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      A Listing of Crystallographic Point Groups in Space and Time

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          Abstract

          Point groups and space groups provide a convenient way to describe the spatial arrangement of atoms in molecules and crystals, and are powerful tools in the prediction of their physical properties. Previous works [1], [2] have extended these groups to include temporal symmetry operations. This work presents a reformulation of the listing of crystallographic point groups with time translations, using a template similar to space group operations. A simple method is presented to visualize these groups by modifying conventional stereographic projections. Examples of physical processes are identified, which may benefit from a group theoretical analysis that considers both spatial and time-translational symmetry.

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          Absence of Quantum Time Crystals

          , (2015)
          In analogy with crystalline solids around us, Wilczek recently proposed the idea of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. The proposal stimulated further studies and vigorous debates whether it can be realized in a physical system. However, a precise definition of the time crystal is needed to resolve the issue. Here we first present a definition of time crystals based on the time-dependent correlation functions of the order parameter. We then prove a no-go theorem that rules out the possibility of time crystals defined as such, in the ground state or in the canonical ensemble of a general Hamiltonian, which consists of not-too-long-range interactions.
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            Impossibility of Spontaneously Rotating Time-Crystals: A No-Go Theorem

            I present arguments indicating the impossibility of spontaneously rotating quantum timecrystals, as recently proposed by Frank Wilczek [arXiv:1202.2539]. In particular, I prove a No-Go Theorem, rigorously ruling out the possibility of spontaneous ground-state (or thermal equilibrium) rotation for a broad class of systems.
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              The effect of Hamiltonian symmetry on generation of odd and even harmonics

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                Author and article information

                Journal
                2017-01-15
                Article
                1701.04088
                b7426d64-43c3-4258-bfa3-c1f4830297c3

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                main text (7 pages), supplemental table, anc images
                cond-mat.mtrl-sci

                Condensed matter
                Condensed matter

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