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Related Concept Videos

State Space to Transfer Function01:21

State Space to Transfer Function

245
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
245
Transfer Function to State Space01:23

Transfer Function to State Space

310
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
310
Shunt Admittances01:26

Shunt Admittances

153
Shunt admittances play a crucial role in the analysis of transmission lines, particularly for three-phase systems with neutral conductors. When a uniformly charged conductor is positioned above the Earth, it induces an equal but opposite charge on its surface. This interaction creates electric field lines between the conductor and the Earth.
To model this effect, the method of images is employed. This method involves replacing the Earth with an image conductor that mirrors the original...
153
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

351
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
351
Two-Dimensional Force System01:20

Two-Dimensional Force System

953
A two-dimensional system in mechanical engineering involves the analysis of motion and forces in a plane. A two-dimensional force vector can be resolved into its components as:
953
Mason's Rule01:20

Mason's Rule

391
Mason's rule is a powerful tool in control systems and signal processing. It simplifies the calculation of transfer functions from signal-flow graphs. This method leverages various elements, including loop gains, forward-path gains, and non-touching loops, to determine the transfer function efficiently.
Loop gain is determined by identifying and tracing a path from a node back to itself. This involves computing the product of branch gains along the loop. Each loop's gain is crucial for...
391

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Transfer matrix in 1D Dirac-like problems.

M Ibarra-Reyes1, R Pérez-Álvarez2, I Rodríguez-Vargas1

  • 1Unidad Académica de Ciencia y Tecnología de la Luz y la Materia, Universidad Autónoma de Zacatecas, Circuto Marie Curie S/N, Parque de Ciencia y Tecnología QUANTUM Ciudad del Conocimiento, 98160 Zacatecas, Zacatecas, Mexico.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|June 19, 2023
PubMed
Summary
This summary is machine-generated.

The transfer matrix method reveals key properties of 1D Dirac-like systems, like graphene. It demonstrates a link between bound states and perfect transmission, applicable to 2D materials.

Keywords:
1D Dirac-like problemsbound statesstates of perfect transmissiontransfer matrix

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Mechanics

Background:

  • The transfer matrix method is a powerful tool for analyzing 1D quantum systems.
  • Monolayer graphene exhibits unique 1D Dirac-like electronic properties.
  • Understanding transmission and bound states is crucial for electronic device applications.

Purpose of the Study:

  • To apply the transfer matrix method to 1D Dirac-like problems in monolayer graphene.
  • To analyze the characteristics of the transfer matrix for Dirac-like versus Schrödinger-like systems.
  • To derive analytic expressions for transmission coefficients and bound states.

Main Methods:

  • Utilizing the transfer matrix method for 1D Dirac-like systems.
  • Analyzing the mathematical properties of the transfer matrix.
  • Deriving analytic formulas for transmission and bound states.
  • Investigating the behavior of electronic states at potential barriers.

Main Results:

  • Analytic expressions for transmission coefficients and bound states were obtained.
  • The transfer matrix for Dirac-like systems was characterized and contrasted with Schrödinger-like systems.
  • A general continuity was demonstrated between bound states and states of perfect transmission.
  • This continuity was specifically shown for single electrostatic barriers in graphene.

Conclusions:

  • The transfer matrix method effectively describes 1D Dirac-like systems.
  • A unified understanding of bound states and perfect transmission is established.
  • The findings are extendable to other 2D materials like silicene and transition metal dichalcogenides.