Theoretical study on martensitic-type transformation path from rutile phase to α-PbO2 phase of TiO2

The martensitic-type phase transformation paths from the rutile to theα-PbO2 phase of TiO2 are studied with linear interpolation and NEB/G-SSNEB methods based on first-principles calculations.Its potential energy surface and the lowest energy path are revealed.Our results indicate that the titanium atoms of the rutile phase shuffle along the[0-11]rut crystal direction to form theα-PbO2 phase.During the phase transition,the oxygen atoms are dragged by the heavier titanium atoms and then reach their new equilibrium positions.The barrier of phase transition from nudged elastic band theory is about 231 meV,which is qualitatively consistent with previous theoretical calculations from the monoclinic phase to the tetragonal phase for ZrO2 and HfO2.Debye model can also be successfully used to predict the pressure and temperature of the phase transformation.

Parametric instability in the pure-quartic nonlinear Schrödinger equation

We study the nonlinear stage of modulation instability(MI)in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically.Using the three-mode truncation,we reveal the complex recurrence of parametric resonance(PR)breathers,where each recurrence is associated with two oscillation periods(PR period and internal oscillation period).The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.

Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation

We show that the nonlinear stage of the dual-wavelength pumped modulation instability(MI)in nonlinear Schrödinger equation(NLSE)can be effectively analyzed by mode truncation methods.The resulting complicated heteroclinic structure of instability unveils all possible dynamic trajectories of nonlinear waves.Significantly,the latticed-Fermi-Pasta-Ulam recurrences on the modulated-wave background in NLSE are also investigated and their dynamic trajectories run along the Hamiltonian contours of the heteroclinic structure.It is demonstrated that there has much richer dynamic behavior,in contrast to the nonlinear waves reported before.This novel nonlinear wave promises to inject new vitality into the study of MI.

Thermal-contact capacity of one-dimensional attractive Gaudin-Yang model

Tan's contact C is an important quantity measuring the two-body correlations at short distances in a dilute system.Here we make use of the technique of exactly solved models to study the thermal-contact capacity K_(T),i.e.,the derivative of C with respect to temperature in the attractive Gaudin-Yang model.It is found that K_(T) is useful in identifying the low temperature phase diagram,and using the obtained analytical expression of K_(T),we study its critical behavior and the scaling law.Especially,we show K_(T) versus temperature and thus the non-monotonic tendency of C in a tiny interval,for both spin-balanced and imbalanced phases.Such a phenomenon is merely observed in multi-component systems such as SU(2)Fermi gases and spinor bosons,indicating the crossover from the Tomonaga-Luttinger liquid to the spin-coherent liquid.

Regulating the dopant clustering in LiZnAs-based diluted magnetic semiconductor

Tuning of the magnetic interaction plays the vital role in reducing the clustering of magnetic dopant in diluted magnetic semiconductors(DMS).Due to the not well understood magnetic mechanism and the interplay between different magnetic mechanisms,no efficient and universal tuning strategy is proposed at present.Here,the magnetic interactions and formation energies of isovalent-doped(Mn) and aliovalent(Cr)-doped LiZnAs are studied based on density functional theory(DFT).It is found that the dopant–dopant distance-dependent magnetic interaction is highly sensitive to the carrier concentration and carrier type and can only be explained by the interplay between two magnetic mechanisms,i.e.,superexchange and Zener’s p–d exchange model.Thus,the magnetic behavior and clustering of magnetic dopant can be tuned by the interplay between two magnetic mechanisms.The insensitivity of the tuning effect to U parameter suggests that our strategy could be universal to other DMS.

Inelastic Interaction of Double-Valley Dark Solitons for the Hirota Equation

For a scalar integrable model,it is generally believed that the solitons interact with each other elastically,for instance,multi-bright solitons from the nonlinear Schrodinger equation and the Korteweg-de Vries equation,etc.We obtain double-valley dark solitons from the defocusing Hirota equation by the Darboux transformation.Particularly,we report a remarkable phenomenon for the inelastic interaction of the double-valley dark solitons,in contrast to the solitons interacting with each other elastically for a scalar integrable model in previous works.Furthermore,we give the explicit conditions for the elastic collision based on the asymptotic analysis results.It is shown that the double-valley dark solitons could also admit elastic interaction under the special parameters settings.

Formation of Square-Shaped Waves in the Biscay Bay

Recently,a report from Elite Readers suggested that a strange phenomenon of ’square-shaped waves’ had occurred at the beaches of the Isle of Rhe in the Bay of Biscay.Based on the hydrological and geological data of the Bay of Biscay,we find that the special phenomenon is closely related to a solitary wave that can be described by the shallow water wave equation.We discuss the formation mechanisms of the square-shaped waves by the Kadomtsev-Petviashvili equation.The combination of exact solutions and actual condition provides the simulated initial state.We then reproduce a square-shaped structure by a numerical method and obtain the result consistent with the observed picture from media.Our work enriches public understanding of strange water waves and has great significance for tourism development and shipping transportation.

Theoretical study on order–disorder phase transition of CH3NH3PbCl3

Order–disorder phase transitions for CH3NH3PbCl3 are studied with density functional theory. Our calculations show that the disorder is manifested in two aspects in the cubic phase, namely, the disorder of orientation and rotation of organic groups. Organic groups of [CH3] and [NH3] in cubic crystals can easily rotate around its C3 axis. At the same time,[CH3NH3]^+ organic groups can also orient to different spatial directions due to the weak interactions between organic group and inorganic frame. Our results show that its possible phase transition path starts from the deviation of organic groups from the crystal c-axis. Its structural transition changes from disordered cubic phase to hydrogen-only disordered tetragonal structure in the process of decreasing symmetry. The disordered high temperature cubic phase can be expressed as a statistical average of substructures we rebuilt. The electrostatic repulsive force between adjacent organic groups triggers out the formation of low temperature phase on cooling.

EOM-CCSD-Based Neural Network Diabatic Potential Energy Matrix for ^(1)πσ^(*)-Mediated Photodissociation of Thiophenol

A new diabatic potential energy matrix(PEM)of the coupled~^(1)ππ^(*)and~1πσ*states for the~1πσ*-mediated photodissociation of thiophenol was constructed using a neural network(NN)approach.The diabatization of the PEM was specifically achieved by our recent method[Chin.J.Chem.Phys.34,825(2021)],which was based on adiabatic energies without the associated costly derivative couplings.The equation of motion coupled cluster with single and double excitations(EOM-CCSD)method was employed to compute adiabatic energies of two excited states in this work due to its high accuracy,simplicity,and efficiency.The PEM includes three dimensionalities,namely the S-H stretch,C-S-H bend,and C-C-S-H torsional coordinates.The root mean square errors of the NN fitting for the S1 and S2 states are 0.89 and 1.33 me V,respectively,suggesting the high accuracy of the NN method as expected.The calculated lifetimes of the S1 vibronic 00 and31 states are found to be in reasonably good agreement with available theoretical and experimental results,which validates the new EOM-CCSD-based PEM fitted by the NN approach.The combination of the diabatization scheme solely based on the adiabatic energies and the use of EOM-CCSD method makes the construction of reliable diabatic PEM quite simple and efficient.

The application of quantum coherence as a resource

Quantum coherence is a basic concept in quantum mechanics, representing one of the most fundamental characteristics that distinguishes quantum mechanics from classical physics. Quantum coherence is the basis for multi-particle interference and quantum entanglement. It is also the essential ingredient for various physical phenomena in quantum optics, quantum information, etc. In recent years, with the proposal of a quantum coherence measurement scheme based on a resource theory framework, quantum coherence as a quantum resource has been extensively investigated. This article reviews the resource theories of quantum coherence and introduces the important applications of quantum coherence in quantum computing,quantum information, and interdisciplinary fields, particularly in quantum thermodynamics and quantum biology. Quantum coherence and its applications are still being explored and developed. We hope this review can provide inspiration for relevant research.

Straight and twisted Weyl nodal line phonons in Ho2CF2 material

Based on first-principles calculations, symmetry analysis and model construction, we predict that Ho2CF2hosts both straight and twisted Weyl nodal lines in its bulk phonon spectrum. We identify that the top two phonon bands entangle with each other, forming two straight Weyl nodal lines on the K–H and K′–H′paths at the Brillouin zone(BZ) boundary,and six twisted Weyl nodal lines within the BZ. All the Weyl nodal lines along the kz direction and across the entire BZ.The symmetry analysis indicates that these Weyl nodal lines are protected by the PT symmetry and crystal symmetry. The Berry phase and drumhead-like nontrivial surface states are calculated. We also construct a tight-binding model to describe these nodal lines. Our work provides an excellent material platform for exploring the fascinating physics associated with straight and twisted Weyl nodal line phonons.

Low-lying electronic states of osmium monoxide OsO

The ground state of osmium monoxide(OsO) has long been controversial. In this paper, the low-lying Λ–S and ? electronic states of OsO have been comprehensively studied by the high-precision multi-reference calculations. The ground state of OsO is unexpectedly the closed-shell1Σ+state with a double bond instead of the previously reported3Φ or5Σ+state;after including the spin–orbit coupling effects, the ground state becomes3Π2. With the help of the theoretical spectroscopic constants and transition dipole moments, the emission spectra in the region of 405 nm–875 nm are assigned.Our results will facilitate the future studies of absorption and emission spectra of OsO.

Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

The U(1)symmetry of the X X Z central spin model with an arbitrary central magnetic field B is broken,since its total spin in the z-direction is not conserved.We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method.The thermodynamic limit is investigated based on the solutions.We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N^(-1)scaling law,where N is the total number of spins.This result makes it possible to investigate the properties of the system in the thermodynamic limit.By assuming the structural form of the Bethe roots in the thermodynamic limit,we obtain the contribution of the direction of B to the ground state energy.It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit.This is the phenomenon caused by the U(1)symmetry breaking of the system.

Special breathing structures induced by bright solitons collision in a binary dipolar Bose–Einstein condensates

We numerically investigate the breathing dynamics induced by collision between bright solitons in a binary dipolar Bose–Einstein condensates, whose dipole–dipole interaction and contact interaction are attractive. We identify three special breathing structures, such as snakelike special breathing structure, mixed breathing structure, and divide breathing structure.The characteristics of these breathing structures can be described by breathing frequency ?, maximum breathing amplitude A and lifetime τ, which can be manipulated by atomic number Ni and interspecies scattering length a12. Meanwhile, the above breathing structures can realize the process of quasi-transition with a reasonable Ni and a12. Additionally, the collision of two special breathing structures also can bring more abundant breathing dynamics. Our results provide a reference for the study of soliton interactions and deepen the understanding of soliton properties in a binary dipolar Bose–Einstein condensates.

Off-diagonal approach to the exact solution of quantum integrable systems

We investigate the t–W scheme for the anti-ferromagnetic X X X spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of the transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated W operator(see Eqs.(10) and(70)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of W operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation(the t–W relation without the W-term) can be used to study the ground state properties of quantum integrable systems with/without U(1)-symmetry in the thermodynamic limit.

Exact surface energy and elementary excitations of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields

We study the physical properties of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields. By using a combination of numerical analysis and analytical method, we obtain the surface energy and elementary excitations of the model. It shows that the contributions of the two boundary fields to the surface energy are additive. We also find that there exists a kind of excitations related to the boundary string.

Thermodynamic phase transition and winding number for the third-order Lovelock black hole

Phase transition is important for understanding the nature and evolution of the black hole thermodynamic system.In this study,we predicted the phase transition of the third-order Lovelock black hole using the winding numbers in complex analysis,and qualitatively validated this prediction by the generalized free energy.For the 7<d<12-dimensional black holes in hyperbolic topology and the 7-dimensional black hole in spherical topology,the winding number obtained is three,which indicates that the system undergoes first-order and second-order phase transitions.For the 7<d<12-dimensional black holes in spherical topology,the winding number is four,and two scenarios of phase transitions exist,one involving a purely second-order phase transition and the other involving simultaneous first-order and second-order phase transitions.This result further deepens the research on black hole phase transitions using the complex analysis.

Modulation Instability and Non-Degenerate Akhmediev Breathers of Manakov Equations

We reveal a special subset of non-degenerate Akhmediev breather(AB)solutions of Manakov equations that only exist in the focusing case.Based on exact solutions,we present the existence diagram of such excitations on the frequency-wavenumber plane.Conventional single-frequency modulation instability leads to simultaneous excitation of three ABs with two of them being non-degenerate.

Quench Dynamics of Bose–Einstein Condensates in Boxlike Traps

By quenching the interatomic interactions, we investigate the nonequilibrium dynamics of two-dimensional Bose–Einstein condensates in boxlike traps with power-law potential boundaries. We show that ring dark solitons can be excited during the quench dynamics for both concave and convex potentials. The quench's modulation strength and the steepness of the boundary are two major factors influencing the system's evolution. In terms of the number of ring dark solitons excited in the condensate, five dynamic regimes have been identified. The condensate undergoes damped radius oscillation in the absence of ring dark soliton excitations. When it comes to the appearance of ring dark solitons, their decay produces interesting structures. The excitation patterns for the concave potential show a nested structure of vortex-antivortex pairs. The dynamic excitation patterns for the convex potential, on the other hand, show richer structures with multiple transport behaviors.

Solitons in nonlinear systems and eigen-states in quantum wells

We study the relations between solitons of nonlinear Schro¨dinger equation and eigen-states of linear Schro¨dinger equation with some quantum wells. Many different non-degenerated solitons are re-derived from the eigen-states in the quantum wells. We show that the vector solitons for the coupled system with attractive interactions correspond to the identical eigen-states with the ones of the coupled systems with repulsive interactions. Although their energy eigenvalues seem to be different, they can be reduced to identical ones in the same quantum wells. The non-degenerated solitons for multi-component systems can be used to construct much abundant degenerated solitons in more components coupled cases.Meanwhile, we demonstrate that soliton solutions in nonlinear systems can also be used to solve the eigen-problems of quantum wells. As an example, we present the eigenvalue and eigen-state in a complicated quantum well for which the Hamiltonian belongs to the non-Hermitian Hamiltonian having parity–time symmetry. We further present the ground state and the first exited state in an asymmetric quantum double-well from asymmetric solitons. Based on these results, we expect that many nonlinear physical systems can be used to observe the quantum states evolution of quantum wells, such as a water wave tank, nonlinear fiber, Bose–Einstein condensate, and even plasma, although some of them are classical physical systems. These relations provide another way to understand the stability of solitons in nonlinear Schro¨dinger equation described systems, in contrast to the balance between dispersion and nonlinearity.