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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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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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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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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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Crossing exceptional points without phase transition.

Qi Zhong1, Ramy El-Ganainy2

  • 1Department of Physics and Henes Center for Quantum Phenomena, Michigan Technological University, Houghton, MI, 49931, USA.

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|January 16, 2019
PubMed
Summary
This summary is machine-generated.

The theoretical framework connecting exceptional points (EPs) to phase transitions in parity-time (PT) symmetric systems is incomplete. Applying a squaring operator alters Riemann surface topology, allowing EPs to be crossed without symmetry breaking.

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Area of Science:

  • Theoretical physics
  • Quantum mechanics
  • Non-Hermitian systems

Background:

  • Exceptional points (EPs) are critical points in non-Hermitian systems where eigenvalues and eigenvectors coalesce.
  • Parity-time (PT) symmetry offers a framework for studying non-Hermitian Hamiltonians, often linked to phase transitions.

Purpose of the Study:

  • To investigate the completeness of the theoretical framework linking EPs to phase transitions in PT symmetric Hamiltonians.
  • To explore the effects of applying a squaring operator to a PT symmetric lattice.

Main Methods:

  • Analysis of the topology of the Riemann surface of a Jx PT lattice.
  • Investigation of phase diagrams in higher dimensional parameter space.
  • Theoretical examination of symmetry breaking in PT symmetric systems.

Main Results:

  • The theoretical framework linking EPs to phase transitions in PT symmetric Hamiltonians is shown to be incomplete.
  • Application of a squaring operator dramatically alters the Riemann surface topology.
  • A system can cross an EP without undergoing symmetry breaking.

Conclusions:

  • The canonical PT symmetry breaking paradigm is only a projection within a higher-dimensional parameter space.
  • The Riemann surface topology plays a crucial role in understanding EP behavior and phase transitions.
  • This work necessitates a revised understanding of EPs and phase transitions in PT symmetric systems.