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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
No Massless Goldstone Bosons in Hamiltonian Time Crystals
1University of Science and Technology of China, Nordita, Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden and Wilczek Quantum Center, Shanghai Institute for Advanced Studies, Shanghai 201315, China.
None:
We present a geometric framework for Hamiltonian quantum time crystals, emphasizing the pivotal role of continuous symmetries and their associated conserved charges. In this approach, a time crystal is identified as a minimum-energy ground state that is parallel transported along a family of Fock spaces, with time evolution realized as a symmetry transformation. This parallel transport is implemented via a generalized, time-dependent Bogoliubov transformation, ensuring coherence across the Fock spaces. Revisiting Goldstone's original analysis, we show that in the presence of a time crystal, the Goldstone mode acquires a mass and its direction oscillates periodically in Higgs space. Our formulation circumvents existing no-go theorems that would otherwise forbid quantum time-crystalline order. We place time crystals within the broader context of quantum many-body physics and field theory, drawing analogies to superconductivity and quantum field theory in time-dependent backgrounds.
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