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

Electric Dipoles and Dipole Moment

Electric Dipoles and Dipole Moment

Consider two charges of equal magnitude but opposite signs. If they cannot be separated by an external electric field, the system is called a permanent dipole. For example, the water molecule is a dipole, making it a good solvent.
Theoretically, studying electric dipoles leads to understanding why the resultant electric forces around us are weak. Since electric forces are strong, remnant net charges are rare. Hence, the interaction between dipoles helps us understand electrical interactions in...

Induced Electric Dipoles

Induced Electric Dipoles

A permanent electric dipole orients itself along an external electric field. This rotation can be quantified by defining the potential energy because the external torque does work in rotating it. Then, the potential energy is minimum at the parallel configuration and maximum at the antiparallel configuration. While the former is a stable equilibrium, the latter is an unstable equilibrium.
Since the absolute value of potential energy holds no physical meaning, its zero value can be chosen as per...

Electric Field of Two Equal and Opposite Charges

Electric Field of Two Equal and Opposite Charges

Atoms generally contain the same number of positively and negatively charged particles, protons, and electrons. Hence, they are electrically neutral. However, the centers of the positive and negative charges do not always coincide. In such a scenario, the electric field of an atom may not be zero.
A separation of the positive and negative charges can lead to a weak, remnant effect of the positive and negative charges. The expectation is that the more the distance between the positive and...

Potential Due to a Polarized Object

Potential Due to a Polarized Object

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...

Molecular Geometry and Dipole Moments

Molecular Geometry and Dipole Moments

The VSEPR theory can be used to determine the electron pair geometries and molecular structures as follows:

The Pauli Exclusion Principle

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

You might also read

Related Articles

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

Sort by

Same author

Fragile many-body ergodicity from action diffusion.

Physical review. E·2021

Same author

The Nernst effect in Corbino geometry.

Proceedings of the National Academy of Sciences of the United States of America·2020

Same author

Finite-Temperature Disordered Bosons in Two Dimensions.

Physical review letters·2018

Same author

Spontaneous Polariton Currents in Periodic Lateral Chains.

Physical review letters·2017

Same author

Nonergodic Phases in Strongly Disordered Random Regular Graphs.

Physical review letters·2016

Same author

Quantum Levy Flights and Multifractality of Dipolar Excitations in a Random System.

Physical review letters·2016

Search research articles

Related Experiment Video

Updated: May 29, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Localization and critical diffusion of quantum dipoles in two dimensions.

I L Aleiner¹, B L Altshuler, K B Efetov

¹Physics Department, Columbia University, New York, New York 10027, USA.

Physical Review Letters

|September 10, 2011

Summary

Quantum dipole excitations in 2D exhibit critical wave functions and scale-independent diffusion. T-invariant systems remain critical, while others may transition from diffusion to Levy flights.

More Related Videos

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Published on: July 29, 2013

Related Experiment Videos

Last Updated: May 29, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Published on: July 29, 2013

Area of Science:

Condensed matter physics
Quantum mechanics
Disordered systems

Background:

Anderson localization typically describes wave function decay in disordered systems.
Conventional models often assume short-range interactions, limiting applicability to systems with long-range correlations.

Purpose of the Study:

Investigate quantum propagation of dipole excitations in two-dimensional systems.
Analyze the impact of long-range hops on localization phenomena.
Characterize the behavior of critical wave functions and diffusion constants.

Main Methods:

Utilized a modified nonlinear supermatrix sigma model.
Performed a two-loop analysis to study quantum propagation.
Examined the conditions for critical states and diffusion-to-Levy flight transitions.

Main Results:

Critical wave functions for dipoles always exist, characterized by a scale-independent diffusion constant.
In T-invariant systems, states remain critical across all parameter values.
Non-T-invariant systems can exhibit a metal-insulator transition between ordinary diffusion and Levy flights.

Conclusions:

The presence of long-range hops fundamentally alters localization dynamics compared to Anderson localization.
The study reveals distinct diffusion regimes and transitions driven by system symmetries.
The findings provide insights into quantum transport in complex, disordered environments.