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In one-dimensional quantum materials, conducting electrons and the underlying lattices can undergo a spontaneous translational symmetry breaking, known as Peierls transition. For nearly a century, the Peierls transition has been understood within the paradigm of electron-electron interactions mediated by longitudinal acoustic phonons. This classical picture has recently been revised in topological semimetals, where transverse acoustic phonons can couple with conducting p-orbital electrons and give rise to an unconventional Fermi surface instability, dubbed the transverse Peierls transition (TPT). Most interestingly, the TPT induced lattice distortions can further break rotation or mirror/inversion symmetries, leading to nematic or chiral charge density waves (CDWs). Quantum materials that host the TPT, however, have not been experimentally established. Here, we report the experimental discovery of an incommensurate TPT in the tetragonal Dirac semimetal EuAl$_4$. Using inelastic x-ray scattering with meV resolution, we observe the complete softening of a transverse acoustic phonon at the CDW wavevector upon cooling, whereas the longitudinal acoustic phonon is nearly unchanged. Combining with first principles calculations, we show that the incommensurate CDW wavevector matches the calculated charge susceptibility peak and connects the nested Dirac bands with Al 3$p_{x}$ and 3$p_{y}$ orbitals. Supplemented by second harmonic generation measurements, we show that the CDW induced lattice distortions break all vertical and diagonal mirrors whereas the four-fold rotational symmetry is retained below the CDW transition. Our observations strongly suggest a chiral CDW in EuAl$_4$ and highlight the TPT as a new avenue for chiral quantum states., Comment: Supplementary materials are available upon request

The bi-photon correlation time, a measure for the conditional uncertainty in the temporal arrival of two photons from a photon pair source, is a key performance identifier for many quantum spectroscopy applications, with shorter correlation times typically yielding better performance. Furthermore, it provides fundamental insight into the effects of dispersion on the bi-photon state. Here, we retrieve ultrashort bi-photon correlation times of around $100\,\mathrm{fs}$ by measuring simultaneously spectral and temporal interferograms at the output of an SU(1,1) interferometer based on an integrated broadband parametric down-conversion source in a $\mathrm{Ti:LiNbO}_3$ waveguide, Comment: 8 pages, 5 figures

Interferometers provide a highly sensitive means to investigate and exploit the coherence properties of light in metrology applications. However, interferometers come in various forms and exploit different properties of the optical states within. In this paper, we introduce a classification scheme that characterizes any interferometer based on the number of involved nonlinear elements by studying their influence on single-photon and photon-pair states. Several examples of specific interferometers from these more general classes are discussed, and the theory describing the expected first-order and second-order coherence measurements for single-photon and single-photon-pair input states is summarized and compared. These theoretical predictions are then tested in an innovative experimental setup that is easily able to switch between implementing an interferometer consisting of only one or two nonlinear elements. The resulting singles and coincidence rates are measured in both configurations and the results are seen to fit well with the presented theory. The measured results of coherence are tied back to the presented classification scheme, revealing that our experimental design can be useful in gaining insight into the properties of the various interferometeric setups containing different degrees of nonlinearity., Comment: 12 pages, 5 figures

Topological semimetals with different types of band crossings provide a rich platform to realize novel fermionic excitations, known as topological fermions. In particular, some fermionic excitations can be direct analogues of elementary particles in quantum field theory when both obey the same laws of physics in the low-energy limit. Examples include Dirac and Weyl fermions, whose solid-state realizations have provided new insights into long-sought phenomena in high-energy physics. Recently, theorists predicted new types of fermionic excitations in condensed-matter systems without any high-energy counterpart, and their existence is protected by crystalline symmetries. By studying the topology of the electronic structure in PdBiSe using density functional theory calculations and bulk-sensitive soft X-ray angle-resolved photoemission spectroscopy, we demonstrate a coexistence of four different types of topological fermions: Weyl, Rarita-Schwinger-Weyl, double class-II three-component, and charge-2 fourfold fermions. Our discovery provides a remarkable platform to realize multiple novel fermions in a single solid, charting the way forward to studies of their potentially exotic properties as well as their interplay.

A simple, novel, non-empirical, constraint-based orbital-free generalized gradient approximation (GGA) non-interacting kinetic energy density functional is presented along with illustrative applications. The innovation is adaptation of constraint-based construction to the essential properties of pseudo-densities from the pseudo-potentials that are essential in plane-wave-basis {\it ab initio} molecular dynamics. This contrasts with constraining to the qualitatively different Kato-cusp-condition densities. The single parameter in the new functional is calibrated by satisfying Pauli potential positivity constraints for pseudo-atom densities. In static lattice tests on simple metals and semiconductors, the new LKT functional outperforms the previous best constraint-based GGA functional, VT84F (Phys.\ Rev.\ B \textbf{88}, 161108(R) (2013)), is generally superior to a recently proposed meta-GGA, is reasonably competitive with parametrized two-point functionals, and is substantially faster., Comment: 3 figures

In this paper, a central-moment-based lattice Boltzmann (CLB) method for incompressible thermal flows is proposed. In the method, the incompressible Navier-Stokes equations and the convection-diffusion equation for the temperature field are sloved separately by two different CLB equations. Through the Chapman-Enskog analysis, the macroscopic governing equations for incompressible thermal flows can be reproduced. For the flow field, the tedious implementation for CLB method is simplified by using the shift matrix with a simplified central-moment set, and the consistent forcing scheme is adopted to incorporate forcing effects. Compared with several D2Q5 multiple-relaxation-time (MRT) lattice Boltzmann methods for the temperature equation, the proposed method is shown to be better Galilean invariant through measuring the thermal diffusivities on a moving reference frame. Thus a higher Mach number can be used for convection flows, which decreases the computational load significantly. Numerical simulations for several typical problems confirm the accuracy, efficiency, and stability of the present method. The grid convergence tests indicate that the proposed CLB method for incompressible thermal flows is of second-order accuracy in space.

In this theoretical study we demonstrate that entangled states are able to significantly extend the functionality of Hong-Ou-Mandel (HOM) interferometers. By generating a coherent superposition of parametric-down-conversion photons and spatial entanglement in the input channel, the coincidence probability measured at the output changes from a typical HOM-type dip (photon bunching) into much richer patterns including an anti-bunching peak and rapid oscillation fringes with twice the optical frequency. The considered system should be realizable on a single chip using current waveguide technology in the $LiNbO_3$ platform.

In this paper, we give a more pellucid derivation for the cascaded lattice Boltzmann method (CLBM) based on a general multiple-relaxation-time (MRT) frame through defining a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The applicability of the non-slip rule, the second-order convergence rate in space and the property of isotropy for the consistent forcing scheme is demonstrated through the simulation of several canonical problems. Several other existing force schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework.

We present and discuss perspectives of current developments on advanced quantum optical circuits monolithically integrated in the lithium niobate platform. A set of basic components comprising photon pair sources based on parametric down conversion (PDC), passive routing elements and active electro-optically controllable switches and polarisation converters are building blocks of a toolbox which is the basis for a broad range of diverse quantum circuits. We review the state-of-the-art of these components and provide models that properly describe their performance in quantum circuits. As an example for applications of these models we discuss design issues for a circuit providing on-chip two-photon interference. The circuit comprises a PDC section for photon pair generation followed by an actively controllable modified Mach-Zehnder structure for observing Hong-Ou-Mandel (HOM) interference. The performance of such a chip is simulated theoretically by taking even imperfections of the properties of the individual components into account.

In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is developed in combination with the double-distribution-function (DDF) approach. A density distribution function relaxed by the cascaded scheme is employed to solve the flow field, and a total energy distribution function relaxed by the BGK scheme is used to solve temperature field, where two distribution functions are coupled naturally. The forcing terms are incorporated by means of central moments, which is consistent with the previous force scheme [Premnath \emph{et al.}, Phys. Rev. E \textbf{80}, 036702 (2009)] but the derivation is more intelligible and the evolution process is simpler. In the method, the viscous heat dissipation and compression work are taken into account, the Prandtl number and specific-heat ratio are adjustable, the external force is considered directly without the Boussinesq assumption, and the low-Mach number compressible flows can also be simulated. The forcing scheme is tested by simulating a steady Taylor-Green flow, and the new TCLBM is then tested by numerical experiments of the thermal Couette flow, low-Mach number shock tube problem, and Rayleigh-B\'{e}nard convection. The simulation results agree well with the analytical solutions and/or results given by previous researchers.

Over the past few decades, tremendous progress has been made in the development of particle-based discrete simulation methods versus the conventional continuum-based methods. In particular, the lattice Boltzmann (LB) method has evolved from a theoretical novelty to a ubiquitous, versatile and powerful computational methodology for both fundamental research and engineering applications. It is a kinetic-based mesoscopic approach that bridges the microscales and macroscales, which offers distinctive advantages in simulation fidelity and computational efficiency. Applications of the LB method have been found in a wide range of disciplines including physics, chemistry, materials, biomedicine and various branches of engineering. The present work provides a comprehensive review of the LB method for thermofluids and energy applications, focusing on multiphase flows, thermal flows and thermal multiphase flows with phase change. The review first covers the theoretical framework of the LB method, revealing the existing inconsistencies and defects as well as common features of multiphase and thermal LB models. Recent developments in improving the thermodynamic and hydrodynamic consistency, reducing the spurious currents, enhancing the numerical stability, etc., are highlighted. These efforts have put the LB method on a firmer theoretical foundation with enhanced LB models that can achieve larger liquid-gas density ratio, higher Reynolds number and flexible surface tension. Examples of applications are provided in fuel cells and batteries, droplet collision, boiling heat transfer and evaporation, and energy storage. Finally, further developments and future prospect of the LB method are outlined for thermofluids and energy applications., Comment: a Review, 127 pages, 28 figures, accepted by Progress in Energy and Combustion Science

A hybrid thermal lattice Boltzmann (LB) model is presented to simulate thermal multiphase flows with phase change based on an improved pseudopotential LB approach [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 87, 053301 (2013)]. The present model does not suffer from the spurious term caused by the forcing-term effect, which was encountered in some previous thermal LB models for liquid-vapor phase change. Using the model, the liquid-vapor boiling process is simulated. The boiling curve together with the three boiling stages (nucleate boiling, transition boiling, and film boiling) is numerically reproduced in the LB community for the first time. The numerical results show that the basic features and the fundamental characteristics of boiling heat transfer are well captured, such as the severe fluctuation of transient heat flux in the transition boiling and the feature that the maximum heat transfer coefficient lies at a lower wall superheat than that of the maximum heat flux. Furthermore, the effects of the heating surface wettability on boiling heat transfer are investigated. It is found that an increase in contact angle promotes the onset of boiling but reduces the critical heat flux, and makes the boiling process enter into the film boiling regime at a lower wall superheat, which is consistent with the findings from experimental studies., Comment: 13 Figures

In this paper, we aim to investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio. The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994)] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model, the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions: the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper, are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles, however, is unable to reproduce static contact angles close to 180 degrees. Meanwhile, it is found that the proposed modified pseudopotential-based interaction performs better in light of the maximum and the minimum densities and is overall more suitable for simulating large contact angles as compared with the other two types of fluid-solid interactions. Furthermore, the spurious currents are found to be enlarged when the fluid-solid interaction force is introduced. Increasing the kinematic viscosity ratio between the vapor and liquid phases is shown to be capable of reducing the spurious currents caused by the fluid-solid interactions., Comment: 11 figures, Accepted by Physical Review E

The pseudopotential lattice Boltzmann (LB) model is a popular model in the LB community for simulating multiphase flows. Recently, several thermal LB models, which are based on the pseudopotential LB model and constructed within the framework of the double-distribution-function LB method, were proposed to simulate thermal multiphase flows [G. H\'azi and A. M\'arkus, Phys. Rev. E 77, 026305 (2008); L. Biferale et al., Phys. Rev. Lett. 108, 104502 (2012); S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)]. The objective of the present paper is to show that the effect of the forcing term on the temperature equation must be eliminated in the pseudopotential LB modeling of thermal flows. First, the effect of the forcing term on the temperature equation is shown via the Chapman-Enskog analysis. For comparison, alternative treatments that are free from the forcing-term effect are provided. Subsequently, numerical investigations are performed for two benchmark tests. The numerical results clearly show that the existence of the forcing-term effect will lead to significant numerical errors in the pseudopotential LB modeling of thermal flows., Comment: 3 Figures, 2 Tables, accepted by Physical Review E

Recent work showed that the exact exchange-correlation potential of time-dependent density functional theory generically displays dynamical step structures. These have a spatially non-local and time-non-local dependence on the density in real time dynamics. The steps are missing in the usual approximations which consequently yield inaccurate dynamics. Yet these same approximations typically yield good linear response spectra. Here we investigate whether the steps appear in the linear response regime, when the response is calculated from a real-time dynamics simulation, by examining the exact correlation potential of model two-electron systems at various times. We find there are no step structures in regions where the system response is linear. Step structures appear in the correlation potential only in regions of space where the density response is non-linear; these regions, having exponentially small density, do not contribute to the observables measured in linear response., Comment: 7 pages, 9 figures

In this paper, we aim to address an important issue about the pseudopotential lattice Boltzmann (LB) model, which has attracted much attention as a mesoscopic model for simulating interfacial dynamics of complex fluids, but suffers from the problem that the surface tension cannot be tuned independently of the density ratio. In the literature, a multi-range potential was devised to adjust the surface tension [Sbragaglia et al., Phys. Rev. E 75, 026702 (2007)]. However, it was recently found that the density ratio of the system will be changed when the multi-range potential is employed to adjust the surface tension. A new approach is therefore proposed in the present work. The basic strategy is to add a source term to the LB equation so as to tune the surface tension of the pseudopotential LB model. The proposed approach can guarantee that the adjustment of the surface tension does not affect the mechanical stability condition of the pseudopotential LB model, and thus provides a separate control of the surface tension and the density ratio. Meanwhile, it still retains the mesoscopic feature and the computational simplicity of the pseudopotential LB model. Numerical simulations are carried out for stationary droplets, capillary waves, and droplet splashing on a thin liquid film. The numerical results demonstrate that the proposed approach is capable of achieving a tunable surface tension over a very wide range and can keep the density ratio unchanged when adjusting the surface tension., Comment: 6 Figures, 5 Tables

Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Li et al., Phys. Rev. E. 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter a in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to 1/sqrt(a). Using a smaller a will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature., Comment: 9 figures, 2 tables, accepted by Physical Review E (in press)

In this paper, we aim to address several important issues about the recently developed lattice Boltzmann (LB) model for relativistic hydrodynamics [M. Mendoza et al., Phys. Rev. Lett. 105, 014502 (2010); Phys. Rev. D 82, 105008 (2010)]. First, we study the conservation law of particle number in the relativistic LB model. Through the Chapman-Enskog analysis, it is shown that in the relativistic LB model the conservation equation of particle number is a convection-diffusion equation rather than a continuity equation, which makes the evolution of particle number dependent on the relaxation time. Furthermore, we investigate the origin of the discontinuities appeared in the relativistic problems with high viscosities, which were reported in a recent study [D. Hupp et al., Phys. Rev. D 84, 125015 (2011)]. A multiple-relaxation-time (MRT) relativistic LB model is presented to examine the influences of different relaxation times on the discontinuities. Numerical experiments show the discontinuities can be eliminated by setting the relaxation time $\tau_e$ (related to the bulk viscosity) to be sufficiently smaller than the relaxation time $\tau_v$ (related to the shear viscosity). Meanwhile, it is found that the relaxation time $\tau_\varepsilon$, which has no effect on the conservation equations at the Navier-Stokes level, will affect the numerical accuracy of the relativistic LB model. Moreover, the accuracy of the relativistic LB model for simulating moderately relativistic problems is also investigated., Comment: 7 figures

The pseudo-potential lattice Boltzmann (LB) model is a widely used multiphase model in the LB community. In this model, an interaction force, which is usually implemented via a forcing scheme, is employed to mimic the molecular interactions that cause phase segregation. The forcing scheme is therefore expected to play an important role in the pseudo-potential LB model. In this paper, we aim to address some key issues about forcing schemes in the pseudo-potential LB model. Firstly, theoretical and numerical analyses will be made for Shan-Chen's forcing scheme and the exact-difference-method (EDM) forcing scheme. The nature of these two schemes and their recovered macroscopic equations will be shown. Secondly, through a theoretical analysis, we will reveal the physics behind the phenomenon that different forcing schemes exhibit different performances in the pseudo-potential LB model. Moreover, based on the analysis, we will present an improved forcing scheme and numerically demonstrate that the improved scheme can be treated as an alternative approach for achieving thermodynamic consistency in the pseudo-potential LB model., Comment: 7 figures

The existing lattice Boltzmann models for incompressible multiphase flows are mostly constructed with two distribution functions, one is the order parameter distribution function, which is used to track the interface between different phases, and the other is the pressure distribution function for solving the velocity field. In this brief report, it is shown that in these models the recovered momentum equation is inconsistent with the target one: an additional interfacial force is included in the recovered momentum equation. The effects of the additional force are investigated by numerical simulations of droplet splashing on a thin liquid film and falling droplet under gravity. In the former test, it is found that the formation and evolution of secondary droplets are greatly affected, while in the latter the additional force is found to increase the falling velocity and limit the stretch of the droplet., Comment: 11 pages, 5 figures

In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard D2Q9 lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small. Meanwhile, the simple structure and basic advantages of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature., Comment: 9 figures

A generalization of the lattice Bhatnagar-Gross-Krook (LBGK) model for the simulation of hydrodynamics is presented, which takes into account the difference and the frame-independence of the relaxation of non-hydrodynamic modes. The present model retains the computationally efficient standard LBGK form with the generalized equilibrium explicitly derived. The two-dimensional realization on the standard lattice is discussed in detail. Performance of the model is assessed through a shear layer simulation and enhanced stability and accuracy with respect to the standard LBGK are reported. The results demonstrate that the present model is a useful upgrade of the standard LBGK without compromising its computational efficiency and accuracy., Comment: Submitted to Phys. Rev. E, 11-MAR-2011; revised