Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions

We present a theory of hydrodynamics for a vector U(1) charge in 2+1 dimensions, whose rotational symmetry is broken to the point group of an equilateral triangle. We show that it is possible for this U(1) to have a chiral anomaly. The hydrodynamic consequence of this anomaly is the introduction of a ballistic contribution to the dispersion relation for the hydrodynamic modes. We simulate classical Markov chains and find compelling numerical evidence for the anomalous hydrodynamic universality class. Generalizations of our theory to other symmetry groups are also discussed

Realizing the Hayden-Preskill Protocol with Coupled Dicke Models

Hayden and Preskill proposed a thought experiment that Bob can recover the information Alice throws into a black hole if he has a quantum computer entangled with the black hole, and Yoshida and Kitaev recently proposed a concrete decoding scheme. The parallel question is that after a small system is thermalized with a large system, how one can decode the initial state information with the help of two entangled many-body systems. Here we propose to realize this protocol in a physical system of two Dicke models, with two cavity fields prepared in a thermofield double state. We show that the Yoshida-Kitaev protocol allows us to read out the initial spin information after it is scrambled into the cavity. We show that the readout efficiency reaches a maximum when the model parameter is tuned to the regime where the system is the most chaotic, characterized by the shortest scrambling time in the out-of-time-ordered correlation function. Our proposal opens up the possibility of discussing this profound thought experiment in a realistic setting.Comment: 5 pages, 4 figure

Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation

We develop a Schwinger-Keldysh effective field theory describing the hydrodynamics of a fluid with conserved charge and dipole moments, together with conserved momentum. The resulting hydrodynamic modes are highly unusual, including sound waves with quadratic (magnon-like) dispersion relation and subdiffusive decay rate. Hydrodynamics itself is unstable below four spatial dimensions. We show that the momentum density is, at leading order, the Goldstone boson for a dipole symmetry which appears spontaneously broken at finite charge density. Unlike an ordinary fluid, the presence or absence of energy conservation qualitatively changes the decay rates of the hydrodynamic modes. This effective field theory naturally couples to curved spacetime and background gauge fields; in the flat spacetime limit, we reproduce the "mixed rank tensor fields" previously coupled to fracton matter.Comment: 20+10 pages. v2, v3: minor edit

Virtual Reality Neurorehabilitation

The present work investigates the application of virtual reality (VR) technology to neurorehabilitation. By consulting a wealth of data, the advantages of VR in neurorehabilitation are introduced, followed by the application status of VR in the rehabilitation of stroke patients, Parkinson's patients, mental and psychological diseases. Besides, many research experiments on the application of VR technology in rehabilitation medicine at the present stage are investigated. The results indicate that compared with traditional balance training, the VR-based neurological rehabilitation training method can more effectively ease the tilt degree and strengthen the trunk control ability and balance function of patients with post-stroke tilt syndrome. When the effect of traditional rehabilitation training on the gait and balance of Parkinson's patients is not good enough, VR-based rehabilitation training can at least be used as an alternative therapy. Moreover, VR games have made great breakthroughs in promoting limb rehabilitation and brain injury rehabilitation, which is of incredible benefit to those with motor and activity disorders. It is also beneficial to the treatment and recovery of mental disorders of patients with nerve injury. Although VR still has limitations such as high cost and technical breakthrough bottleneck, it has great advantages in relieving pain, enhancing interest, and recovering patients' mental health in neurological rehabilitation training

On the bounds of feedback rates for pilot-assisted MIMO systems

For pilot-assisted multiple-input-multiple-output (MIMO) systems with imperfect feedback, we investigate the relationship between the feedback transmission rate and the resulting closed-loop capacity gain. Based on this relationship quantified via rate-distortion theory, we investigate the lower and upper bounds of the feedback rate that would effect positive closed-loop capacity gains without overly consuming feedback transmission resources. Extensive simulations are carried out to validate the analytic results and to shed light on the achievable closed-loop MIMO capacity given the system configuration parameterized by the number of antennas, transmit signal-to-noise ratio, pilot power allotment, and finite feedback rate. Such results provide guideline on the feedback channel for meaningful designs of practical pilot-assisted MIMO systems. © 2007 IEEE

On the Bounds of Feedback Rates for Pilot-Assisted MIMO Systems

(MIMO) systems with imperfect feedback, we investigate the relationship between the feedback transmission rate and the resulting closed-loop capacity gain. Based on this relationship quantified via rate-distortion theory, we investigate the lower and upper bounds of the feedback rate that would effect positive closed-loop capacity gains without overly consuming feedback transmission resources. Extensive simulations are carried out to validate the analytic results and to shed light on the achievable closed-loop MIMO capacity given the system configuration parameterized by the number of antennas, transmit signal-to-noise ratio, pilot power allotment, and finite feedback rate. Such results provide guideline on the feedback channel for meaningful designs of practical pilot-assisted MIMO systems. Index Terms—Closed-loop capacity, feedback rate, lower and upper bounds, multiple-input–multiple-output (MIMO), pilotassisted systems, rate distortion. I