effective Short-Range Interaction.

The journal of physical chemistry letters·2025

Related Experiment Video

Updated: Apr 12, 2026

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

12.4K

Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT).

Katarzyna Pernal1, Klaas J H Giesbertz

  • 1Institute of Physics, ul. Wolczanska 219, 90-924, Lodz, Poland, pernalk@gmail.com.

Topics in Current Chemistry
|May 15, 2015
PubMed
Summary

Recent advances in reduced density matrix functional theory (RDMFT) and its time-dependent extension (TD-RDMFT) are reviewed. New functionals and methods for molecular and solid-state properties are discussed, with a focus on two-electron systems.

More Related Videos

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

4.3K

Related Experiment Videos

Last Updated: Apr 12, 2026

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

12.4K
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

9.1K
Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

4.3K

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Reduced Density Matrix Functional Theory (RDMFT) offers a pathway to solve electronic structure problems.
  • Developing accurate density matrix functionals is crucial for RDMFT's predictive power.
  • Linear response time-dependent RDMFT (TD-RDMFT) is an emerging theory for excited-state properties.

Purpose of the Study:

  • To review recent advancements in RDMFT and TD-RDMFT.
  • To present and evaluate approximate density matrix functionals.
  • To discuss novel RDMFT-based methods and TD-RDMFT formulations.

Main Methods:

  • Development and application of approximate density matrix functionals.
  • Formulation of RDMFT-based methods for molecular and solid-state properties.
  • Analysis of TD-RDMFT response equations and adiabatic approximations.

Main Results:

  • Overview of various density matrix functional approximations and their performance.
  • Discussion of novel RDMFT methods for predicting system properties.
  • Exploration of TD-RDMFT, including adiabatic approximations and a phase-dependent extension (PINOs).

Conclusions:

  • Progress in RDMFT and TD-RDMFT is enabling new computational approaches.
  • Existing adiabatic approximations in TD-RDMFT require further refinement.
  • Applications to two-electron systems provide insights into functional development for TD-RDMFT.