Dynamical Fractal in Quantum Gases with Discrete Scaling Symmetry

Abstract

Inspired by the similarity between the fractal Weierstrass function and quantum systems with discrete scaling symmetry, we establish general conditions under which the dynamics of a quantum system will exhibit fractal structure in the time domain. As an example, we discuss the dynamics of the Loschmidt amplitude and the zero-momentum occupation of a single particle moving in a scale invariant $1/r^2$ potential. In order to show these conditions can be realized in ultracold atomic gases, we perform numerical simulations with practical experimental parameters, which shows that the dynamical fractal can be observed in realistic time scales. The predication can be directly verified in current cold atom experiments.

5 pages, 4 figures

References in corpus (3)

• Dynamics of Loschmidt echoes and fidelity decay
• Time dependent impurity in ultracold fermions: orthogonality catastrophe and beyond
• Multi-wavelength holography with a single Spatial Light Modulator for ultracold atom experiments

Cited by in corpus (6)

• High Temperature Virial Expansion to Universal Quench Dynamics
• Odd thermodynamic limit for the Loschmidt echo
• Single- to many-body crossover of a quantum carpet
• Quench Dynamics of Thermal Bose Gases Across Wide and Narrow Feshbach
• The fractal geometry and the mapping of Efimov states to Bloch states
• Bound-like State in a 1D Self-Similar Delta-Barrier Array