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Related Concept Videos

Continuous Charge Distributions01:17

Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Gauss's Law in Dielectrics01:17

Gauss's Law in Dielectrics

Consider a polar dielectric placed in an external field. In such a dielectric, opposite charges on adjacent dipoles neutralize each other, such that the net charge within the dielectric is zero. When a polar dielectric is inserted in between the capacitor plates, an electric field is generated due to the presence of net charges near the edge of the dielectric and the metal plates interface. Since the external electrical field merely aligns the dipoles, the dielectric as a whole is neutral. An...
Magnetic Field due to Moving Charges01:23

Magnetic Field due to Moving Charges

A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...
Boundary Conditions for Current Density01:25

Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Non-Gaussian fluctuations of mesoscopic persistent currents.

J Danon1, P W Brouwer

  • 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin, Germany.

Physical Review Letters
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

Researchers calculated the leading non-Gaussian correction to persistent current fluctuations in normal-metal rings. This third-order correction, though small, reveals crucial insights into the transition towards Anderson localization.

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Area of Science:

  • Condensed matter physics
  • Quantum transport phenomena

Background:

  • Persistent currents in normal-metal rings exhibit sample-to-sample fluctuations.
  • These fluctuations are generally Gaussian but show non-Gaussian corrections near the Anderson localization transition.

Purpose of the Study:

  • To calculate the leading non-Gaussian correction to the current autocorrelation function.
  • To investigate the implications of this correction for understanding Anderson localization.

Main Methods:

  • Theoretical calculation of the third-order current autocorrelation function.
  • Analysis of the dependence on dimensionless conductance (g).

Main Results:

  • The leading non-Gaussian correction to the current autocorrelation function is of third-order.
  • This third-order correction is inversely proportional to the dimensionless conductance (g).
  • The non-zero nature of this odd moment of the current distribution is a significant finding.

Conclusions:

  • The calculated third-order correction provides a precursor signature for the Anderson localization regime.
  • Understanding these non-Gaussian corrections is vital for characterizing electron transport in disordered systems.