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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

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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

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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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Metal-Semiconductor Junctions

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The contact of metal and semiconductor can lead to the formation of a junction with either Schottky or Ohmic behavior.
Schottky Barriers
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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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Steady-State Phase Transition in One-Dimensional Quantum Contact Process.

Lin Shang1, Shuai Geng1, Xingli Li2

  • 1Dalian University of Technology, School of Physics, 116024 Dalian, China.

Physical Review Letters
|February 22, 2026
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Summary
This summary is machine-generated.

We reveal the discontinuous phase transition in a 1D quantum contact process model, uncovering system metastability. Our findings on steady-state phases may be tested using Rydberg atom quantum simulators.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • The one-dimensional quantum contact process is a key model for studying non-equilibrium quantum dynamics.
  • Understanding steady-state phases and phase transitions is crucial for characterizing complex quantum systems.

Purpose of the Study:

  • To investigate the steady-state phases and phase transitions of the one-dimensional quantum contact process.
  • To analyze the system's metastability and the nature of its phase transition.

Main Methods:

  • Calculation of the Liouvillian gap in the thermodynamic limit.
  • Application of mean-field approximations with a novel self-consistent effective field condition.
  • Linked-cluster expansion to analyze magnetic susceptibility.

Main Results:

  • Uncovered metastability in the one-dimensional quantum contact process.
  • Identified a discontinuous phase transition characterized by saddle-node bifurcation of the order parameter.
  • Extracted the phase transition point for an infinite-size system.
  • Demonstrated monotonic decrease in steady-state magnetic susceptibility, refuting correlation length divergence.

Conclusions:

  • The one-dimensional quantum contact process exhibits metastability and discontinuous phase transitions.
  • The employed mean-field approach effectively bypasses metastable state interference.
  • Results provide testable predictions for quantum simulators, particularly those using Rydberg atoms.