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Related Concept Videos

Force and Potential Energy in One Dimension01:13

Force and Potential Energy in One Dimension

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Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
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The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
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Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function of the coordinates. The potential energy function U is also a function of all three spatial coordinates. Force in one dimension can be written as the negative ratio of potential energy change to the displacement along that coordinate. For minimal displacement, the ratios become derivatives. If a function has many variables, the derivative only...
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Open channel flow, where a fluid flows with a free surface exposed to the atmosphere, is primarily governed by gravitational and surface effects, distinguishing it from closed conduit or pipe flow. In open channels such as rivers, canals, and artificial channels, energy analysis provides valuable insights into flow behavior and the relationship between depth, velocity, and slope.Specific Energy and Flow DepthIn open channel flow, the specific energy, E, combines the gravitational potential...
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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
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Electric potential can be pictorially represented as a three-dimensional surface. On such a surface, the electric potential is constant everywhere. The equipotential surface is always perpendicular to the electric field lines, and while it is three-dimensional, it can be treated as an equipotential line in a two-dimensional case. These equipotential lines are also always perpendicular to electric field lines. The term equipotential is often used as a noun, referring to an equipotential line or...
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Updated: Aug 9, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Surface crossing and energy flow in many-dimensional quantum systems.

Chenghao Zhang1, Martin Gruebele1,2, David E Logan3

  • 1Department of Physics, University of Illinois at Urbana-Champaign, IL 61801.

Proceedings of the National Academy of Sciences of the United States of America
|February 23, 2023
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Summary

Quantum energy flow in molecules is facilitated by couplings between electronic and vibrational states. This study reveals a phase diagram predicting localized dynamics versus global energy flow, validated by simulations.

Keywords:
excitonnonadiabatic couplingphotosynthesisquantum scramblingvibrational energy flow

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Area of Science:

  • Physical Chemistry
  • Quantum Dynamics
  • Molecular Spectroscopy

Background:

  • Energy flow in molecules is crucial for processes like photosynthesis.
  • This flow typically involves quantum transport through a dense network of resonant states.
  • Anharmonic vibrational Fermi resonances and electronic surface crossings drive chaotic motion and energy redistribution.

Purpose of the Study:

  • To investigate the interplay between vibrational energy flow and nonadiabatic electronic state mixing.
  • To develop a theoretical framework predicting the transition between localized and global quantum dynamics.
  • To test theoretical predictions using a model relevant to photosynthetic energy transfer.

Main Methods:

  • Generalized Logan-Wolynes theory for quantum energy flow in two-electronic-state systems.
  • Development of a phase diagram delineating localized dynamics from global energy flow.
  • Explicit numerical solution of the time-dependent Schrödinger equation for a ten-dimensional model.

Main Results:

  • Demonstrated that nonadiabatic coupling enhances vibrational energy flow, while vibrational couplings promote electronic state mixing.
  • The generalized theory successfully predicts a phase boundary for quantum energy flow.
  • Numerical simulations of a photosynthetic reaction center model showed good agreement with theoretical predictions.

Conclusions:

  • Interconnected electronic and vibrational couplings govern molecular energy dynamics.
  • The developed phase diagram offers a valuable tool for understanding quantum transport in complex molecular systems.
  • Theoretical insights are crucial for controlling energy flow in molecular processes.