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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: 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 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: 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 Diagrams02:39

Phase Diagrams

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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Properties of Transition Metals02:58

Properties of Transition Metals

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Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3–12 are transition elements. The f-block elements, also called inner transition metals (the lanthanides and actinides), also meet this criterion because the d orbital is partially occupied before the f orbitals.
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Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions
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Dynamical Phase Transitions in Sampling Complexity.

Abhinav Deshpande1,2, Bill Fefferman1,3, Minh C Tran1,2

  • 1Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.

Physical Review Letters
|August 8, 2018
PubMed
Summary
This summary is machine-generated.

Studying quantum system sampling complexity reveals insights beyond quantum supremacy, aiding in phase transition diagnosis. This research establishes a dynamical phase transition in sampling complexity, showing Anderson-localized phases are always easy to sample.

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Area of Science:

  • Quantum Information Science
  • Computational Complexity
  • Condensed Matter Physics

Background:

  • Quantum computational supremacy focuses on problems intractable for classical computers.
  • Diagnosing phase transitions in quantum systems is crucial for understanding their behavior.
  • Approximate quantum system simulation (sampling) complexity is an underexplored area.

Purpose of the Study:

  • To investigate the sampling complexity of quantum systems beyond quantum computational supremacy.
  • To explore the role of sampling complexity in diagnosing phase transitions.
  • To establish bounds on the efficiency of classically simulating quantum systems.

Main Methods:

  • Analyzing sampling complexity as a function of time (t) for spatially local quadratic bosonic Hamiltonians.
  • Deriving upper bounds for classically efficient approximate sampling.
  • Establishing lower bounds by reducing the boson sampling problem to demonstrate hardness, assuming Aaronson-Arkhipov conjectures.

Main Results:

  • An upper bound on the scaling of time (t) with the number of bosons (n) for classically efficient approximate sampling was obtained.
  • A lower bound on the scaling of t with n was established, proving the problem's hardness under specific conjectures.
  • A dynamical phase transition in sampling complexity was identified, with Anderson-localized phases shown to be always easy to sample from.

Conclusions:

  • The study establishes a link between quantum system phases and their sampling complexity.
  • Combining mathematical physics and computational complexity offers new insights into condensed matter and quantum optics systems.
  • Sampling complexity is a valuable tool for understanding quantum systems and their phase transitions.