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Phase space crystal is the state of a physical system that displays discrete symmetry in phase space instead of real space. For a single-particle system, the phase space crystal state refers to the eigenstate of the Hamiltonian for a closed quantum system[1] or the eigenoperator of the Liouvillian for an open quantum system.[2] For a many-body system, phase space crystal is the solid-like crystalline state in phase space.[3][4] The general framework of phase space crystals is to extend the study of solid state physics and condensed matter physics into phase space of dynamical systems.[5] While real space has Euclidean geometry, phase space is embedded with classical symplectic geometry or quantum noncommutative geometry.
^Guo, Lingzhen; Marthaler, Michael; Schön, Gerd (13 November 2013). "Phase Space Crystals: A New Way to Create a Quasienergy Band Structure". Physical Review Letters. 111 (20): 205303. arXiv:1305.1800. Bibcode:2013PhRvL.111t5303G. doi:10.1103/PhysRevLett.111.205303. PMID 24289695. S2CID 9337383.
^Lang, Ben; Armour, Andrew D (1 March 2021). "Multi-photon resonances in Josephson junction-cavity circuits". New Journal of Physics. 23 (3): 033021. arXiv:2012.10149. Bibcode:2021NJPh...23c3021L. doi:10.1088/1367-2630/abe483. S2CID 229332222.
^Liang, Pengfei; Marthaler, Michael; Guo, Lingzhen (3 April 2018). "Floquet many-body engineering: topology and many-body physics in phase space lattices". New Journal of Physics. 20 (2): 023043. arXiv:1710.09716. Bibcode:2018NJPh...20b3043L. doi:10.1088/1367-2630/aaa7c3. S2CID 3275846.
^Guo, Lingzhen; Peano, Vittorio; Marquardt, Florian (3 March 2022). "Phase space crystal vibrations: Chiral edge states with preserved time-reversal symmetry". Physical Review B. 105 (9): 094301. arXiv:2105.06989. Bibcode:2022PhRvB.105i4301G. doi:10.1103/PhysRevB.105.094301. S2CID 234680134.
^Guo, Lingzhen (2021). Phase space crystals : condensed matter in dynamical systems. Bristol UK: IOP Publishing Ltd. ISBN 978-0-7503-3563-8.
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Phasespacecrystal is the state of a physical system that displays discrete symmetry in phasespace instead of real space. For a single-particle system...
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crystalline phase at a certain temperature and pressure (the inversion point) to another phase of the same chemical composition with a different crystal structure...
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of crystals and liquid (like a "slurry"). Working fluids are often categorized on the basis of the shape of their phase diagram. The simplest phase diagrams...
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There are various different crystal structures, and the same substance can have more than one structure (or solid phase). For example, iron has a body-centred...
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