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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: 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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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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Exceptions to the Octet Rule02:55

Exceptions to the Octet Rule

37.9K
Many covalent molecules have central atoms that do not have eight electrons in their Lewis structures. These molecules fall into three categories:
37.9K
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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Related Experiment Video

Updated: Feb 14, 2026

Optogenetic Phase Transition of TDP-43 in Spinal Motor Neurons of Zebrafish Larvae
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Optogenetic Phase Transition of TDP-43 in Spinal Motor Neurons of Zebrafish Larvae

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Exceptional points near first- and second-order quantum phase transitions.

Pavel Stránský1, Martin Dvořák1, Pavel Cejnar1

  • 1Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00 Prague, Czech Republic.

Physical Review. E
|February 17, 2018
PubMed
Summary
This summary is machine-generated.

Quantum phase transitions (QPTs) influence exceptional points (EPs) in quantum systems. Their distribution near critical points reveals QPT type, offering a universal signature of quantum criticality.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Quantum phase transitions

Background:

  • Exceptional points (EPs) are unique degeneracies in non-Hermitian systems.
  • Quantum phase transitions (QPTs) signify drastic changes in quantum system properties.
  • Understanding EP behavior near QPTs is crucial for characterizing quantum criticality.

Purpose of the Study:

  • To investigate how quantum phase transitions (QPTs) affect the distribution of exceptional points (EPs).
  • To determine if EP distribution can serve as a universal signature of criticality.
  • To analyze the impact of perturbations on EP distributions near QPTs.

Main Methods:

  • Analysis of first- and second-order QPTs within the Lipkin-Meshkov-Glick model.
  • Examination of exceptional point distributions in the complex-extended parameter domain.
  • Study of averaged EP distributions under random perturbations.

Main Results:

  • Exceptional points (EPs) exhibit exponential and polynomial approach to critical points with increasing system size.
  • Averaged EP distributions near critical points retain information about the QPT type, even with perturbations.
  • EP distribution properties are independent of parametrization, indicating robustness.

Conclusions:

  • The distribution of exceptional points serves as a robust, parametrization-independent signature of quantum criticality.
  • This finding offers a new method for identifying and characterizing QPTs in quantum systems.
  • The study highlights the deep connection between non-Hermitian degeneracies and quantum phase transitions.