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This "accordion lattice" was able to vary the lattice periodicity from 1.30 to 9.3 μm. More recently, a different method of real-time control of the lattice periodicity was demonstrated, [9] in which the center fringe moved less than 2.7 μm while the lattice periodicity was changed from 0.96 to 11.2 μm. Keeping atoms (or other particles ...
When talking about solid materials, the discussion is mainly around crystals – periodic lattices. Here we will discuss a 1D lattice of positive ions. Assuming the spacing between two ions is a, the potential in the lattice will look something like this: The mathematical representation of the potential is a periodic function with a period a.
Here is the amplitude of the variation of the onsite energies, is a relative phase, and is the period of the onsite potential modulation in units of the lattice constant. This Hamiltonian is self-dual as it retains the same form after a Fourier transformation interchanging the roles of position and momentum.
The resulting crystal net will induce a lattice of vectors so that given three vectors that generate the lattice, those three vectors will bound a unit cell, i.e. a parallelepiped which, placed anywhere in space, will enclose a fragment of the net that repeats in the directions of the three axes.
α-Sm type has a period of 9 layers A,B,A,B,C,B,C,A,C,... [22] Precisely speaking, the structures of many of the elements in the groups above are slightly distorted from the ideal closest packing. While they retain the lattice symmetry as the ideal structure, they often have nonideal c/a ratios for their unit cell.
Ultracold atom trapping in optical lattices is an experimental tool commonly used in condensed matter physics, and in atomic, molecular, and optical physics. The method involves using optical lasers to form an interference pattern , which acts as a lattice , in which ions or atoms can be placed at very low temperatures.
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An algebraic lattice is complete. (def) 10. A complete lattice is bounded. 11. A heyting algebra is bounded. (def) 12. A bounded lattice is a lattice. (def) 13. A heyting algebra is residuated. 14. A residuated lattice is a lattice. (def) 15. A distributive lattice is modular. [3] 16. A modular complemented lattice is relatively complemented ...