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Related Concept Videos

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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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 Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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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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Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
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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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Updated: Feb 10, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor
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Quasiperiodic Quantum Ising Transitions in 1D.

P J D Crowley1, A Chandran1, C R Laumann1

  • 1Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Physical Review Letters
|May 15, 2018
PubMed
Summary

Quasiperiodic modulation in quantum Ising chains creates new localized phases and quantum criticality. This differs from random disorder, with unique critical exponents observed.

Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Disordered Systems

Background:

  • Quasiperiodic potentials can drive unique phase transitions in quantum systems.
  • Symmetry breaking in one-dimensional quantum models is a key area of study.

Purpose of the Study:

  • To investigate the impact of quasiperiodic modulation on symmetry breaking in the quantum Ising chain.
  • To characterize the resulting phases and quantum criticality.

Main Methods:

  • Analysis of the quasiperiodically modulated quantum Ising chain.
  • Identification of localized and gapless phases.
  • Calculation of critical exponents.

Main Results:

  • Weak modulation is irrelevant, but strong modulation induces new ferromagnetic and paramagnetic phases.

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  • These phases are fully localized and gapless.
  • Quantum criticality is observed with exponents intermediate to clean and random models (ν=1⁺, z≈1.9).

    • Conclusions:

    • Quasiperiodic modulation fundamentally alters the quantum Ising transition.
    • Logarithmic wandering of couplings destabilizes the clean transition.
    • A wandering coefficient (w) is conjectured to control the universality class of the quasiperiodic transition.