Related Experiment Video
Updated: Jul 4, 2026
13:58
Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics
Published on: September 28, 2016
Full counting statistics as the geometry of two planes
Y B Sherkunov1, A Pratap, B Muzykantskii
1Department of Physics, University of Warwick, Coventry, UK.
Physical Review Letters
|June 4, 2008
Summary
This study simplifies calculating charge pumping full counting statistics (FCS) by relating it to a two-plane geometry. This method avoids complex transport theory and infinite matrix calculations, reducing computations to N x N matrix diagonalization for N pulses.
Area of Science:
- Quantum transport theory
- Mesoscopic physics
- Charge pumping
Background:
- Full counting statistics (FCS) typically require complex nonequilibrium (Keldysh) transport theory.
- Calculating FCS often involves computationally intensive methods like determinant computation of infinite-dimensional matrices.
Purpose of the Study:
- To develop a simplified formulation for calculating the FCS of charge pumped across a barrier.
- To establish an equivalence between FCS and a two-plane geometry under specific conditions.
- To avoid the need for advanced theoretical frameworks and complex matrix computations.
Main Methods:
- Formulating the problem in terms of a two-plane geometry.
- Applying the formulation to series of voltage pulses, specifically N Lorentzian pulses.
- Reducing FCS computation to the diagonalization of an N x N matrix.
- Utilizing the formulation for the x-ray edge problem and square wave pulse-trains.
Main Results:
- Demonstrated that FCS is equivalent to a two-plane geometry for short measuring times.
- Showed that for N Lorentzian pulses, FCS calculation simplifies to diagonalizing an N x N matrix.
- Successfully computed the core-hole response in the x-ray edge problem and FCS for low-transmission square wave pulse-trains.
Conclusions:
- The proposed geometric formulation offers a significantly simpler approach to calculating FCS.
- This method bypasses the complexities of Keldysh theory and infinite matrix determinants.
- The approach is versatile, applicable to various pulse shapes and physical phenomena like the x-ray edge problem.
More Related Videos
09:35Preparation of a Corannulene-functionalized Hexahelicene by Copper(I)-catalyzed Alkyne-azide Cycloaddition of Nonplanar Polyaromatic Units
Published on: September 18, 2016
08:44Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
Published on: August 22, 2017
Related Concept Videos
01:27Gauss's Law: Planar Symmetry
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
01:28Quadric Surfaces
Quadric surfaces are three-dimensional surfaces characterized by second-degree equations in the variables x, y, and z. These surfaces are smooth and continuous, and specific combinations of squared and linear terms define their shapes. The main types of quadric surfaces include ellipsoids, cones, paraboloids, and hyperboloids. Each type exhibits distinct geometric features depending on how the variables are arranged and related within the equation.Ellipsoids are closed surfaces formed when all...
01:31Planes in Space
A plane in three-dimensional space is fundamentally characterized by a point that lies on the plane and a normal vector that is perpendicular to its surface. This normal vector uniquely determines the orientation of the plane, making it an essential geometric descriptor. In architectural applications, such as the installation of a sloped glass panel on a building façade, this mathematical model provides a precise representation of the panel’s position and orientation in space.Let r₀ be the...
01:19Tangent Planes to Surfaces
In multivariable calculus, the concept of a tangent plane plays a central role in approximating curved surfaces. When dealing with a surface defined by a function of two variables, such as z = f(x, y), the tangent plane at a given point provides the best linear approximation to the surface near that point. This local linearization allows complex, nonlinear geometries to be treated using simpler, planar models.The construction of the tangent plane involves taking vertical slices of the surface...
01:30Geometry of Hyperbolas
A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
01:22Tangent Planes to a Parametric Surface
A tangent plane provides a linear approximation to a curved surface at a specific point, capturing the local behavior of the surface. It can be understood as the plane that just touches the surface at that point and is defined by the tangent directions of curves lying on the surface. These tangent directions arise naturally when the surface is described parametrically, allowing systematic construction of the plane.For a surface expressed in parametric form, the position of any point is...