The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a butterfly velocity, which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, we construct a family of simple 2-local Hamiltonians for understanding the asymmetric hydrodynamics of operator spreading. Our models live on a one dimensional lattice and exhibit asymmetric butterfly velocities between the left and right spatial directions. This asymmetry is transparently understood in a free (non-interacting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities.
Chaotic dynamics in quantum many-body systems scrambles local information so that at late times it can no longer be accessed locally. This is reflected quantitatively in the out-of-time-ordered correlator of local operators, which is expected to decay to zero with time. However, for systems of finite size, out-of-time-ordered correlators do not decay exactly to zero and in this paper we show that the residual value can provide useful insights into the chaotic dynamics. When energy is conserved, the late-time saturation value of the out-of-time-ordered correlator of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We provide both analytical arguments and numerical simulations to support this conclusion.
Hypocycloid and epicycloid motions of irregular grain (pine pollen) are observed for the first time in unmagnetized dust plasma in 2D horizontal plane. Hypocycloid motions occur both inside and outside the glass ring which confines the grain. Epicycloid motion only appears outside the glass ring. Cuspate cycloid motions, circle motion, and stationary grain are also observed. All these motions are related with both the initial conditions of dropped grain and the discharge parameters. The Magnus force originated from the spin of the irregular grain is confirmed by comparison experiments with regular microspheres, and it plays important role on these (cuspate) cycloid motions. The observed complex motions are explained in term of force analysis and numerical simulations. Periodical change of the cyclotron radius as the grain travelling results in the (cuspate) cycloid motions. Our results show that the (cuspate) cycloid motions are distinctive features of irregular grain immersed in plasma.
We propose a quantum fitting scheme to estimate the magnetic field gradient with $N$-atom spins preparing in W state, which attains the Heisenberg-scaling accuracy. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cram{e}r-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. In single parameter estimation with assumption that the magnetic field is strictly linear, two optimal measurements can achieve the identical Heisenberg-scaling accuracy. Proper interpretation of the super-Heisenberg-scaling accuracy is presented. The scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.
We propose a quantum method to judge whether two spatially separated clocks have been synchronized within a specific accuracy $sigma$. If the measurement result of the experiment is obviously a nonzero value, the time difference between two clocks is smaller than $sigma$; otherwise the difference is beyond $sigma$. On sharing the 2$N$-qubit bipartite maximally entangled state in this scheme, the accuracy of judgement can be enhanced to $sigmasim{pi}/{(omega(N+1))}$. This criterion is consistent with Heisenberg scaling that can be considered as beating standard quantum limit, moreover, the unbiased estimation condition is not necessary.
We generalize the geometrical model of transformation optics to Rieman-Cartan space with torsion by introducing topological defects in physical space. By relaxing the integrable condition, we show explicitly that the generalized equivalent medium are bi-anisotropic where the magnetoelectric coupling parameters emergent as the dislocation density. We also show the generation of orbital angular momentum of light. Our theory may open intriguing venues for controlling the vectorial degree of freedom of light with metamaterials.
