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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: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

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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

Phase Transitions: Vaporization and Condensation

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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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Phase Transitions: Sublimation and Deposition02:33

Phase Transitions: Sublimation and Deposition

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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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The de Broglie Wavelength02:32

The de Broglie Wavelength

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In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
33.8K
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

1.6K
Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Size-driven quantum phase transitions.

Johannes Bausch1, Toby S Cubitt2, Angelo Lucia3,4,5

  • 1Centre for Quantum Information and Foundations, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom; jkrb2@cam.ac.uk.

Proceedings of the National Academy of Sciences of the United States of America
|December 21, 2017
PubMed
Summary
This summary is machine-generated.

Extrapolating quantum system properties from finite sizes can be misleading. Some systems exhibit a size-driven quantum phase transition, changing from classical to topologically degenerate ground states as size increases.

Keywords:
Wang tilingcondensed matter physicsfinite-size effectsquantum phase transitiontoric code

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Analyzing thermodynamic limits of many-body quantum systems often relies on finite-size scaling.
  • Classical product ground states are typical for small systems.
  • Topological degeneracy in ground states indicates unique quantum phases.

Purpose of the Study:

  • To investigate if finite-size scaling accurately predicts thermodynamic limit properties of quantum systems.
  • To explore novel quantum phase transitions driven by system size.

Main Methods:

  • Development of translationally invariant, local Hamiltonians on a square lattice with open boundary conditions.
  • Analysis of ground state properties across varying system sizes, focusing on spectral gap and degeneracy.
  • Mathematical proof of the growth rate of the threshold size with increasing local spin dimension.

Main Results:

  • Demonstrated models where finite-size analysis yields misleading results for thermodynamic properties.
  • Identified systems transitioning from classical product ground states to topologically degenerate ground states above a critical size.
  • Showcased that the threshold size grows faster than any computable function with increasing local spin dimension.

Conclusions:

  • Finite-size scaling is not universally reliable for extrapolating thermodynamic properties of quantum systems.
  • A novel quantum phase transition, driven by system size rather than external parameters, has been identified.
  • The described phenomena are thermally robust and experimentally observable.