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QUANTUM TIME CRYSTALS. “To create such a ‘quantum time crystal’, he considered the possibility of spontaneous breaking of continuous time-translation symmetry in the ground state of a many-body system, in analogy with the formation of an ordinary crystal in space.” https://lnkd.in/e5UXiem5 View in LinkedIn

NON-SPONTANEOUS SPACE CRYSTALS. “However, crystalline structures in space can also be created externally without any spontaneous process.” https://lnkd.in/e5UXiem5 View in LinkedIn

OUT OF THE BOX. “In 2012 Frank Wilczek speculated whether crystalline structures in space could be extended to the fourth dimension – time?” https://lnkd.in/e5UXiem5 View in LinkedIn

SPONTANEOUS SPACE CRYSTALS. “Spontaneous breaking of continuous space translation symmetry into discrete space translation symmetry results in the formation of ordinary space crystals.” https://lnkd.in/e5UXiem5 View in LinkedIn

DEFINITION. “Time crystals are physical systems whose time translation symmetry is spontaneously broken.” https://lnkd.in/e5jENMEg View in LinkedIn

EXPANSION. “The second quantization formalism allows us to switch from a single particle to many indistinguishable particles by introducing the bosonic field operator ψˆ, which can be expanded in terms of operators that annihilate a boson in time-independent single-particle basis states.” https://lnkd.in/e5UXiem5 View in LinkedIn

AUTHORS: Distinguished Professor Peter Hannaford, Optical Sciences Centre, Swinburne University of Technology, Australia; and Professor Krzysztof Sacha, institute of Theoretical Physics, Jagiellonian University, Poland. https://lnkd.in/e5UXiem5 View in LinkedIn

PREDICTED PHENOMENA. “Temporal condensed matter phenomena that have been predicted to date include Mott insulator phases in the time dimension: Anderson localization and many-body localization in the time dimension; topologically protected edge states in time; quasi-crystal structures in time; two-dimensional time lattices supporting a Möbius strip geometry and flat-band physics; and time-space crystals exhibiting a six-dimensional quantum Hall effect.” https://lnkd.in/e5UXiem5 View in LinkedIn

FRAGMENT FROM NATURE is a Mind warp, touching the extraordinary world of condensed matter physics, higher dimensions, and broken symmetry in time. The ideas explored, including quite magical mathematics, are straight out of Alice in Wonderland. There are, it seems, few limits to creative thinking. https://lnkd.in/e5UXiem5 View in LinkedIn

DURABLE. “Such discrete time crystals are robust against external perturbations and quantum fluctuations and live for extremely long times.” https://lnkd.in/e5UXiem5 View in LinkedIn