Quantum integrability and chaos in a periodic Toda lattice with balanced loss-gain.

We consider an equal-mass quantum Toda lattice with balanced loss-gain for two and three particles. The two-particle Toda lattice is integrable, and two integrals of motion that are in involution have been found. The bound-state energy and the corresponding eigenfunctions have been obtained numerically for a few low-lying states. The three-particle quantum Toda lattice with balanced loss-gain and velocity-mediated coupling admits mixed phases of integrability and chaos depending on the value of the loss-gain parameter. We have obtained analytic expressions for two integrals of motion that are in involution. Although an analytic expression for the third integral has not been found, the numerical investigation suggests integrability below a critical value of the loss-gain strength and chaos above this critical value. The level spacing distribution changes from the Wigner-Dyson to the Poisson distribution as the loss-gain parameter passes through this critical value and approaches zero. An identical behavior is seen in terms of the gap-ratio distribution of the energy levels. The existence of mixed phases of quantum integrability and chaos in the specified ranges of the loss-gain parameter has also been confirmed independently via the study of level repulsion and complexity in higher order excited states.

Coherent-interface-induced strain in large lattice-mismatched materials: A new approach for modeling Raman shift.

Strain engineering as one of the most powerful techniques for tuning optical and electronic properties of Ill-nitrides requires reliable methods for strain investigation. In this work, we reveal, that the linear model based on the experimental data limited to within a small range of biaxial strains (< 0.2%), which is widely used for the non-destructive Raman study of strain with nanometer-scale spatial resolution is not valid for the binary wurtzite-structure group-III nitrides GaN and AlN. Importantly, we found that the discrepancy between the experimental values of strain and those calculated via Raman spectroscopy increases as the strain in both GaN and AlN increases. Herein, a new model has been developed to describe the strain-induced Raman frequency shift in GaN and AlN for a wide range of biaxial strains (up to 2.5%). Finally, we proposed a new approach to correlate the Raman frequency shift and strain, which is based on the lattice coherency in the epitaxial layers of superlattice structures and can be used for a wide range of materials. Electronic Supplementary Material: Supplementary material (Table S1: Values of bulk phonon deformation potentials and elastic constants for GaN and AlN from each reference used in Table 1, Fig. S1: Lattice parameters of SL layers using Eq. (8), and Fig. S2: Raman mapping using Eq. (7)) is available in the online version of this article at 10.1007/s12274-021-3855-4.

Quantum phase transition in a pseudo-Hermitian Dicke model.

We show that a Dicke-type non-Hermitian Hamiltonian admits entirely real spectra by mapping it to the "dressed Dicke model" through a similarity transformation. We find a positive-definite metric in the Hilbert space of the non-Hermitian Hamiltonian so that the time evolution is unitary and allows a consistent quantum description. We then show that this non-Hermitian Hamiltonian describing nondissipative quantum processes undergoes quantum phase transition. The exactly solvable limit of the non-Hermitian Hamiltonian has also been discussed.

Level statistics of a pseudo-Hermitian Dicke model.

A non-Hermitian operator that is related to its adjoint through a similarity transformation is defined as a pseudo-Hermitian operator. We study the level statistics of a pseudo-Hermitian Dicke Hamiltonian that undergoes quantum phase transition (QPT). We find that the level-spacing distribution of this Hamiltonian near the integrable limit is close to Poisson distribution, while it is Wigner distribution for the ranges of the parameters for which the Hamiltonian is nonintegrable. We show that the assertion in the context of the standard Dicke model that QPT is a precursor to a change in the level statistics is not valid in general.

Calculated thickness dependent plasmonic properties of gold nanobars in the visible to near-infrared light regime.

Metallic, especially gold, nanostructures exhibit plasmonic behavior in the visible to near-infrared light range. In this study, we investigate optical enhancement and absorption of gold nanobars with different thicknesses for transverse and longitudinal polarizations using finite element method simulations. This study also reports on the discrepancy in the resonance wavelengths and optical enhancement of the sharp-corner and round-corner nanobars of constant length 100 nm and width 60 nm. The result shows that resonance amplitude and wavelength have strong dependences on the thickness of the nanostructure as well as the sharpness of the corners, which is significant since actual fabricated structure often have rounded corners. Primary resonance mode blue-shifts and broadens as the thickess increases due to decoupling of charge dipoles at the surface for both polarizations. The broadening effect is characterized by measuring the full width at half maximum of the spectra. We also present the surface charge distribution showing dipole mode oscillations at resonance frequency and multimode resonance indicating different oscillation directions of the surface charge based on the polarization direction of the field. Results of this work give insight for precisely tuning nanobar structures for sensing and other enhanced optical applications.

Symmetries and exact solutions of a class of nonlocal nonlinear Schrödinger equations with self-induced parity-time-symmetric potential.

A class of nonlocal nonlinear Schrödinger equations (NLSEs) is considered in an external potential with a space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization of a recently introduced integrable nonlocal NLSE with self-induced potential that is parity-time-symmetric in the corresponding stationary problem. Exact soliton solutions are obtained for the inhomogeneous and/or nonautonomous nonlocal NLSE by using similarity transformation, and the method is illustrated with a few examples. It is found that only those transformations are allowed for which the transformed spatial coordinate is odd under the parity transformation of the original one. It is shown that the nonlocal NLSE without the external potential and a (d+1)-dimensional generalization of it admits all the symmetries of the (d+1)-dimensional Schrödinger group. The conserved Noether charges associated with the time translation, dilatation, and special conformal transformation are shown to be real-valued in spite of being non-Hermitian. Finally, the dynamics of different moments are studied with an exact description of the time evolution of the "pseudowidth" of the wave packet for the special case in which the system admits a O(2,1) conformal symmetry.

A note on the topological insulator phase in non-Hermitian quantum systems.

Examples of non-Hermitian quantum systems admitting a topological insulator phase are presented in one, two and three space dimensions. All of these non-Hermitian Hamiltonians have entirely real bulk eigenvalues and unitarity is maintained with the introduction of appropriate inner products in the corresponding Hilbert spaces. The topological invariant characterizing a particular phase is shown to be identical for a non-Hermitian Hamiltonian and its Hermitian counterpart, to which it is related through a non-unitary similarity transformation. A classification scheme for topological insulator phases in pseudo-Hermitian quantum systems is suggested.