Fractional winding numbers in open quantum systems recover integer quantization over multiple momentum periods.
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Strong symmetries in open quantum systems always break spontaneously to weak symmetry or completely, producing gapless Goldstone modes, charge diffusion, and time crystalline order in some cases.
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Fractional topology and multi-period re-quantization in open quantum systems
Fractional winding numbers in open quantum systems recover integer quantization over multiple momentum periods.
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Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
Strong symmetries in open quantum systems always break spontaneously to weak symmetry or completely, producing gapless Goldstone modes, charge diffusion, and time crystalline order in some cases.