One-dimensional L{é}vy Quasicrystal
arXiv:2210.10772 · doi:10.1088/1361-648X/acf9d4
Abstract
Space-fractional quantum mechanics (SFQM) is a generalization of the standard quantum mechanics when the Brownian trajectories in Feynman path integrals are replaced by L{é}vy flights. We introduce L{é}vy quasicrystal by discretizing the space-fractional Schrdinger equation using the Grnwald-Letnikov derivatives and adding on-site quasiperiodic potential. The discretized version of the usual Schrdinger equation maps to the Aubry-Andr{é} Hamiltonian, which supports localization-delocalization transition even in one dimension. We find the similarities between L{é}vy quasicrystal and the Aubry-Andr{é} (AA) model with power-law hopping and show that the L{é}vy quasicrystal supports a delocalization-localization transition as one tunes the quasiperiodic potential strength and shows the coexistence of localized and delocalized states separated by mobility edge. Hence, a possible realization of SFQM in optical experiments should be a new experimental platform to test the predictions of AA models in the presence of power-law hopping.
arXiv comment12 pages, 10 figures
References in corpus (55)
- The scaling laws of human travel
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Many-body localization, thermalization, and entanglement
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- Fractional Quantum Mechanics and Levy Path Integrals
- Fractional Schrodinger equation
- Quantum thermalization through entanglement in an isolated many-body system
- Unbounded growth of entanglement in models of many-body localization
- Fractional Quantum Mechanics
- Observation of entanglement propagation in a quantum many-body system
- Non-local propagation of correlations in long-range interacting quantum systems
- Nearest neighbor tight binding models with an exact mobility edge in one dimension
- Many-body localization in one dimension as a dynamical renormalization group fixed point
- Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
- Exact results for anomalous transport in one dimensional Hamiltonian systems
- One-dimensional quasicrystals with power-law hopping
- Observation of tunable mobility edges in generalized Aubry-André lattices
- Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
- Simulating non-Hermitian quasicrystals with single-photon quantum walks
- Some properties of the one-dimensional Lévy crystal
- Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials
- Many body localization in the presence of a single particle mobility edge
- Engineering a flux-dependent mobility edge in disordered zigzag chains
- Experimental realisations of the fractional Schrödinger equation in the temporal domain
- Soliton dynamics in a fractional complex Ginzburg-Landau model
- One-dimensional solitons in fractional Schrödinger equation with a spatially modulated nonlinearity: nonlinear lattice
- One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential
- Anomalous transport in the Aubry-André-Harper model in isolated and open systems
- Symmetry breaking of spatial Kerr solitons in fractional dimension
- Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension
- Exact solution of a Levy walk model for anomalous heat transport
- Many-body localization in incommensurate models with a mobility edge
- Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
- Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
- Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities
- Current fluctuations for anharmonic chains in thermal equilibrium
- Anomalous transport through algebraically localized states in one-dimension
- Many-body mobility edges in a one-dimensional model of interacting fermions
- Non-Hermitian Aubry-André model with Power-Law Hopping
- Quadratic fractional solitons
- Many-body dynamics in long-range hopping model in the presence of correlated and uncorrelated disorder
- Stable and oscillating solitons of -symmetric couplers with gain and loss in fractional dimension
- Many Body Localization Due to Correlated Disorder in Fock Space
- Scaling of Fock-space propagator and multifractality across the many-body localization transition
- Many-body dynamical phase transition in quasi-periodic potential
- Eigenstate entanglement entropy in invariant non-Hermitian system
- Criterion for the occurrence of many body localization in the presence of a single particle mobility edge
- Bubbles and W-shaped solitons in Kerr media with fractional diffraction
- Fractional diffusion equation description of an open anomalous heat conduction set-up
- Tunneling time in space fractional quantum mechanics
- Fractional Schrödinger equation in gravitational optics
- Domain walls in fractional media
- Uncertainty Relation for Non-Hermitian Systems
- Quantum adiabatic protocols using emergent local Hamiltonians
- A 2D Levy-flight model for the complex dynamics of real-life financial markets