Subjects: Mathematics >> Statistics and Probability Subjects: Psychology >> Statistics in Psychology submitted time 2023-07-02
Abstract： Taking the goodness of fit test (Chi test) as an example, this paper attempts to calculate the Bayesian factor BF10 of n-fold Bernoulli test by the Excel software (using JASP software as the evidence). The results showed that in the range of 0.15-0.55 (the rate of samples which are all "true"), the calculated results of Excel were more accurate, and the differences between the two (Excel and JASP) were not statistically significant (P>0.3).
Peer Review Status:
Awaiting Review
Subjects: Optics >> Quantum optics submitted time 2023-02-25
Abstract： We study the open XXZ spin chain with a PT-symmetric non-Hermitian boundary field. We find an interaction-induced scale-free non-Hermitian skin effect by using the coordinate Bethe ansatz. The steady state and the ground state in the PT broken phase are constructed, and the formulas of their eigen-energies in the thermodynamic limit are obtained. The differences between the many-body scale-free states and the boundary string states are explored, and the transition between the two at isotropic point is investigated. We also discuss an experimental scheme to verify our results.
Peer Review Status:Awaiting Review
Subjects: Optics >> Quantum optics submitted time 2023-02-19
Abstract： The non-Hermitian skin effect dramatically reshapes the energy bands of non-Hermitian systems, meaning that the usual Bloch band theory is fundamentally inadequate as their characterization. The non-Bloch band theory, in which the concept of Brillouin zone is generalized, has been widely applied to investigate non-Hermitian systems in one spatial dimension. However, its generalization to higher dimensions has been challenging. Here, we develop a formulation of the non-Hermitian skin effect and non-Bloch band theory in arbitrary spatial dimensions, which is based on a natural geometrical object known as the amoeba. Our theory provides a general framework for studying non-Hermitian bands beyond one dimension. Key quantities of non-Hermitian bands, including the energy spectrum, eigenstates profiles, and the generalized Brillouin zone, can be efficiently obtained from this approach.
Peer Review Status:Awaiting Review
Subjects: Optics >> Quantum optics submitted time 2023-02-19
Abstract： The parity-time (PT) symmetry of a non-Hermitian Hamiltonian leads to real (complex) energy spectrum when the non-Hermiticity is below (above) a threshold. Recently, it has been demonstrated that the non-Hermitian skin effect generates a new type of PT symmetry, dubbed the non-Bloch PT symmetry, featuring unique properties such as high sensitivity to the boundary condition. Despite its relevance to a wide range of non-Hermitian lattice systems, a general theory is still lacking for this generic phenomenon even in one spatial dimension. Here, we uncover the geometric mechanism of non-Bloch PT symmetry and its breaking. We find that non-Bloch PT symmetry breaking occurs by the formation of cusps in the generalized Brillouin zone (GBZ). Based on this geometric understanding, we propose an exact formula that efficiently determines the breaking threshold. Finally, we predict a new type of spectral singularities associated with the symmetry breaking, dubbed non-Bloch van Hove singularities, whose physical mechanism fundamentally differs from their Hermitian counterparts.
Peer Review Status:Awaiting Review
Subjects: Optics >> Quantum optics submitted time 2023-02-19
Abstract： We show that a local non-Hermitian perturbation in a Hermitian lattice system generically induces scale-free localization for the continuous-spectrum eigenstates. Furthermore, when the local non-Hermitian perturbation enjoys parity-time (PT) symmetry, the PT symmetry breaking of continuous spectrum is always accompanied by the emergence of scale-free localization. This type of PT symmetry breaking is highly sensitive to boundary conditions: The continuous spectrum of a periodic system undergoes a PT symmetry breaking as long as the non-Hermitian perturbation is strong enough; however, the counterpart under open boundary condition allows PT symmetry breaking only when the band structure satisfies certain condition that we unveil here. We also obtain the precise energy window in which the PT symmetry breaking is possible. Our results uncover a generic boundary-induced non-Hermitian phenomenon, which has unexpected interplay with PT symmetry.
Peer Review Status:Awaiting Review
Subjects: Optics >> Quantum optics submitted time 2023-02-19
Abstract： Parity-time (PT)-symmetric Hamiltonians have widespread significance in non-Hermitian physics. A PT-symmetric Hamiltonian can exhibit distinct phases with either real or complex eigenspectrum, while the transition points in between, the so-called exceptional points, give rise to a host of critical behaviors that holds great promise for applications. For spatially periodic non-Hermitian systems, PT symmetries are commonly characterized and observed in line with the Bloch band theory, with exceptional points dwelling in the Brillouin zone. Here, in nonunitary quantum walks of single photons, we uncover a novel family of exceptional points beyond this common wisdom. These "non-Bloch exceptional points" originate from the accumulation of bulk eigenstates near boundaries, known as the non-Hermitian skin effect, and inhabit a generalized Brillouin zone. Our finding opens the avenue toward a generalized PT-symmetry framework, and reveals the intriguing interplay between PT symmetry and non-Hermitian skin effect.
Peer Review Status:Awaiting Review
Subjects: Optics >> Quantum optics submitted time 2023-02-19
Abstract： We unveil an unexpected non-Hermitian phenomenon, dubbed edge burst, in non-Hermitian quantum dynamics. Specifically, in a class of non-Hermitian quantum walk in periodic lattices with open boundary condition, an exceptionally large portion of loss occurs at the system boundary. The physical origin of this edge burst is found to be an interplay between two unique non-Hermitian phenomena: non-Hermitian skin effect and imaginary gap closing. Furthermore, we establish a universal bulk-edge scaling relation underlying the non-Hermitian edge burst. Our predictions are experimentally accessible in various non-Hermitian systems including quantum-optical and cold-atom platforms.
Peer Review Status:Awaiting Review
Subjects: Optics >> Quantum optics submitted time 2023-02-19
Abstract： Among the many far-reaching consequences of the potential existence of a magnetic monopole, it induces topological zero modes in the Dirac equation, which were derived by Jackiw and Rebbi 46 years ago and have been elusive ever since. Here, we show that the monopole and multi-monopole solutions can be constructed in the band theory by coupling the three-dimensional Dirac points in hedgehog spatial configurations through Dirac-mass engineering. We then experimentally demonstrate such a monopole bound state in a structurally-modulated acoustic crystal as a cavity device. These monopole resonators not only support an arbitrary number of degenerate mid-gap modes, but also offer the optimal single-mode behavior possible -- whose modal spacing is inversely proportional to the cubic root of the modal volume. Our work completes the kink-vortex-monopole trilogy of zero modes and provides the largest free spectral range for sizable resonators.
Peer Review Status:Awaiting Review
Subjects: Optics >> Quantum optics submitted time 2023-02-19
Abstract： Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is complicated by the high sensitivity of energy spectrums to boundary conditions, which invalidates the straightforward generalization of Hermitian formulas. Here, based on the non-Bloch band theory, we obtain simple Green's function formulas of general one-dimensional non-Hermitian bands. Furthermore, in the large-size limit, these formulas dramatically reduce to finding the roots of a simple algebraic equation. As an application, our formulation provides the desirable formulas for the defining quantities, the gain and directionality, of directional amplification. Thus, our formulas provide an efficient guide for designing directional amplifiers.
Peer Review Status:Awaiting Review
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