We introduce a method for computing the Helmholtz free energy using the flow matching technique. Unlike previous work that utilized flow-based models for variational free energy calculations, this method provides bounds for free energy estimation based on targeted free energy perturbation by performing calculations on samples from both ends of the mapping. We demonstrate applications of the present method by estimating the free energy of a classical Coulomb gas in a harmonic trap.

The $b$-family fifth-order Camassa–Holm model is a nontrivial extension of the celebrated Camassa–Holm model. This work investigates single-pseudo and multi-pseudo peakon solutions of this model via analytical calculations and numerical simulations. Some intriguing phenomena of multi-pseudo peakon which do not appear in the classical Camassa–Holm model interactions are observed, such as two-pseudo peakon collapses, three-pseudo peakon resonance, and multi-pseudo peakon inelastic collisions. The present work will inspire further studies on the higher-dimensional integrable Camassa–Holm systems which may have high value in investigating the related higher-dimensional physical problems.

We calculate the entropy of spherically symmetric regular black holes by the path-integral method in Einstein's gravity. This method provides evidence that the entropy of spherically symmetric regular black holes is proportional to a quarter of horizon area, indicating no violation of the entropy-area law.

We introduce a new form of the Painlevé integrable (3+1)-dimensional combined potential Kadomtsev–Petviashvili equation incorporating the B-type Kadomtsev–Petviashvili equation (pKP–BKP equation). We perform the Painlevé analysis to emphasize the complete integrability of this new (3+1)-dimensional combined integrable equation. We formally derive multiple soliton solutions via employing the simplified Hirota bilinear method. Moreover, a variety of lump solutions are determined. We also develop two new (3+1)-dimensional pKP–BKP equations via deleting some terms from the original form of the combined pKP–BKP equation. We emphasize the Painlevé integrability of the newly developed equations, where multiple soliton solutions and lump solutions are derived as well. The derived solutions for all examined models are all depicted through Maple software.

In the past 20 years, many new hadrons that are difficult to explain within the conventional quark model have been discovered in the quarkonium region; these are called exotic hadrons. The Belle II experiment, as the next-generation $B$ factory, provides a good platform for exploring them. The charmonium-like states can be produced at Belle II in several ways, such as $B$ meson decays, initial-state radiation processes, two-photon collisions and double charmonium production. Bottomonium-like states can be produced directly in $e^+e^-$ colliding energies at Belle II with low continuum backgrounds. Belle II plans to perform a high-statistics energy scan from the $B\bar B$ threshold up to the highest possible energy of 11.24 GeV to search for new $Y_b$ states with $J^{\scriptscriptstyle{\rm PC}}$ = $1^{--}$, $X_b$ [the bottom counterpart of $\chi_{c1}(3872)$, also known as $X(3872)$] and partners of $Z_b$ states. We give a mini-review on the status and prospects of exotic hadrons at Belle II.

In recent years, machine learning (ML) techniques have emerged as powerful tools for studying many-body complex systems, and encompassing phase transitions in various domains of physics. This mini review provides a concise yet comprehensive examination of the advancements achieved in applying ML to investigate phase transitions, with a primary focus on those involved in nuclear matter studies.

We investigate the harmonic emission from bichromatic periodic potential by numerically solving the time-dependent Schrödinger equation in the velocity gauge. The results show that the harmonic minimum is sensitive to the wavelength. Moreover, distinct crystal momentum states contribute differently to harmonic generation. In momentum space, the electron dynamics reveal a close relationship between the spectral minimum and the electron distribution in higher conduction bands. Additionally, by introducing an ultraviolet pulse to the fundamental laser field, the suppression of the harmonic minimum occurs as a result of heightened electron populations in higher conduction bands. This work sheds light on the harmonic emission originating from a solid with a two-atom basis.

Tungsten sulphoselenide (WSSe) alloys, belonging to the transition metal dichalcogenide family, have attracted significant interest in the area of optoelectronics because of their unique optical and electronic properties. However, there has been a dearth of sufficient research on the saturable absorption features and ultrafast lasers applications. Herein, we fabricated a WSSe-microfiber saturable absorber (SA) based on WSSe nanosheets prepared by liquid exfoliation technique. The SA provided a saturation intensity of a modulation depth of 27.95% and a nonsaturable loss of 21.34%. To investigate the potential applications of WSSe in ultrafast photonics, the prepared WSSe-microfiber was incorporated into an Er-doped fiber laser ring cavity. The results demonstrated that the WSSe-based SA successfully generated mode-locking laser pulses with a remarkably short pulse width of 231 fs. Furthermore, the output power of this ultrafast fiber laser reached an impressive value of 15.68 mW. These findings provide valuable views into the unique features of WSSe alloys in the areas of ultrafast optics and develop recipes for SA in ultrafast fiber lasers.

Interactions among optical solitons can be used to develop photonic information processing devices such as all-optical switches and all-optical logic gates. It is the key to achieve high-speed, high-capacity all-optical networks and optical computers, which is also important in academy. We study the properties of all-optical switches of optical solitons in birefringent fibers, based on the coupled nonlinear Schrödinger equations. It is found that under different initial conditions we can achieve all-optical switching functions. We also study the influence of different physical parameters of birefringent fibers on all-optical soliton switching. The relevant conclusions are conducive to achieving the all-optical switching function of optical solitons in birefringent fibers, providing useful guidance for widespread applications of optical soliton all-optical switches in birefringent fibers of communications.

We demonstrate a method to realize unidirectional negative refraction in an acoustic parity-time ($PT$)-symmetric system, which is composed of a pair of metasurfaces sandwiching an air gap. The pair of metasurfaces possesses loss and gain modulations. The unidirectional negative refraction, which is strictly limited to the case of incident wave imposing on the loss end of the metasurface, is demonstrated at the exception point (EP) in this $PT$-symmetric system, while the incidence from the other side leads to strong reflection. Based on rigorous calculations, we explicitly show the underlying mechanism of this model to achieve unidirectional wave scatterings around the EP in the parametric space. In addition, the perfect imaging of a point source in the three-dimensional space, as a signature of negative refraction, is simulated to provide a verification of our work. We envision that this work may sharpen the understanding of $PT$-symmetric structures and inspire more acoustic functional devices.

Introducing porosity with different degrees of disorder has been widely used to regulate thermal properties of materials, which generally results in decrease of thermal conductivity. We investigate the thermal conductivity of porous metamaterials in the ballistic transport region by using the Lorentz gas model. It is found that the introduction of asymmetry and Gaussian disorder into porous metamaterials can lead to a strong enhancement of thermal conductivity. By dividing the transport process into ballistic transport, non-ballistic transport, and unsuccessful transport processes, we find that the enhancement of thermal conductivity originates from the significant increase ballistic transport ratio. The findings enhance the understanding of ballistic thermal transport in porous materials and may facilitate designs of high-performance porous thermal metamaterials.

Predicting thermal conductance of complex networks poses a formidable challenge in the field of materials science and engineering. This challenge arises due to the intricate interplay between the parameters of network structure and thermal conductance, encompassing connectivity, network topology, network geometry, node inhomogeneity, and others. Our understanding of how these parameters specifically influence heat transfer performance remains limited. Deep learning offers a promising approach for addressing such complex problems. We find that the well-established convolutional neural network models AlexNet can predict the thermal conductance of complex network efficiently. Our approach further optimizes the calculation efficiency by reducing the image recognition in consideration that the thermal transfer is inherently encoded within the Laplacian matrix. Intriguingly, our findings reveal that adopting a simpler convolutional neural network architecture can achieve a comparable prediction accuracy while requiring less computational time. This result facilitates a more efficient solution for predicting the thermal conductance of complex networks and serves as a reference for machine learning algorithm in related domains.

Auxetic two-dimensional (2D) materials, known from their negative Poisson's ratios (NPRs), exhibit the unique property of expanding (contracting) longitudinally while being laterally stretched (compressed), contrary to typical materials. These materials offer improved mechanical characteristics and hold great potential for applications in nanoscale devices such as sensors, electronic skins, and tissue engineering. Despite their promising attributes, the availability of 2D materials with NPRs is limited, as most 2D layered materials possess positive Poisson's ratios. In this study, we employ first-principles high-throughput calculations to systematically explore Poisson's ratios of 40 commonly used 2D monolayer materials, along with various bilayer structures. Our investigation reveals that BP, GeS and GeSe exhibit out-of-plane NPRs due to their hinge-like puckered structures. For 1T-type transition metal dichalcogenides such as $MX_{2}$ ($M$ = Mo, W; $X$ = S, Se, Te) and transition metal selenides/halides the auxetic behavior stems from a combination of geometric and electronic structural factors. Notably, our findings unveil V$_{2}$O$_{5}$ as a novel material with out-of-plane NPR. This behavior arises primarily from the outward movement of the outermost oxygen atoms triggered by the relaxation of strain energy under uniaxial tensile strain along one of the in-plane directions. Furthermore, our computations demonstrate that Poisson's ratio can be tuned by varying the bilayer structure with distinct stacking modes attributed to interlayer coupling disparities. These results not only furnish valuable insights into designing 2D materials with a controllable NPR but also introduce V$_{2}$O$_{5}$ as an exciting addition to the realm of auxetic 2D materials, holding promise for diverse nanoscale applications.

Machine learning opens up new possibilities for research of plasma confinement. Specifically, models constructed using machine learning algorithms may effectively simplify the simulation process. Previous first-principles simulations could provide physics-based transport information, but not fast enough for real-time applications or plasma control. To address this issue, this study proposes SExFC, a surrogate model of the Gyro-Landau Extended Fluid Code (ExFC). As an extended version of our previous model ExFC-NN, SExFC can capture more features of transport driven by the ion temperature gradient mode and trapped electron mode, using an extended database initially generated with ExFC simulations. In addition to predicting the dominant instability, radially averaged fluxes and radial profiles of fluxes, the well-trained SExFC may also be suitable for physics-based rapid predictions that can be considered in real-time plasma control systems in the future.

In a Dirac semimetal, the massless Dirac fermion has zero chirality, leading to surface states connected adiabatically to a topologically trivial surface state as well as vanishing anomalous Hall effect. Recently, it is predicted that in the nonrelativistic limit of certain collinear antiferromagnets, there exists a type of chiral “Dirac-like” fermion, whose dispersion manifests four-fold degenerate crossing points formed by spin-degenerate linear bands, with topologically protected Fermi arcs. Such an unconventional chiral fermion, protected by a hidden $SU(2)$ symmetry in the hierarchy of an enhanced crystallographic group, namely spin space group, is not experimentally verified yet. Here, by angle-resolved photoemission spectroscopy measurements, we reveal the surface origin of the electron pocket at the Fermi surface in collinear antiferromagnet CoNb$_{3}$S$_{6}$. Combining with neutron diffraction and first-principles calculations, we suggest a multidomain collinear antiferromagnetic configuration, rendering the existence of the Fermi-arc surface states induced by chiral Dirac-like fermions. Our work provides spectral evidence of the chiral Dirac-like fermion caused by particular spin symmetry in CoNb$_{3}$S$_{6}$, paving an avenue for exploring new emergent phenomena in antiferromagnets with unconventional quasiparticle excitations.

Using ab initio nonadiabatic molecular dynamics simulation, we study the time-dependent charge transport dynamics in a single-molecule junction formed by gold (Au) electrodes and a single benzene-1,4-dithiol (BDT) molecule. Two different types of charge transport channels are found in the simulation. One is the routine non-resonant charge transfer path, which occurs in several picoseconds. The other is activated when the electronic state of the electrodes and that of the molecule get close in energy, which is referred to as the resonant charge transport. More strikingly, the resonant charge transfer occurs in an ultrafast manner within 100 fs, which notably increases the conductance of the device. Further analysis shows that the resonant charge transport is directly assisted by the $B_{2}$ and $A_{1}$ molecular vibration modes. Our study provides atomic insights into the time-dependent charge transport dynamics in single-molecule junctions, which is important for designing highly efficient single-molecule devices.

Memory can remarkably modify the collective behavior of active particles. We show that, in a micellar fluid, Quincke particles driven by a square-wave electric field exhibit a frequency-dependent memory. Upon increasing the frequency, a memory of directions emerges, whereas the activity of particles decreases. As the activity is dominated by interaction, Quincke particles aggregate and form dense clusters, in which the memory of the direction is further enhanced due to the stronger electric interactions. The density-dependent memory and activity result in dynamic heterogeneity in flocking and offer a new opportunity for research of collective motions.

An active system consisting of many self-spinning dimers is simulated, and a distinct local rotational jamming transition is observed as the density increases. In the low density regime, the system stays in an absorbing state, in which each dimer rotates independently subject to the applied torque; while in the high density regime, a fraction of the dimers become rotationally jammed into local clusters, and the system exhibits microphase-separation like two-phase morphologies. For high enough densities, the system becomes completely jammed in both rotational and translational degrees of freedom. Such a simple system is found to exhibit rich and multiscale disordered hyperuniformities among the above phases: the absorbing state shows a critical hyperuniformity of the strongest class and subcritically preserves the vanishing density fluctuation scaling up to some length scale; the locally jammed state shows a two-phase hyperuniformity conversely beyond some length scale with respect to the phase cluster sizes; the totally jammed state appears to be a monomer crystal, but intrinsically loses large-scale hyperuniformity. These results are inspiring for designing novel phase-separation and disordered hyperuniform systems through dynamical organization.

The quantum spin liquid (QSL) state of Kitaev-like materials, such as iridium oxides $A_2$IrO$_3$ and $\alpha$-RuCl$_3$, has been explored in depth. The half-filled Kitaev–Hubbard model with bond-dependent hopping terms is used to describe the Kitaev-like materials, which is calculated using the state-of-the-art fermionic projected entangled pair states method. We find a QSL phase near the Mott insulator transition, which has a strong first-order transition to the semi-metal phase with the decrease of Hubbard $U$. We suggest that a promising approach to finding QSL states is by finding iridium oxides that are near the Mott insulator transition.

The $k\!\cdot\! p$ method is significant in condensed matter physics for the compact and analytical Hamiltonian. In the presence of magnetic field, it is described by the effective Zeeman's coupling Hamiltonian with Landé $g$-factors. Here, we develop an open-source package VASP2KP (including two parts: vasp2mat and mat2kp) to compute $k\!\cdot\! p$ parameters and Landé $g$-factors directly from the wavefunctions provided by the density functional theory (DFT) as implemented in Vienna ab initio Simulation Package (VASP). First, we develop a VASP patch vasp2mat to compute matrix representations of the generalized momentum operator $\hat{\boldsymbol \pi}=\hat{\boldsymbol p}+\frac{1}{2mc^2}[\hat{{\boldsymbol s}}\times\nabla V({\boldsymbol r})]$, spin operator $\hat{\boldsymbol s}$, time reversal operator $\hat{T}$, and crystalline symmetry operators $\hat{R}$ on the DFT wavefunctions. Second, we develop a python code mat2kp to obtain the unitary transformation $U$ that rotates the degenerate DFT basis towards the standard basis, and then automatically compute the $k\!\cdot\! p$ parameters and $g$-factors. The theory and the methodology behind VASP2KP are described in detail. The matrix elements of the operators are derived comprehensively and computed correctly within the projector augmented wave method. We apply this package to some materials, e.g., Bi$_2$Se$_3$, Na$_3$Bi, Te, InAs and 1H-TMD monolayers. The obtained effective model's dispersions are in good agreement with the DFT data around the specific wave vector, and the $g$-factors are consistent with experimental data. The VASP2KP package is available at https://github.com/zjwang11/VASP2KP.

Nonreciprocal effects are consistently observed in noncentrosymmetric materials due to the intrinsic symmetry breaking and in high-conductivity systems due to the extrinsic thermoelectric effect. Meanwhile, nonreciprocal charge transport is widely utilized as an effective experimental technique for detecting intrinsic unidirectional electrical contributions. Here, we show an unconventional nonreciprocal voltage transition in topological insulator Ag$_{2}$Te nanobelts. The nonreciprocal voltage develops from nearly zero to giant values under the applied current $I_{\rm ac}$ and external magnetic fields, while remaining unchanged under various current $I_{\rm dc}$. This unidirectional electrical contribution is further evidenced by the differential resistance ($dV/dI$) measurements. Furthermore, the transition possesses two-dimensional properties under a tilted magnetic field and occurs when the voltage between two electrodes exceeds a certain value. We propose a possible mechanism based on the development of edge channels in Ag$_{2}$Te nanobelts to interpret the phenomenon. Our results not only introduce a peculiar nonreciprocal voltage transition in topological materials but also enrich the understanding of the intrinsic mechanism that strongly affects nonreciprocal charge transport.

Electron systems in low dimensions are enriched with many superior properties for both fundamental research and technical developments. Wide tunability of electron density, high mobility of motion, and feasible controllability in microscales are the most prominent advantages that researchers strive for. Nevertheless, it is always difficult to fulfill all in one solid-state system. Two-dimensional electron systems (2DESs) floating above the superfluid helium surfaces are thought to meet these three requirements simultaneously, ensured by the atomic smoothness of surfaces and the electric neutrality of helium. Here we report our recent work in preparing, characterizing, and manipulating 2DESs on superfluid helium. We realized a tunability of electron density over one order of magnitude and tuned their transport properties by varying electron distribution and measurement frequency. The work we engage in is crucial for advancing research in many-body physics and for development of single-electron quantum devices rooted in these electron systems.

High-$T_{\rm c}$ superconductivity with possible $T_{\rm c}\approx 80$ K has been reported in the single crystal of ${\rm La}_{3}{\rm Ni}_{2}{\rm O}_{7}$ under high pressure. Based on the electronic structure given by the density functional theory calculations, we propose an effective bi-layer model Hamiltonian including both $3d_{z^{2}}$ and $3d_{x^{2}-y^{2}}$ orbital electrons of the nickel cations. The main feature of the model is that the $3d_{z^{2}}$ electrons form inter-layer $\sigma$-bonding and anti-bonding bands via the apical oxygen anions between the two layers, while the $3d_{x^{2}-y^{2}}$ electrons hybridize with the $3d_{z^{2}}$ electrons within each NiO$_2$ plane. The chemical potential difference of these two orbital electrons ensures that the $3d_{z^{2}}$ orbitals are close to half-filling and the $3d_{x^{2}-y^{2}}$ orbitals are near quarter-filling. The strong on-site Hubbard repulsion of the $3d_{z^{2}}$ orbital electrons gives rise to an effective inter-layer antiferromagnetic spin super-exchange $J$. Applying pressure can self dope holes on the $3d_{z^{2}}$ orbitals with the same amount of electrons doped on the $3d_{x^{2}-y^{2}}$ orbitals. By performing numerical density-matrix renormalization group calculations on a minimum setup and focusing on the limit of large $J$ and small doping of $3d_{z^{2}}$ orbitals, we find the superconducting instability on both the $3d_{z^{2}}$ and $3d_{x^{2}-y^{2}}$ orbitals by calculating the equal-time spin singlet pair–pair correlation function. Our numerical results may provide useful insights in the high-$T_{\rm c}$ superconductivity in single crystal La$_3$Ni$_2$O$_7$ under high pressure.

Three-dimensional (3D) degenerate Fermi gases in the presence of spin-orbit coupling, inducing various kinds of physical findings and phenomena, have attracted tremendous attention in these years. We investigate the 3D spin-orbit coupled degenerate Fermi gases in theory and first present the analytic expression of their ground state. Our study provides an innovative perspective into understanding of the topological properties of 3D unconventional superconductors, and describes the topological phase transitions in trivial and topological phase areas. Further, such a system is provided with a richer set of Cooper pairings than traditional superconductors. The dual Cooper pairs with same spin directions emerge and exhibit peculiar behaviors, leading to topological phase transitions. Our study and discussion can be generalized to some other types of unconventional superconductors and areas of optical lattices.

Mn$_{3}$Sn$_{2}$ has been proposed as an ideal material for magnetic refrigeration. It undergoes two successive ferromagnetic transitions ($T_{\rm C1} = 262$ K and $T_{\rm C2} = 227$ K) and one antiferromagnetic transition ($T_{\rm N} = 192$ K). Herein we report, for the first time, the preparation of single crystals of Mn$_{3}$Sn$_{2}$ from Bi flux. The resultant anisotropic magnetic properties and magnetocaloric effect are investigated along the three principal crystallographic directions of the crystal. Significant anisotropy of magnetic susceptibility and multiple field-induced metamagnetic transitions were found at low fields, whereas the magnetocaloric effect was found to be almost isotropic and larger than that of the polycrystalline one. The maximum magnetic entropy change amounts to $-\Delta S_{\rm M} = 4.01$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ near $T_{\rm C1}$ under a magnetic field change of $\mu_{0}\Delta H = 5$ T along the $c$-axis, with the corresponding refrigerant capacity of 1750 mJ$\cdot$cm$^{-3}$. Combined with a much wider cooling temperature span ($\sim$ $80$ K), our results demonstrate Mn$_{3}$Sn$_{2}$ single crystal to be an attractive candidate working material for active magnetic refrigeration at low temperatures.

Ce:YIG thin films are taken as an ideal candidate for magneto-optical devices with giant Faraday effect in the near-infrared range, but it is hindered by a limited Ce$^{3+}$/Ce$^{4+}$ ratio and a high saturation driving field. To address this issue, Eu doping can increase the Faraday rotation angle by $\sim$ 40% to $1.315\times 10^{4}$ deg/cm and decrease the saturation driving field by $\sim$ 38% to 1.17 kOe in Eu$_{0.75}$Ce$_{1}$Y$_{1.25}$Fe$_{5}$O$_{12}$ compared to Ce$_{1}$Y$_{2}$Fe$_{5}$O$_{12}$ pristine. The mechanism is attributed to the conversion of Ce$^{4+}$ to Ce$^{3+}$ and the weakening of ferrimagnetism by Eu doping. This work not only provides strategies for improving Ce$^{3+}$/Ce$^{4+}$ ratio in Ce:YIG, but also develops (Eu,Ce):YIG with a promising Faraday rotation angle for magneto-optical devices.

Silicon carbide (SiC) is a promising platform for fabricating high-voltage, high-frequency and high-temperature electronic devices such as metal oxide semiconductor field effect transistors in which many junctions or interfaces are involved. The work function (WF) plays an essential role in these devices. However, studies of the effect of conductive type and polar surfaces on the WF of SiC are limited. Here, we report the measurement of WFs of Si- and C-terminated polar surfaces for both p-type and n-type conductive 4H-SiC single crystals by scanning Kelvin probe microscopy (SKPFM). The results show that p-type SiC exhibits a higher WF than n-type SiC. The WF of a C-terminated polar surface is higher than that of a Si-terminated polar surface, which is further confirmed by first-principles calculations. By revealing this long-standing knowledge gap, our work facilitates the fabrication and development of SiC-based electronic devices, which have tremendous potential applications in electric vehicles, photovoltaics, and so on. This work also shows that SKPFM is a good method for identifying polar surfaces of SiC and other polar materials nondestructively, quickly and conveniently.

A novel hybrid system consisting of a direct carbon fuel cell (DCFC), a thermionic generator (TIG), and a regenerator is developed to recover the exhaust heat from the fuel cell. Expressions for the power output and efficiency of subsystems and the hybrid system are derived. Based on the energy balance equation, the area matching problem between the DCFC and the TIG is discussed and solved. By considering the main irreversibilities, the influences of the DCFC's current density and the TIG's voltage on the performance of the hybrid system are revealed. The maximum power output density and the corresponding efficiency of the hybrid system are, respectively, equal to 379 W/m$^{2}$ and 36%. To enhance the maximum power density of the single DCFC, the optimal regions of the main parameters are determined.

Cell movement behavior is one of the most interesting biological problems in physics, biology, and medicine. We experimentally investigate the characteristics of random cell motion during migration. Observing cell motion trajectories under a microscope, we employ a nonlinear dynamics method to construct a speed–acceleration phase diagram. Our analysis reveals the presence of a fixed point in this phase diagram, which suggests that migrating cells possess a stable state. Cells that deviate from this stable state display a tendency to return to it, following the streamline trends of an attractor structure in the phase diagram. We derive a set of characteristic values describing cell motion, encompassing inherent speed, inherent acceleration, characteristic time for speed change, and characteristic time for acceleration change. We develop a differential equation model based on experimental data and conduct numerical calculations. The computational results align with the findings obtained from experiments. Our research suggests that the asymmetrical characteristics observed in cell motion near an inherent speed primarily arise from properties of inherent acceleration of cells.