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BREAKING SYMMETRY. “In particular, it was shown that a periodically driven many-body system can spontaneously break discrete time-translation symmetry and self-reorganize its motion so that it evolves with a period longer than the drive.” https://lnkd.in/e5UXiem5 View in LinkedIn

IMPETUS. “However, his idea inspired further proposals in time-independent and time-dependent quantum systems.” https://lnkd.in/e5UXiem5 View in LinkedIn

TOO FAR OUT. “While a classical particle can perform periodic motion even if its energy is the lowest possible and a classical time crystal can form, the quantum time crystal proposed by Wilczek turned out not to be feasible.” https://lnkd.in/e5UXiem5 View in LinkedIn

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