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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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The internal energy of a substance—the total kinetic energy of all its molecules and the potential energy of their associated forces—depends on the strength of the intermolecular forces in the condensed phases and the pressure exerted on the substance. The internal energy of a substance is the highest in the gaseous state, the lowest in the solid state, and intermediate in the liquid state. Phase transitions are caused by changes in physical conditions, such as temperature and...
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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 Diagram01:19

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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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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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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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Uhlmann Connection in Fermionic Systems Undergoing Phase Transitions.

Bruno Mera1,2,3, Chrysoula Vlachou3,4, Nikola Paunković3,4

  • 1CeFEMA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal.

Physical Review Letters
|July 22, 2017
PubMed
Summary
This summary is machine-generated.

The Uhlmann connection effectively signals phase transitions in fermionic systems by detecting changes in the system's eigenbasis. This research explores topological insulators, superconductors, and Majorana modes, offering insights into quantum memories.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Topological phases of matter

Background:

  • Fermionic systems exhibit complex behaviors during phase transitions.
  • The Uhlmann connection is a mathematical tool used to study quantum states.
  • Topological insulators and superconductors possess unique electronic properties.

Purpose of the Study:

  • To investigate the Uhlmann connection's behavior in fermionic systems undergoing phase transitions.
  • To analyze its application in one-dimensional topological insulators and superconductors, and three-dimensional BCS superconductivity.
  • To clarify the parameter space for Uhlmann connection to signal order in mixed states.

Main Methods:

  • Analysis of the Uhlmann connection in paradigmatic models like the Kitaev chain and BCS theory.
  • Utilizing the fidelity approach to study quantum state evolution.
  • Investigating edge states and Majorana modes at finite temperatures.

Main Results:

  • The Uhlmann connection signals phase transitions characterized by eigenbasis changes.
  • Absence of thermally driven phase transitions in topological insulators/superconductors confirmed.
  • Identified the relevant parameter space for Uhlmann connection to detect order in mixed states.
  • Demonstrated temperature dependence of the superconducting gap in realistic scenarios.

Conclusions:

  • The Uhlmann connection is a robust indicator of phase transitions in fermionic systems.
  • Findings suggest potential applications for Majorana modes in quantum memory.
  • The temperature dependence of the gap in topological superconductors is a key realistic consideration.