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.

arXiv comment5 pages, 4 figures

References in corpus (13)

• Universality in Few-body Systems with Large Scattering Length
• Dynamics of Loschmidt echoes and fidelity decay
• Ultrafast many-body interferometry of impurities coupled to a Fermi sea
• Time dependent impurity in ultracold fermions: orthogonality catastrophe and beyond
• Direct imaging of a digital-micromirror device for configurable microscopic optical potentials
• Singular Potentials and Limit Cycles
• Ultra-precise holographic beam shaping for microscopic quantum control
• Orthogonality catastrophe as a consequence of qubit embedding in an ultra-cold Fermi gas
• Robust Digital Holography For Ultracold Atom Trapping
• The Renormalization Group Limit Cycle for the 1/r^2 Potential
• Nonrelativistic inverse square potential, scale anomaly, and complex extension
• Multi-wavelength holography with a single Spatial Light Modulator for ultracold atom experiments
• Time fractals and discrete scale invariance with trapped ions

Cited by in corpus (7)

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