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Related Concept Videos

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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Phase Transitions: Sublimation and Deposition02:33

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Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
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Phase Transitions: Melting and Freezing02:39

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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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Phase Transitions: Vaporization and Condensation02:39

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The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
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The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Quantum Numbers02:43

Quantum Numbers

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It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
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Quantum Phase Transition in the Spin-Boson Model: A Multilayer Multiconfiguration Time-Dependent Hartree Study.

Haobin Wang1,2, Jiushu Shao3

  • 1Department of Chemistry , University of Colorado Denver , Denver , Colorado 80217-3364 , United States.

The Journal of Physical Chemistry. A
|February 9, 2019
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Summary
This summary is machine-generated.

This study investigates quantum phase transitions in the spin-boson model using multilayer improved relaxation. Researchers successfully analyzed the delocalization-localization transition at zero temperature, confirming findings with key properties.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Computational physics

Background:

  • The spin-boson model is a fundamental system for studying quantum phase transitions.
  • Understanding delocalization-localization transitions is crucial in various quantum phenomena.
  • Zero-temperature quantum phase transitions exhibit unique behaviors.

Purpose of the Study:

  • To apply the multilayer improved relaxation method to the spin-boson model.
  • To investigate the delocalization-localization transition at zero temperature.
  • To analyze quantum phase transition properties using specific metrics.

Main Methods:

  • Utilized multilayer improved relaxation for quantum phase transition studies.
  • Employed iterative diagonalization of the Boltzmann operator matrix.
  • Applied Lanczos/Arnoldi method and multilayer multiconfiguration time-dependent Hartree imaginary time propagation.
  • Relaxed single-particle functions across all layers.

Main Results:

  • Successfully analyzed the delocalization-localization transition in the spin-boson model.
  • Calculated energy eigenstates and properties relevant to quantum phase transitions.
  • Observed consistent findings with appropriate scaling parameters.

Conclusions:

  • The multilayer improved relaxation method is effective for studying quantum phase transitions.
  • The delocalization-localization transition in the spin-boson model at zero temperature was accurately characterized.
  • Energy splitting and magnetic susceptibility serve as reliable indicators for quantum phase transitions.