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Related Concept Videos

State Space Representation01:27

State Space Representation

388
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
388
Transfer Function to State Space01:23

Transfer Function to State Space

591
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 RLC...
591
Classification of Systems-I01:26

Classification of Systems-I

454
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
454
State Space to Transfer Function01:21

State Space to Transfer Function

428
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:
428
Second Order systems I01:20

Second Order systems I

386
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
386
Classification of Systems-II01:31

Classification of Systems-II

383
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
383

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Complex Systems in Phase Space.

David K Ferry1, Mihail Nedjalkov2,3, Josef Weinbub4

  • 1School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 25287-5706, USA.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

Modeling quantum effects in phase space using the Wigner transport equation is crucial for advancing semiconductor technology. This approach effectively simulates complex quantum systems and reveals phenomena like entanglement.

Keywords:
hysteresisnon-Hermitian behaviornonlinearityquantum transport

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Area of Science:

  • Quantum physics
  • Semiconductor device physics
  • Computational physics

Background:

  • Semiconductor devices are shrinking to nanometer scales, introducing complex quantum effects.
  • The Wigner transport equation is an effective model for quantum effects in phase space.
  • Simulating these systems requires advanced computational techniques.

Purpose of the Study:

  • To discuss challenges, myths, and opportunities in modeling quantum effects in nanoscale semiconductor devices.
  • To highlight the advantages of using phase space notions for complex quantum systems.
  • To explore efficient simulation approaches for the Wigner transport equation.

Main Methods:

  • Utilizing the Wigner transport equation for phase space modeling.
  • Developing particle-based techniques to solve the transport equation.
  • Obtaining the Wigner function for simulation.
  • Coupling quantum simulations with classical dynamics.

Main Results:

  • Phase space modeling effectively describes quantum effects from full quantum processes to dissipation-dominated transport.
  • Particle-based techniques offer efficient simulation approaches.
  • These methods couple well with classical dynamics.
  • Quantum entanglement in systems can be directly observed.

Conclusions:

  • Phase space modeling via the Wigner transport equation is a powerful tool for understanding nanoscale semiconductor devices.
  • Particle-based methods provide efficient and versatile simulation capabilities.
  • This approach facilitates the direct observation and study of quantum phenomena such as entanglement.