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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

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Classification of Systems-I01:26

Classification of Systems-I

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:
RL Circuit with Source01:14

RL Circuit with Source

When an RL (Resistor-Inductor) circuit is connected to a DC source, the complete response of the circuit can be divided into two parts: the transient response and the steady-state response.
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Electrical Systems01:21

Electrical Systems

In electrical engineering, the analysis of networks composed of passive linear components — resistors (R), capacitors (C), and inductors (L) — is fundamental. These components are organized into circuits where the relationship between input and output can be analyzed using transfer functions. The transfer function of an RLC circuit, which relates the voltage across a capacitor to the input voltage, can be derived using Kirchhoff's laws.
To derive the transfer function, consider an RLC circuit...
Series RLC Circuit with Source01:12

Series RLC Circuit with Source

Consider the operation of an automobile ignition system, a crucial component responsible for generating a spark by producing high voltage from the battery. This system can be described as a simple series RLC circuit, allowing for an in-depth analysis of its complete response.
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Linear response formula for open systems.

Onuttom Narayan1

  • 1Department of Physics, University of California, Santa Cruz, California 95064, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 30, 2011
PubMed
Summary
This summary is machine-generated.

Researchers derived an exact formula for the frequency response of open classical systems. This new method for analyzing conserved currents differs from standard Green-Kubo formulas, offering new insights into system dynamics.

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Area of Science:

  • * Theoretical physics
  • * Statistical mechanics
  • * Quantum and classical open systems

Background:

  • * Understanding the behavior of open classical systems interacting with their environment (reservoirs) is crucial in various scientific fields.
  • * Current methods often rely on approximations or specific assumptions about the system and reservoirs.

Purpose of the Study:

  • * To derive an exact expression for the finite frequency response of open classical systems coupled to reservoirs.
  • * To develop a method applicable to any conserved current without restrictive assumptions on the reservoirs.

Main Methods:

  • * Derivation of an exact mathematical expression for the system's response function.
  • * Analysis of systems coupled to reservoirs in thermodynamic equilibrium.
  • * Focus on conserved currents within the open system.

Main Results:

  • * An exact expression for the finite frequency response was obtained for open classical systems.
  • * The derived expression is valid for any conserved current.
  • * At nonzero frequencies, the response involves correlation functions of boundary currents, not internal currents.

Conclusions:

  • * The new expression provides a more general framework for studying open classical systems compared to the standard Green-Kubo formalism.
  • * The findings highlight the importance of boundary currents in determining the system's response at finite frequencies.
  • * This work offers a valuable tool for theoretical analysis in condensed matter physics and statistical mechanics.