AI Insight
This paper demonstrates that a closed quantum system can exhibit persistent time-crystal-like behavior without external periodic driving, using the Bateman dual oscillator framework applied to a nonrelativistic (2+1)-dimensional system where spin-induced spatial deformation generates coupled damped and amplified oscillator sectors. By tracing over the amplified sector, the authors derive a non-Markovian reduced dynamics that sustains persistent oscillations and emergent temporal ordering through quantum memory effects rather than equilibrium spontaneous symmetry breaking. The system additionally produces logarithmic-spiral trajectories and self-similar fractal scaling, linking coherent dissipative dynamics to emergent temporal structure within a globally unitary framework.
Why it matters
Understanding how time-crystal-like order can arise without driving or symmetry breaking could inform the design of stable quantum memory and coherence-preserving devices, with potential relevance to quantum computing architectures where decoherence control is critical.
arXiv:2605.19917v1 Announce Type: cross
Abstract: Can a closed quantum system generate persistent time-crystal-like dynamics without external driving? Within the Bateman dual oscillator framework, we show that the answer is affirmative. We consider a nonrelativistic (2+1)-dimensional system in which spin-induced spatial deformation generates an effective Bateman oscillator structure. After quantization, the system is governed by a time-independent Hermitian Hamiltonian describing coherent coupling between damped and amplified oscillator sectors while preserving the total energy of the global doubled system. Tracing over the amplified sector, we derive an effective non-Markovian reduced dynamics for the observable subsystem. The resulting memory effects sustain persistent oscillations of subsystem observables and generate emergent time-crystal-like temporal ordering without external periodic driving or equilibrium spontaneous symmetry breaking. Since the oscillatory behavior originates from nonequilibrium reduced subsystem dynamics rather than equilibrium expectation values of the full Hamiltonian, the mechanism lies outside the assumptions of conventional no-go theorems for equilibrium time crystals. The same dynamics further exhibits logarithmic-spiral trajectories and self-similar fractal scaling, revealing a direct connection between coherent dissipative dynamics, non-Markovian memory effects, and emergent temporal ordering in a globally unitary quantum system. In this specific sense, “watching the growth” of these self-similar structures corresponds to observing the gradual formation of time-crystal-like ordering.