Biorthogonal Dynamical Quantum Phase Transitions in Non-Hermitian Systems.

By utilizing biorthogonal bases, we develop a comprehensive framework for studying biorthogonal dynamical quantum phase transitions in non-Hermitian systems. With the help of the previously overlooked associated state, we define the automatically normalized biorthogonal Loschmidt echo. This approach is capable of handling arbitrary non-Hermitian systems with complex eigenvalues and naturally eliminates the negative value of Loschmidt rate obtained without the biorthogonal bases. Taking the non-Hermitian Su-Schrieffer-Heeger model as a concrete example, a 1/2 change of dynamical topological order parameter in biorthogonal bases is observed which is not shown in self-normal bases. Furthermore, we discover that the periodicity of biorthogonal dynamical quantum phase transitions depends on whether the two-level subsystem at the critical momentum oscillates or reaches a steady state.

Quantum Phases in a Quantum Rabi Triangle.

The interplay of interactions, symmetries, and gauge fields usually leads to intriguing quantum many-body phases. To explore the nature of emerging phases, we study a quantum Rabi triangle system as an elementary building block for synthesizing an artificial magnetic field. We develop an analytical approach to study the rich phase diagram and the associated quantum criticality. Of particular interest is the emergence of a chiral-coherent phase, which breaks both the Z_{2} and the chiral symmetry. In this chiral phase, photons flow unidirectionally and the chirality can be tuned by the artificial gauge field, exhibiting a signature of broken time-reversal symmetry. The finite-frequency scaling analysis further confirms the associated phase transition to be in the universality class of the Dicke model. This model can simulate a broad range of physical phenomena of light-matter coupling systems, and may have an application in future developments of various quantum information technologies.

Scaling analysis of the non-Abelian quasiparticle tunneling in [Formula: see text] FQH states.

Quasiparticle tunneling between two counter propagating edges through point contacts could provide information on its statistics. Previous study of the short distance tunneling displays a scaling behavior, especially in the conformal limit with zero tunneling distance. The scaling exponents for the non-Abelian quasiparticle tunneling exhibit some non-trivial behaviors. In this work, we revisit the quasiparticle tunneling amplitudes and their scaling behavior in a full range of the tunneling distance by putting the electrons on the surface of a cylinder. The edge-edge distance can be smoothly tuned by varying the aspect ratio for a finite size cylinder. We analyze the scaling behavior of the quasiparticles for the Read-Rezayi [Formula: see text] states for [Formula: see text] and 4 both in the short and long tunneling distance region. The finite size scaling analysis automatically gives us a critical length scale where the anomalous correction appears. We demonstrate this length scale is related to the size of the quasiparticle at which the backscattering between two counter propagating edges starts to be significant.

Inhibition of Parkinsonian tremor with cutaneous afferent evoked by transcutaneous electrical nerve stimulation.

BACKGROUND: Recent study suggests that tremor signals are transmitted by way of multi-synaptic corticospinal pathway. Neurophysiological studies have also demonstrated that cutaneous afferents exert potent inhibition to descending motor commands by way of spinal interneurons. We hypothesize in this study that cutaneous afferents could also affect the transmission of tremor signals, thus, inhibit tremor in patients with PD. METHODS: We tested this hypothesis by activating cutaneous afferents in the dorsal hand skin innervated by superficial radial nerve using transcutaneous electrical nerve stimulation (TENS). Eight patients with PD having tremor dominant symptom were recruited to participate in this study using a consistent experimental protocol for tremor inhibition. Resting tremor and electromyogram (EMG) of muscles in the upper extremity of these subjects with PD were recorded, while surface stimulation was applied to the dorsal skin of the hand. Fifteen seconds of data were recorded for 5 s prior to, during and post stimulation. Power spectrum densities (PSDs) of tremor and EMG signals were computed for each data segment. The peak values of PSDs in three data segments were compared to detect evidence of tremor inhibition. RESULTS: At stimulation intensity from 1.5 to 1.75 times of radiating sensation threshold, apparent suppressions of tremor at wrist, forearm and upper arm and in the EMGs were observed immediately at the onset of stimulation. After termination of stimulation, tremor and rhythmic EMG bursts reemerged gradually. Statistical analysis of peak spectral amplitudes showed a significant difference in joint tremors and EMGs during and prior to stimulation in all 8 subjects with PD. The average percentage of suppression was 61.56% in tremor across all joints of all subjects, and 47.97% in EMG of all muscles. The suppression appeared to occur mainly in distal joints and muscles. There was a slight, but inconsistent effect on tremor frequency in the 8 patients with PD tested. CONCLUSIONS: Our results provide direct evidence that tremor in the upper extremity of patients with PD can be inhibited to a large extent with evoked cutaneous reflexes via surface stimulation of the dorsal hand skin area innervated by the superficial radial nerve.

Publisher's Note: Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect [Phys. Rev. Lett. 118, 146403 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.118.146403.

Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect.

We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems that are physically realized, e.g., in tilted magnetic field experiments or anisotropic band structures. This formalism allows us to expand any translation-invariant interaction over a complete basis, and directly reveals the intrinsic metric of incompressible FQH fluids. We show that purely anisotropic pseudopotentials give rise to new types of bound states for small particle clusters in the infinite plane, and can be used as a diagnostic of FQH nematic order. We also demonstrate that generalized pseudopotentials quantify the anisotropic contribution to the effective interaction potential, which can be particularly large in models of fractional Chern insulators.

Neural computational modeling reveals a major role of corticospinal gating of central oscillations in the generation of essential tremor.

Essential tremor, also referred to as familial tremor, is an autosomal dominant genetic disease and the most common movement disorder. It typically involves a postural and motor tremor of the hands, head or other part of the body. Essential tremor is driven by a central oscillation signal in the brain. However, the corticospinal mechanisms involved in the generation of essential tremor are unclear. Therefore, in this study, we used a neural computational model that includes both monosynaptic and multisynaptic corticospinal pathways interacting with a propriospinal neuronal network. A virtual arm model is driven by the central oscillation signal to simulate tremor activity behavior. Cortical descending commands are classified as alpha or gamma through monosynaptic or multisynaptic corticospinal pathways, which converge respectively on alpha or gamma motoneurons in the spinal cord. Several scenarios are evaluated based on the central oscillation signal passing down to the spinal motoneurons via each descending pathway. The simulated behaviors are compared with clinical essential tremor characteristics to identify the corticospinal pathways responsible for transmitting the central oscillation signal. A propriospinal neuron with strong cortical inhibition performs a gating function in the generation of essential tremor. Our results indicate that the propriospinal neuronal network is essential for relaying the central oscillation signal and the production of essential tremor.

Model wave functions for the collective modes and the magnetoroton theory of the fractional quantum Hall effect.

We construct model wave functions for the collective modes of fractional quantum Hall systems. The wave functions are expressed in terms of symmetric polynomials characterized by a root partition that defines a "squeezed" basis, and show excellent agreement with exact diagonalization results for finite systems. In the long wavelength limit, we prove that the model wave functions are identical to those predicted by the single-mode approximation, leading to intriguing interpretations of the collective modes from the perspective of the ground-state guiding-center metric.

Realizing universal edge properties in graphene fractional quantum Hall liquids.

Universal chiral Luttinger liquid behavior has been predicted for fractional quantum Hall edge states, but so far has not been observed experimentally in semiconductor-based two-dimensional electron gases. One likely cause of this absence of universality is the generic occurrence of edge reconstruction in such systems, which is the result of a competition between confinement potential and Coulomb repulsion. We show that due to a completely different mechanism of confinement, edge reconstruction can be avoided in graphene, which allows for the observation of the predicted universality.