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ENERGY BANDS. “It is worth mentioning that we consider here deep optical lattice potentials which can host many energy bands, and highly excited bands (with energies close to the barrier between the potential wells) are resonantly coupled by the shaking.” https://lnkd.in/e5UXiem5 View in LinkedIn

EXPANDING DIMENSIONS. “We live in a 3D space and spatial crystals of dimension up to three can be observed and investigated. We have seen that time appears as a degree of freedom where a crystalline behavior can be created too. Combining space and time lattices, we should be able to create crystals of dimension higher than three. Surprisingly, such time-space crystals can be even six-dimensional as we will show in the following.” https://lnkd.in/e5UXiem5 View in LinkedIn

The Fibonacci numbers for n=1, 2, ... are 1, 1, 2, 3, 5, 8, 13, 21. https://lnkd.in/gTPGqVp5 View in LinkedIn

COLLECTIVE BEHAVIOR. “Condensed matter physics is the study of the macroscopic properties of materials. It seeks to use the well-established laws of microscopic physics to predict the collective properties of very large numbers of electrons, atoms or molecules.” https://lnkd.in/g7GeBSuk View in LinkedIn

FLAT INFINITY LOOP. “Möbius strip geometry. Atoms loaded to lattices fulfill the boundary conditions of the Möbius strip geometry.” https://lnkd.in/e5UXiem5 View in LinkedIn

FIBONACCI SERIES. “Then, when the discrete time translation symmetry (defined by the oscillation period of the mirrors) is spontaneously broken, the sequence of atoms reflected from one mirror and the other mirror forms a Fibonacci quasi-crystal in time.” https://lnkd.in/e5UXiem5 View in LinkedIn

GOLDEN NUMBER. “Use of a 2D time lattice allows a range of 2D condensed matter phenomena to be investigated with two oscillating mirrors. For example, it is possible to realize spontaneous formation of time quasi-crystals when the ratio of the resonance numbers along the x and y directions, s /s , approximates the golden number ≈ 1.618.” https://lnkd.in/e5UXiem5 View in LinkedIn

ELECTRON ORBITAL SHAPES. “In condensed matter physics, the angular distribution of a spin-polarized electron cloud around a nucleus can be characterized by spherical harmonics.” https://journals.jps.jp/doi/full/10.7566/JPSJ.87.041008 View in LinkedIn

THE PLAN. “Although time is a single degree of freedom, crystalline structures in time with the properties of 2D (or 3D) condensed matter systems can be created by a BEC bouncing resonantly between two (or three) oscillating atom mirrors.” (BEC = Bose-Einstein condensate). https://lnkd.in/e5UXiem5 View in LinkedIn

OFF-DIAGONAL RESPONSES. “As the multipole classification scheme can be generalized to systems characterized by a specific point group symmetry, multipole theory is becoming used for the classification of off-diagonal response phenomena, such as the electric-magnetic effect and the anomalous Hall effect in antiferromagnets.” https://journals.jps.jp/doi/full/10.7566/JPSJ.87.041008 View in LinkedIn