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Related Concept Videos

Phase Transitions02:31

Phase Transitions

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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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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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Phase Diagrams02:39

Phase Diagrams

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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Casimir amplitudes in topological quantum phase transitions.

M A Griffith1, M A Continentino1

  • 1Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150-Urca, 22290-180, Rio de Janeiro, RJ, Brazil.

Physical Review. E
|February 17, 2018
PubMed
Summary

Topological phase transitions are a new class of quantum critical phenomena. A finite-size scaling approach, using Casimir force calculations, successfully determined universal Casimir amplitudes and confirmed critical exponents.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Critical Phenomena

Background:

  • Topological phase transitions represent a novel class of quantum critical phenomena.
  • These transitions often lack order parameters or symmetry changes, defying traditional Landau theory.
  • A characteristic diverging length scale typically emerges at these transitions.

Purpose of the Study:

  • To investigate quantum topological transitions using a scaling approach.
  • To determine critical exponents and universality classes for these phenomena.
  • To obtain universal Casimir amplitudes at quantum critical points.

Main Methods:

  • Application of a finite-size scaling approach to models of quantum topological transitions.
  • Utilizing techniques adapted from Casimir force calculations in electromagnetism.
  • Analysis of critical exponents and their relation via quantum hyperscaling.

Main Results:

  • Successful determination of universal Casimir amplitudes at quantum critical points.
  • Verification of the validity of finite-size scaling in topological transition systems.
  • Confirmation of previously obtained critical exponent values.

Conclusions:

  • Finite-size scaling is a valid and effective method for studying quantum topological transitions.
  • The study provides universal Casimir amplitudes, offering new insights into critical phenomena.
  • The findings reinforce the understanding of critical exponents and universality in these systems.