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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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An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
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Genuine Quantum Effects in Dicke-Type Models at Large Atom Numbers.

Kai Müller1, Walter T Strunz1

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Genuine quantum effects persist in unbalanced open Dicke models with mesoscopic atom numbers. This contrasts with balanced models where these effects vanish as atom numbers increase, revealing non-commuting limits in quantum many-body systems.

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Area of Science:

  • Quantum physics
  • Quantum many-body systems
  • Open quantum systems

Background:

  • Dicke models describe collective quantum phenomena in systems with many atoms.
  • Mean-field theory often predicts system behavior in the thermodynamic limit (N→∞).
  • Recent experiments realize driven and dissipative quantum many-body systems using ultracold gases in optical cavities.

Purpose of the Study:

  • To investigate quantum effects beyond mean-field predictions in open Dicke models.
  • To explore the influence of atom number (N) on these quantum effects.
  • To identify conditions where genuine quantum phenomena survive for large, finite N.

Main Methods:

  • Numerical investigation of balanced and unbalanced open Dicke models.
  • Application of a novel open-system dynamics method for exact quantum dynamical results.
  • Analysis of systems with atom numbers up to a mesoscopic N≈1000.

Main Results:

  • Beyond-mean-field effects diminish rapidly with increasing N in the balanced Dicke model.
  • Parameter regimes in the unbalanced Dicke model identified where quantum effects persist for mesoscopic N.
  • Observed quantum effects include strong steady-state squeezing and modified phase diagrams absent in mean-field descriptions.

Conclusions:

  • The steady-state limit and thermodynamic limit do not commute for these systems.
  • Genuine quantum effects can survive in mesoscopic systems under specific conditions in unbalanced Dicke models.
  • Mean-field descriptions are insufficient for capturing all quantum phenomena in large, finite open quantum systems.