${ \mathcal P }{ \mathcal T }$-symmetry berry phases,topology and ${ \mathcal P }{ \mathcal T }$-symmetry breaking

We study the complex Berry phases in non-Hermitian systems with parity- and time-reversal $\left({ \mathcal P }{ \mathcal T }\right)$ symmetry. We investigate a kind of two-level system with ${ \mathcal P }{ \mathcal T }$ symmetry. We find that the real part of the the complex Berry phases have two quantized values and they are equal to either 0 or π, which originates from the topology of the Hermitian eigenstates. We also find that if we change the relative parameters of the Hamiltonian from the unbroken-${ \mathcal P }{ \mathcal T }$-symmetry phase to the broken-${ \mathcal P }{ \mathcal T }$-symmetry phase, the imaginary part of the complex Berry phases are divergent at the exceptional points. We exhibit two concrete examples in this work, one is a two-level toys model, which has nontrivial Berry phases; the other is the generalized Su–Schrieffer–Heeger (SSH) model that has physical loss and gain in every sublattice. Our results explicitly demonstrate the relation between complex Berry phases, topology and ${ \mathcal P }{ \mathcal T }$-symmetry breaking and enrich the field of the non-Hermitian physics.     

Effects of Quantum Fluctuations on $\mathcal{PT}$-Symmetric Solitons of a Trapped Bose Gas *

Considering the quantum fluctuation effects, the existence and stabilityof solitons in a Bose-Einstein condensate subjected in a $\mathcal{PT}$-symmetric potentialare discussed. Using the variational approach, we investigate how the quantum fluctuationaffects the self-localization and stability of the condensate with attractivetwo-body interactions. The results show that the quantum fluctuation dramaticallyinfluences the shape, width, and chemical potential of the condensate.Analytical variational computation also predicts there exists a positive critical quantumfluctuation strength $q_{c}$ with each fixed attractive two-body interaction $g_{0}$, if thequantum fluctuation strength $q_{0}$ is bigger than $q_{c}$, there is no bright solitonsolution existence. We also study the effects of the quantum fluctuations on the stabilityof solitons using the Vakhitov-Kolokolov (VK) stability criterion. A robust stable brightsoliton will always exist when the quantum fluctuation strength $q_{0}$ belongs tothe parameter regimes $q_{c}\geq q_{0}＞0$.     

Gap solitons of spin-orbit-coupled Bose-Einstein condensates in $\mathcal{PT}$ periodic potential

We numerically investigate the gap solitons in Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) in the parity-time ($\mathcal{PT}$)-symmetric periodic potential. We find that the depths and periods of the imaginary lattice have an important influence on the shape and stability of these single-peak gap solitons and double-peak gap solitons in the first band gap. The dynamics of these gap solitons are checked by the split-time-step Crank-Nicolson method. It is proved that the depths of the imaginary part of the $\mathcal{PT}$-symmetric periodic potential gradually increase, and the gap solitons become unstable. But the different periods of imaginary part hardly affect the stability of the gap solitons in the corresponding parameter interval.     

Geometry of time-dependent $\mathcal{PT}$-symmetric quantum mechanics

A new type of quantum theory known as time-dependent $\mathcal{PT}$-symmetric quantum mechanics has received much attention recently. It has a conceptually intriguing feature of equipping the Hilbert space of a $\mathcal{PT}$-symmetric system with a time-varying inner product. In this work, we explore the geometry of time-dependent $\mathcal{PT}$-symmetric quantum mechanics. We find that a geometric phase can emerge naturally from the cyclic evolution of a $\mathcal{PT}$-symmetric system, and further formulate a series of related differential-geometry concepts, including connection, curvature, parallel transport, metric tensor, and quantum geometric tensor. These findings constitute a useful, perhaps indispensible, tool to investigate geometric properties of $\mathcal{PT}$-symmetric systems with time-varying system's parameters. To exemplify the application of our findings, we show that the unconventional geometric phase [Phys. Rev. Lett. 91 187902 (2003)], which is the sum of a geometric phase and a dynamical phase proportional to the geometric phase, can be expressed as a single geometric phase unveiled in this work.     

One-dimensional $\mathcal{PT}$-symmetric acoustic heterostructure

The explorations of parity-time ($\mathcal{PT}$)-symmetric acoustics have resided at the frontier in physics, and the pre-existing accessing of exceptional points typically depends on Fabry-Perot resonances of the coupling interlayer sandwiched between balanced gain and loss components. Nevertheless, the concise $\mathcal{PT}$-symmetric acoustic heterostructure, eliminating extra interactions caused by the interlayer, has not been researched in depth. Here we derive the generalized unitary relation for one-dimensional (1D) $\mathcal{PT}$-symmetric heterostructure of arbitrary complexity, and demonstrate four disparate patterns of anisotropic transmission resonances (ATRs) accompanied by corresponding spontaneous phase transitions. As a special case of ATR, the occasional bidirectional transmission resonance reconsolidates the ATR frequencies that split when waves incident from opposite directions, whose spatial profiles distinguish from a unitary structure. The derived theoretical relation can serve as a predominant signature for the presence of $\mathcal{PT}$ symmetry and $\mathcal{PT}$-symmetry-breaking transition, which may provide substantial support for the development of prototype devices with asymmetric acoustic responses.     

PT symmetric Floquet topological phase in SSH model

We consider periodically modulated Su–Schrieffer–Heeger (SSH) model with gain and loss. This model, which can be realized with current technology in photonics using waveguides, allows us to study Floquet topological insulating phase. By using Floquet theory, we find the quasi-energy spectrum of this one dimensional PT symmetric topological insulator. We show that stable Floquet topological phase exists in our model provided that oscillation frequency is large and the non-Hermitian degree is below than a critical value.     

Effect of power-law nonlinearity on ${ \mathcal P }{ \mathcal T }$-symmetric optical system with fourth-order diffraction

Gaussian-type soliton solutions of the nonlinear Schrödinger (NLS) equation with fourth order dispersion, and power law nonlinearity in the novel parity-time (${ \mathcal P }{ \mathcal T }$)-symmetric quartic Gaussian potential are derived analytically and numerically. The exact analytical expressions of the solutions are obtained in the first two-dimensional (1D and 2D) power law NLS equations. By means of the linear stability analysis, the effect of power law nonlinearity on the stability of Gauss type solitons in different nonlinear media is carried out. Numerical investigations do confirm the stability of our soliton solutions in both focusing and defocusing cases, specially around the propagation parameters.     

$\mathcal{H}_{\infty }$ state estimation for Markov jump neural networks with transition probabilities subject to the persistent dwell-time switching rule

We investigate the problem of $\mathcal{H}_{\infty}$ state estimation for discrete-time Markov jump neural networks. The transition probabilities of the Markov chain are assumed to be piecewise time-varying, and the persistent dwell-time switching rule, as a more general switching rule, is adopted to describe this variation characteristic. Afterwards, based on the classical Lyapunov stability theory, a Lyapunov function is established, in which the information about the Markov jump feature of the system mode and the persistent dwell-time switching of the transition probabilities is considered simultaneously. Furthermore, via using the stochastic analysis method and some advanced matrix transformation techniques, some sufficient conditions are obtained such that the estimation error system is mean-square exponentially stable with an $\mathcal{H}_{\infty}$ performance level, from which the specific form of the estimator can be obtained. Finally, the rationality and effectiveness of the obtained results are verified by a numerical example.     

Phantom Cosmological Model with Observational Constraints in f(Q)$f(Q)$ Gravity

In this paper, the cosmological model of the Universe has been presented in $f(Q)$ gravity and the parameters are constrained from the cosmological data sets. At the beginning, a well motivated form of $f(Q)=\alpha +\beta Q^n$ has been employed, where α, β, and n are model parameters. The Hubble parameter is obtained in redshift with some algebraic manipulation from the considered form of $f(Q)$. Then it is parameterized with the recent $\text{Hubble}$ data and $\text{Pantheon}+\text{SHOES}$ data using Markov chain Monte Carlo analysis. The obtained model parameter values are validated with the baryon acoustic oscillation data set. A parametrization of the cosmographic parameters shows the early deceleration and late time acceleration with the transition at $z_{\mathrm{t}}\approx 0.75$. The $Om(z)$ diagnostics gives positive slope which shows that the model is in the phantom phase. Also the current age of the Universe has been obtained as, $t_0=13.85\text{Gyrs}$. Based on the present analysis, it indicates that the $f(Q)$ gravity may provide an alternative to dark energy for addressing the current cosmic acceleration.     

Thermoluminescence and optically stimulated luminescence disadvantages of α-Al2O3:C crystal grown by the temperature gradient technique

Recently, α-Al₂O₃:C crystal with highly sensitive thermoluminescence (TL) and optically stimulated luminescence (OSL) has been successfully grown by the temperature gradient technique. This paper investigates the heating rate dependence of TL sensitivity, light-induced fading of TL signals and thermal stability of OSL of α-Al₂O₃:C crystals. As the heating rate increases, the integral TL response decreases and the dosimetric glow peak shifts to higher temperatures in α-Al₂O₃:C crystals. Light-induced fading of TL increases with the irradiation dose, and TL response decreases as the exposure time increases, especially in the first 15 minutes. With the increasing intensity of the exposure light, the TL fading of α-Al₂O₃:C crystal increases sharply. The OSL response of as-grown α-Al₂O₃:C crystal is quite stable below 373 K and decreases sharply for higher temperatures.     

Ghost busting: Making sense of non-Hermitian Hamiltonians

The Lee model is an elementary quantum field theory in which mass, wave-function, and charge renormalization can be performed exactly. In early studies of this model in the 1950's it was found that there is a critical value of g ², the square of the renormalized coupling constant, above which g ₀ ² , the square of the unrenormalized coupling constant, is negative. For g ² larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. In this non-Hermitian regime a new state appears whose norm is negative. This state is called a ghost. It has always been thought that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a time-independent operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore, it has been shown that time evolution in such a theory is unitary. In this talk the C operator for the Lee model in the ghost regime is constructed in the V/Nθ sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum field theory for all values of g ². Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Investigation of isotope effects of dynamic properties for H(D) +OF reactions by the quasi-classical trajectory method

Quasi-classical trajectory (QCT) calculations are employed to study the dynamic properties for \mbox{H(D)} + \mbox{OF} reactions on the adiabatic potential energy surface (PES) of the \mbox{1}{ }^{3}\mbox{A}' triplet state. Obvious differences between the reaction probabilities for J = 0, integral cross sections for J \ne 0, branch ratios of the product and internuclear distances as well as product rotational alignments between the title reactions are found. These differences are attributed mainly to the different reduced masses of the reactants and the different zero-point energies (ZPEs) of the transition state.     

The effects of interstitial oxygen on superconducting electronic phases in strontium and oxygen co-doped La1.937Sr0.063CuO4＋δ

Strontium and oxygen co-doped La1.937Sr0.063CuO4＋δ superconductor with Tc≈ 40K, which is obtained by oxidizing strontium-doped starting ceramic sample La1.937Sr0.063CuO4 in NaC10 solution, is annealed under different conditions to allow interstitial oxygen to redistribute. The evolution of the intrinsic superconducting property with the oxygen redistribution is studied in detail by magnetic measurements in various fields. It is found that there occurs the electronic phase separation from the single superconducting phase with Tc ≈ 40 K into two coexisting superconducting states with values of Tc： 15 and 40K or of 15 and 35 K in this system, depending on annealing condition. Our results indicate that the 15, 35 and 40 K superconducting phases associated with the excess oxygen redistribution are all thermodynamically meta-stable intrinsic states in this Sr/O co-doped cuprate.     

Asymptotic solution for a class of sea-air oscillator model for El Nin^～o-southern oscillation

The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.     

Asymptotic solution of a sea--air oscillator for ENSO mechanism

The EI Ni\~{n}o/La Ni\~{n}a--Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific ocean--atmosphere interactions. In this paper, a class of coupled system of the ENSO mechanism is considered. Based on a class of oscillator of ENSO model, the asymptotic solution of a corresponding problem is studied by employing the approximate method. It is proved from the results that the perturbation method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere--ocean oscillation for the ENSO model.     

Deposition mechanism of nano-structured single-layered C36 film on a diamond （100） crystal plane

The Brenner-LJ potential is adopted to describe the interaction between C36 clusters and diamond surface, and the deposition mechanism of multi-C36 clusters on the diamond surface is also studied by using the method of molecular dynamics simulation. The simulation results show that the competition effects of two interactions, i.e. the interaction between cluster and cluster and the interaction between cluster and crystal plane, are studied, and then the influence of these competition effects on C36 cluster deposition is analysed. The finding is that when an incident energy is appropriately chosen, C36 clusters can be chemically adsorbed and deposited steadily on the diamond surface in the form of single-layer, and in the deposition process the multi-C36 clusters present a phenomenon of energy transmission. The experimental result shows that at a temperature of 300K, in order to deposit C36 clusters into a steady nanostructured single-layered film, the optimal incident energy is between 10 and 18 eV, if the incident energy is larger than 18 eV, the C36 clusters will be deposited into an island nano-structured film.     

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- PT\mathcal{PT} -symmetry

Non-Hermitian but -symmetrized spherically-separable Dirac and Schr?dinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H _r , H _θ , and H _φ play essential roles and offer some “user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian. Considering a -symmetrized H _φ , we have shown that the conventional Dirac (relativistic) and Schr?dinger (non-relativistic) energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction V(θ)≠0 in the descendant Hamiltonian H _θ would manifest a change in the angular θ-dependent part of the general solution too. Whilst some -symmetrized H _φ Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the -symmetric ones (here the non-Hermitian -symmetric Hamiltonians) are nicknamed as pseudo- -symmetric.     

Analysis of two-torus in a new four-dimensional autonomous system

In this paper, we report the dynamical behaviours of a four-dimenslonal autonomous continuous dissipative system analysed when the parameter is varied in the range we are interested in. The system changes its dynamical modes between periodic motion and quasiperiodic motion. Furthermore, the existence of two-torus is investigated numerically by means of Lyapunov exponents. By taking advantage of phase portraits and Poincaré sections, two types of the two-torus are observed and proved to have the structure of ring torus and horn torus, both of which are known to be the standard tori.     

Analysis of two-torus in a new four-dimensional autonomous system

In this paper, we report the dynamical behaviours of a four-dimensional autonomous continuous dissipative system analysed when the parameter is varied in the range we are interested in. The system changes its dynamical modes between periodic motion and quasiperiodic motion. Furthermore, the existence of two-torus is investigated numerically by means of Lyapunov exponents. By taking advantage of phase portraits and Poincar\'{e} sections, two types of the two-torus are observed and proved to have the structure of ring torus and horn torus, both of which are known to be the standard tori.     

Correspondence between classical dynamics and recurrence spectra of Rydberg hydrogen atom near a metal surface

The chaotic behaviours of the Rydberg hydrogen atom near a metal surface are presented. A numerical comparison of Poincare surfaces of section with recurrence spectra for a few selected scaled energies indicates the correspondence between classical motion and quantum properties of an excited electron. Both results demonstrate that the scaled energy dominates sensitively the dynamical properties of system. There exists a critical scaled energy εc, for ε 〈 εc, the system is near-integrable, and as the decrease of ε the spectrum is gradually rendered regular and finally turns into a pure Coulomb field situation. On the contrary, if ε 〉 εc, with the increase of ε, the system tends to be non-integrable, the ergodic motion in phase space presages that chaotic motion appears, and more and more electrons are adsorbed on the metal surface, thus the spectrum becomes gradually simple.