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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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The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Phase transitions in spin systems generate heat during slow magnetic field quenches.
  • Kibble-Zurek scaling describes universal heat production in short-range interacting systems.
  • The Lipkin-Meshkov-Glick (LMG) model provides a framework for studying fully connected quantum spins.

Purpose of the Study:

  • To analyze slow magnetic field quenches in the LMG model.
  • To determine the quantum contribution to residual heat as a function of quench rate.
  • To investigate deviations from Kibble-Zurek scaling in fully connected systems.

Main Methods:

  • Analytical determination of quantum heat contribution.
  • Utilizing a Holstein-Primakoff expansion around the mean-field value.
  • Examining quench dynamics starting, ending, or symmetric around the critical point.

Main Results:

  • Scaling laws in the LMG model are observed only for ramps initiating or concluding at the critical point.
  • Symmetric ramps lead to crossover behavior in excitation number, converging to a constant in the thermodynamic limit.
  • Identified previous contradictory findings as specific limiting cases of the derived dynamics.

Conclusions:

  • The LMG model exhibits distinct heat production dynamics compared to short-range systems.
  • The findings clarify previously conflicting theoretical results on quench dynamics.
  • Experimental verification is possible using quantum gases and trapped ions.