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Related Concept Videos

Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.
RL Circuit without Source01:14

RL Circuit without Source

When a DC source is suddenly disconnected from an RL (Resistor-Inductor) circuit, the circuit becomes source-free. Assuming the inductor has an initial current denoted as I0, the initial energy stored in the inductor can be determined.
Applying Kirchhoff's voltage law around the loop of the circuit and substituting the voltages across the inductor and resistor yields a first-order differential equation. A logarithmic equation is obtained by rearranging the terms in this equation, integrating...
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.
In this context, the input DC voltage serves as a forcing step function, resulting in a forced step response that mirrors the characteristics of the input. Applying Kirchhoff's voltage law to the circuit yields a...
Series RLC Circuit without Source01:21

Series RLC Circuit without Source

Within the field of electrical circuits, source-free RLC circuits present an intriguing domain. These circuits comprise a series arrangement of a resistor, inductor, and capacitor, operating independently of external energy sources. Their initiation hinges upon utilizing the initial energy stored within the capacitor and inductor to instigate their functionality. Their mathematical equation, a second-order differential equation, sets these circuits apart. This equation captures how the...
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.
The transient response of the circuit is its temporary reaction to the sudden application of the DC source. This response is characterized by a current that exponentially decays to zero as time approaches infinity. During this transitional period, the inductor behaves like a short circuit, causing the source...
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.

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Related Experiment Video

Updated: Jul 2, 2026

All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics
11:33

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Universal response functions in driven dissipative tunneling dynamics.

Krishna Kingkar Pathak1

  • 1Department of Physics, Arya Vidyapeeth College, Guwahati 781016, India and Department of Physics, Gauhati University, Guwahati 781014, Assam, India.

Chaos (Woodbury, N.Y.)
|July 1, 2026
PubMed
Summary

Universality in driven dissipative systems is revealed through a two-parameter response function, not just scaling laws. This finding applies to barrier-crossing processes in periodically driven systems with memory.

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Area of Science:

  • Nonlinear dynamics
  • Quantum tunneling
  • Statistical mechanics

Background:

  • Universality in nonlinear systems typically relies on scaling laws.
  • The behavior of driven open systems with periodic forcing and memory is not fully understood.
  • Investigating universality under simultaneous periodic forcing and nonlocal dissipative memory is crucial.

Purpose of the Study:

  • To demonstrate a universal response function for barrier-crossing in periodically driven dissipative systems.
  • To explore how periodic forcing and nonlocal memory affect universality.
  • To establish a distinct universality class for driven dissipative barrier crossing.

Main Methods:

  • Semiclassical instanton framework with Floquet modulation and Ohmic coupling.
  • Analysis of tunneling exponent factorization.
  • Numerical evaluation of nonlocal instanton action.

Main Results:

  • Barrier-crossing processes exhibit a two-parameter universal response function.
  • The tunneling exponent factorizes into system-dependent and universal parts.
  • A universal dependence on driving parameters is observed across different models.

Conclusions:

  • Driven dissipative barrier crossing defines a new two-parameter universality class.
  • The findings provide a predictive functional description of tunneling universality.
  • A unifying framework for response phenomena in driven systems with memory is established.