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Related Concept Videos

Phase Transitions02:31

Phase Transitions

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 occupy...
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

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...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
Phase Diagram01:19

Phase Diagram

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).
Phase Transitions01:21

Phase Transitions

A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
The Phase Rule01:20

The Phase Rule

The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...

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Related Experiment Video

Updated: Jul 26, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Zero-temperature phases of many-atom Bose systems.

Bo Gao1

  • 1Department of Physics and Astronomy, University of Toledo, Toledo, Ohio 43606, USA.

Physical Review Letters
|December 31, 2005
PubMed
Summary

Many-atom Bose systems exhibit a liquid phase alongside the gaseous phase at zero temperature. This finding impacts the stability of Bose-Einstein condensates (BECs) under dilute experimental conditions.

Area of Science:

  • Quantum physics
  • Condensed matter physics

Background:

  • Bose systems are known to have a gaseous phase at zero temperature.
  • The behavior of many-atom Bose systems with specific interactions is not fully understood.

Purpose of the Study:

  • To investigate the existence of additional phases in many-atom Bose systems at zero temperature.
  • To develop a universal phase diagram for Bose systems with -C6/r6 interactions.
  • To analyze the implications of the phase structure on Bose-Einstein condensate (BEC) stability.

Main Methods:

  • Theoretical analysis of many-atom Bose systems.
  • Development of a universal phase diagram based on interparticle interactions.
  • Investigation of phase stability at dilute densities.

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Main Results:

  • A liquid phase exists in many-atom Bose systems at zero temperature, in addition to the gaseous phase.
  • A universal phase diagram is presented for Bose systems with -C6/r6 interactions.
  • The predicted phase structure affects the stability of gaseous Bose-Einstein condensates (BECs).

Conclusions:

  • The existence of a liquid phase has significant implications for understanding Bose systems.
  • The universal phase diagram provides a framework for studying various Bose systems.
  • A gaseous BEC phase is predicted below a critical density of 5.58 x 10^15 1/cm^3.