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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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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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Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
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Universal Holographic Prediction for Quantum-Critical Dynamics.

Sergei Khlebnikov1

  • 1Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA.

Physical Review Letters
|August 4, 2020
PubMed
Summary

We explore how perturbations decay near quantum critical points. Holography predicts universal decay rates at high wave numbers, confirmed by analytical and numerical methods, offering insights into quantum systems.

Area of Science:

  • Condensed matter physics
  • Quantum criticality
  • Holography

Background:

  • Quantum critical points (QCPs) exhibit unique phenomena at absolute zero temperature.
  • Finite temperature effects complicate the study of QCPs.
  • Emergent Lorentz invariance is a key feature in some QCP systems.

Purpose of the Study:

  • Investigate the decay of density or current perturbations at finite temperature near a QCP.
  • Establish a connection between perturbation decay and holographic principles.
  • Provide a testable prediction for experimentally accessible systems.

Main Methods:

  • Analytical calculations of perturbation decay rates.
  • Holographic computations utilizing dual gravitational descriptions.

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  • Numerical analysis of quasinormal modes.
  • Focus on high wave number (k≫T) perturbations.

    • Main Results:

    • Holographic calculations reveal that large wave number decay rates depend universally on the leading metric correction.
    • A scaling law for decay rate is derived in the zero detuning limit.
    • The exponent in the scaling law is found to be dimensionality-dependent.
    • Analytical arguments and numerical simulations of quasinormal modes confirm the predicted scaling.

    Conclusions:

    • Decay of high wave number perturbations near QCPs serves as a robust test for holography.
    • The universality of holographic predictions offers a pathway to experimentally verify theoretical models.
    • The study provides a framework for understanding quantum dynamics in strongly correlated systems.