We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder.To achieve this,we introduce a method to generate random on-site energies with...We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder.To achieve this,we introduce a method to generate random on-site energies with prescribed correlations.We verify this method with a one-dimensional(1D)cross-stitch model,and find good agreement with analytical results obtained from the disorder-dressed evolution equations.This allows us to reproduce previous findings,that disorder can mobilize 1D flat-band states which would otherwise remain localized.As explained by the corresponding disorder-dressed evolution equations,such mobilization requires an asymmetric disorder-induced coupling to dispersive bands,a condition that is generically not fulfilled when the flat-band is resonant with the dispersive bands at a Dirac point-like crossing.We exemplify this with the 1D Lieb lattice.While analytical expressions are not available for the two-dimensional(2D)system due to its complexity,we extend the numerical method to the 2D a–T3 model,and find that the initial flat-band wave packet preserves its localization when a=0,regardless of disorder and intersections.However,when a̸=0,the wave packet shifts in real space.We interpret this as a Berry phase controlled,disorder-induced wave-packet mobilization.In addition,we present density functional theory calculations of candidate materials,specifically Hg1−xCdxTe.The flat-band emerges near the G point(α=0)in the Brillouin zone.展开更多
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...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.展开更多
We introduce a generalized Rashba coupling approximation to analytically solve confined two-dimensional electron systems with both the Rashba and Dresselhaus spin–orbit couplings in an external magnetic field.A solva...We introduce a generalized Rashba coupling approximation to analytically solve confined two-dimensional electron systems with both the Rashba and Dresselhaus spin–orbit couplings in an external magnetic field.A solvable Hamiltonian is obtained by performing a simple change of basis,which has the same form as that with only Rashba coupling.Each Landau state becomes a new displaced-Fock state instead of the original Harmonic oscillator Fock state.Analytical energies are consistent with the numerical ones in a wide range of coupling strength even for a strong Zeeman splitting,exhibiting the validity of the analytical approximation.By using the eigenstates,spin polarization correctly displays a jump at the energy-level crossing point,where the corresponding spin conductance exhibits a pronounced resonant peak.As the component of the Dresselhaus coupling increases,the resonant point shifts to a smaller value of the magnetic field.In contrast to pure Rashba couplings,we find that the Dresselhaus coupling and Zeeman splittings tend to suppress the resonant spin Hall effect.Our method provides an easy-to-implement analytical treatment to two-dimensional electron gas systems with both types of spin–orbit couplings by applying a magnetic field.展开更多
For the numerical simulation of the fractional quantum Hall(FQH) effects on a finite disk, the rotational symmetry is the only symmetry that is used in diagonalizing the Hamiltonian. In this work, we propose a method ...For the numerical simulation of the fractional quantum Hall(FQH) effects on a finite disk, the rotational symmetry is the only symmetry that is used in diagonalizing the Hamiltonian. In this work, we propose a method of using the weak translational symmetry for the center of mass of the many-body system. With this approach, the bulk properties, such as the energy gap and the magneto-roton excitation are consistent with those in the closed manifolds like the sphere and torus. As an application, we consider the FQH phase and its phase transition in the fast rotated dipolar fermions. We thus demonstrate the disk geometry having versatility in analyzing the bulk properties beside the usual edge physics.展开更多
By exactly solving the effective two-body interaction for a two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that the effective interaction can be described by the...By exactly solving the effective two-body interaction for a two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that the effective interaction can be described by the generalized pseudopoten- tials （PPs） without the rotational symmetry. With this pseudopotential description, we numerically investigate the behavior of the fractional quantum Hall （FQH） states both in the lowest Landau level （LLL） and first excited Landau level （1LL）. The enhancements of the 7/3 FQH state on the 1LL for a small tilted magnetic field are observed when layer thickness is larger than some critical values, while the gap of the 1/3 state in the LLL monotonically reduced with increasing the in-plane field. From the static structure factor calculation, we find that the systems are strongly anisotropic and finally enter into a stripe phase with a large tilting. With considering the Landau level mixing correction on the two-body interaction, we find the strong LL mixing cancels the enhancements of the FQH states in the 1LL.展开更多
基金the National Natural Sci-ence Foundation of China(Grant No.61988102)the Key Research and Development Program of Guangdong Province(Grant No.2019B090917007)+5 种基金the Science and Technology Planning Project of Guangdong Province(Grant No.2019B090909011)Q.L.acknowledges Guangzhou Basic and Applied Basic Research Project(Grant No.2023A04J0018)Z.L.acknowledges the support of fund-ing from Chinese Academy of Sciences E1Z1D10200 and E2Z2D10200from ZJ project 2021QN02X159 and from JSPS(Grant Nos.PE14052 and P16027)We gratefully ac-knowledge HZWTECH for providing computation facilities.Z.-X.H.was supported by the National Natural Science Foun-dation of China(Grant Nos.11974064 and 12147102)the Fundamental Research Funds for the Central Universities(Grant No.2020CDJQY-Z003).
文摘We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder.To achieve this,we introduce a method to generate random on-site energies with prescribed correlations.We verify this method with a one-dimensional(1D)cross-stitch model,and find good agreement with analytical results obtained from the disorder-dressed evolution equations.This allows us to reproduce previous findings,that disorder can mobilize 1D flat-band states which would otherwise remain localized.As explained by the corresponding disorder-dressed evolution equations,such mobilization requires an asymmetric disorder-induced coupling to dispersive bands,a condition that is generically not fulfilled when the flat-band is resonant with the dispersive bands at a Dirac point-like crossing.We exemplify this with the 1D Lieb lattice.While analytical expressions are not available for the two-dimensional(2D)system due to its complexity,we extend the numerical method to the 2D a–T3 model,and find that the initial flat-band wave packet preserves its localization when a=0,regardless of disorder and intersections.However,when a̸=0,the wave packet shifts in real space.We interpret this as a Berry phase controlled,disorder-induced wave-packet mobilization.In addition,we present density functional theory calculations of candidate materials,specifically Hg1−xCdxTe.The flat-band emerges near the G point(α=0)in the Brillouin zone.
基金supported in part by the National Natural Science Foundation of China,No.61361160415,81271684,81501570the Major State Basic Research Development of China(973 Program),No.2011CB013304+1 种基金the Medicine-Engineering Interdisciplinary Research Grant from Shanghai Jiao Tong University in China,No.YG2014ZD09a grant from the Youth Eastern Scholar Program at Shanghai Institutions of Higher Learning in China,No.QD2015007
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12075040,11875231,11974064,and 12047564)the Chongqing Research Program of Basic Research and Frontier Technology(Grant No.cstc2020jcyj-msxmX0890).
文摘We introduce a generalized Rashba coupling approximation to analytically solve confined two-dimensional electron systems with both the Rashba and Dresselhaus spin–orbit couplings in an external magnetic field.A solvable Hamiltonian is obtained by performing a simple change of basis,which has the same form as that with only Rashba coupling.Each Landau state becomes a new displaced-Fock state instead of the original Harmonic oscillator Fock state.Analytical energies are consistent with the numerical ones in a wide range of coupling strength even for a strong Zeeman splitting,exhibiting the validity of the analytical approximation.By using the eigenstates,spin polarization correctly displays a jump at the energy-level crossing point,where the corresponding spin conductance exhibits a pronounced resonant peak.As the component of the Dresselhaus coupling increases,the resonant point shifts to a smaller value of the magnetic field.In contrast to pure Rashba couplings,we find that the Dresselhaus coupling and Zeeman splittings tend to suppress the resonant spin Hall effect.Our method provides an easy-to-implement analytical treatment to two-dimensional electron gas systems with both types of spin–orbit couplings by applying a magnetic field.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674041,91630205,11474144,and 11847301)Chongqing Research Program of Basic Research and Frontier Technology(Grant No.cstc2017jcyjAX0084)FRF for the Central Universities(Grant No.2019CDJDWL0005)
文摘For the numerical simulation of the fractional quantum Hall(FQH) effects on a finite disk, the rotational symmetry is the only symmetry that is used in diagonalizing the Hamiltonian. In this work, we propose a method of using the weak translational symmetry for the center of mass of the many-body system. With this approach, the bulk properties, such as the energy gap and the magneto-roton excitation are consistent with those in the closed manifolds like the sphere and torus. As an application, we consider the FQH phase and its phase transition in the fast rotated dipolar fermions. We thus demonstrate the disk geometry having versatility in analyzing the bulk properties beside the usual edge physics.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674041 and 91630205)Chongqing Research Program for Basic Research and Frontier Technology(Grant No.cstc2017jcyj AX0084)
文摘By exactly solving the effective two-body interaction for a two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that the effective interaction can be described by the generalized pseudopoten- tials （PPs） without the rotational symmetry. With this pseudopotential description, we numerically investigate the behavior of the fractional quantum Hall （FQH） states both in the lowest Landau level （LLL） and first excited Landau level （1LL）. The enhancements of the 7/3 FQH state on the 1LL for a small tilted magnetic field are observed when layer thickness is larger than some critical values, while the gap of the 1/3 state in the LLL monotonically reduced with increasing the in-plane field. From the static structure factor calculation, we find that the systems are strongly anisotropic and finally enter into a stripe phase with a large tilting. With considering the Landau level mixing correction on the two-body interaction, we find the strong LL mixing cancels the enhancements of the FQH states in the 1LL.
