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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Crystal Field Theory
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Color in Coordination Complexes
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The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
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Nonlinear Topological Effects in Optical Coupled Hexagonal Lattice.

Fude Li1, Kang Xue1, Xuexi Yi1

  • 1Center for Quantum Sciences and School of Physics, Northeast Normal University, Renmin Street 5268, Changchun 130024, China.

Entropy (Basel, Switzerland)
|November 27, 2021
PubMed
Summary
This summary is machine-generated.

This study explores nonlinear Dirac cones in optical lattices, revealing quantized Berry and Aharonov-Bohm phases. Topological phase transitions occur differently than in linear systems.

Keywords:
nonlinear Berry phasenonlinear energy bandtopological phase transition

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Area of Science:

  • Topological physics
  • Nonlinear optics
  • Condensed matter theory

Background:

  • Topological physics in optical lattices is a rapidly advancing field.
  • Nonlinear effects in optical systems are crucial for understanding complex phenomena.
  • Previous research has established significant progress in nonlinear optical systems.

Purpose of the Study:

  • To investigate nonlinear Dirac cones in a hexagonal optical lattice system.
  • To analyze the dependence of these cones on system parameters.
  • To explore the quantization of Berry and Aharonov-Bohm phases and their relation to topological phase transitions.

Main Methods:

  • Mean-field approximation applied to a nonlinear optical coupled boson-hexagonal lattice.
  • Calculation of nonlinear Dirac cones and their parameter dependence.
  • Numerical computation of Berry phase (2D Zak phase) and Aharonov-Bohm phase.

Main Results:

  • The nonlinear Dirac cone exhibits quantized Berry phase, tunable by inter-site interactions.
  • The overall Aharonov-Bohm phase is also quantized, serving as a topological number.
  • Topological phase transitions are identified by band gap closure at nonlinear Dirac points.

Conclusions:

  • The study characterizes quantum phases in nonlinear optical lattices using quantized topological numbers.
  • A novel mechanism for topological phase transitions is observed, distinct from linear systems.
  • Findings offer new insights into topological phenomena in nonlinear optical systems.