Flat-bottom Potential Research Articles

Higher-order vortex solitons in Kerr nonlinear media with a flat-bottom potential

Higher-order vortex solitons in Kerr nonlinear media with a flat-bottom potential

Efficient Simulations of Solvent Asymmetry Across Lipid Membranes Using Flat-Bottom Restraints.

The routinely employed periodic boundary conditions complicate molecular simulations of physiologically relevant asymmetric lipid membranes together with their distinct solvent environments. Therefore, separating the extracellular fluid from its cytosolic counterpart has often been performed using a costly double-bilayer setup. Here, we demonstrate that the lipid membrane and solvent asymmetry can be efficiently modeled with a single lipid bilayer by applying an inverted flat-bottom potential to ions and other solute molecules, thereby restraining them to only interact with the relevant leaflet. We carefully optimized the parameters of the suggested method so that the results obtained using the flat-bottom and double-bilayer approaches become mutually indistinguishable. Then, we apply the flat-bottom approach to lipid bilayers with various compositions and solvent environments, covering ions and cationic peptides to validate the approach in a realistic use case. We also discuss the possible limitations of the method as well as its computational efficiency and provide a step-by-step guide on how to set up such simulations in a straightforward manner.

Position-Dependent Diffusion Constant of Molecules in Heterogeneous Systems as Evaluated by the Local Mean Squared Displacement.

The authors propose a novel method to evaluate the position-dependent diffusion constant by analyzing unperturbed segments of a trajectory determined by the additional flat-bottom potential. The accuracy of this novel method is first established by studying homogeneous systems, where the reference value can be obtained by the Einstein relation. The applicability of this new method to heterogeneous systems is then demonstrated by studying a hydrophobic solute near a hydrophobic wall. The proposed method is also comprehensively compared with popular conventional methods, whereby the significance of the present method is illustrated. The novel method is powerful and useful for studying kinetics in heterogeneous systems based on molecular dynamics calculations.

Prediction of Protein-Ligand Binding Pose and Affinity Using the gREST+FEP Method.

The accurate prediction of protein-ligand binding affinity is a central challenge in computational chemistry and in-silico drug discovery. The free energy perturbation (FEP) method based on molecular dynamics (MD) simulation provides reasonably accurate results only if a reliable structure is available via high-resolution X-ray crystallography. To overcome the limitation, we propose a sequential prediction protocol using generalized replica exchange with solute tempering (gREST) and FEP. At first, ligand binding poses are predicted using gREST, which weakens protein-ligand interactions at high temperatures to sample multiple binding poses. To avoid ligand dissociation at high temperatures, a flat-bottom restraint potential centered on the binding site is applied in the simulation. The binding affinity of the most reliable pose is then calculated using FEP. The protocol is applied to the bindings of ten ligands to FK506 binding proteins (FKBP), showing the excellent agreement between the calculated and experimental binding affinities. The present protocol, which is referred to as the gREST+FEP method, would help to predict the binding affinities without high-resolution structural information on the ligand-bound state.

Enhanced visibility of the Fulde-Ferrel-Larkin-Ovchinnikov state in one-dimensional Bose-Fermi mixtures near the immiscibility point

Based on the matrix product states method, we investigate numerically the ground state properties of one-dimensional mixtures of repulsive bosons and spin-imbalanced attractive fermions, the latter being in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where Cooper pairs condense at a finite momentum $k=k_{FFLO}$. We find that the visibility of such a state is dramatically enhanced as the repulsive Bose-Fermi mixture is brought close to the phase-separation point. In particular, large amplitude self-induced oscillations with wave-vector $2k_{FFLO}$ appear in both the fermion total density and the boson density profiles, leaving sharp fingerprints in the corresponding static structure factors. We show that these features remain well visible in cold atoms systems trapped longitudinally by a smooth flat-bottom potential. Hence bosons can be used to directly reveal the modulated Fermi superfluid in experiments.

De Novo Prediction of Binders and Nonbinders for T4 Lysozyme by gREST Simulations.

Molecular recognition underpins all specific protein-ligand interactions and is essential for biomolecular functions. The prediction of canonical binding poses and distinguishing binders from nonbinders are much sought after goals. Here, we apply the generalized replica exchange with solute tempering method, gREST, combined with a flat-bottom potential to evaluate binder and nonbinder interactions with a T4 lysozyme Leu99Ala mutant. The buried hydrophobic cavity and possibility of coupled conformational changes in this protein make binding predictions difficult. The present gREST simulations, enabling enhanced flexibilities of the ligand and protein residues near the binding site, sample bindings in multiple poses, and correct portrayal of X-ray structures. The free-energy profiles of binders (benzene, ethylbenzene, and n-hexylbenzene) are distinct from those of nonbinders (phenol and benzaldehyde). Bindings of the two larger molecules seem to be associated with a structural change toward an excited conformation of the protein, which agrees with experimental findings. The protocol is generally applicable to various proteins having buried cavities with limited access for ligands with different shapes, sizes, and chemical properties.

Loading and compression of a single two-dimensional Bose gas in an optical accordion

The experimental realization of 2D Bose gases with a tunable interaction strength is an important challenge for the study of ultracold quantum matter. Here we report on the realization of an optical accordion creating a lattice potential with a spacing that can be dynamically tuned between 11$\,\mu$m and 2$\,\mu$m. We show that we can load ultracold $^{87}$Rb atoms into a single node of this optical lattice in the large spacing configuration and then decrease nearly adiabatically the spacing to reach a strong harmonic confinement with frequencies larger than $\omega_z/2\pi=10\,$kHz. Atoms are trapped in an additional flat-bottom in-plane potential that is shaped with a high resolution. By combining these tools we create custom-shaped uniform 2D Bose gases with tunable confinement along the transverse direction and hence with a tunable interaction strength.

Dark matter in axion landscape

If there are a plethora of axions in nature, they may have a complicated potential and create an axion landscape. We study a possibility that one of the axions is so light that it is cosmologically stable, explaining the observed dark matter density. In particular we focus on a case in which two (or more) shift-symmetry breaking terms conspire to make the axion sufficiently light at the potential minimum. In this case the axion has a flat-bottomed potential. In contrast to the case in which a single cosine term dominates the potential, the axion abundance as well as its isocurvature perturbations are significantly suppressed. This allows an axion with a rather large mass to serve as dark matter without fine-tuning of the initial misalignment, and further makes higher-scale inflation to be consistent with the scenario.

Quantum distillation and confinement of vacancies in a doublon sea

Ultracold atomic gases have revolutionized the study of non-equilibrium dynamics in quantum many-body systems. Many counterintuitive non-equilibrium effects have been observed, such as suppressed thermalization in a one-dimensional (1D) gas1, the formation of repulsive self-bound dimers2, and identical behaviours for attractive and repulsive interactions3. Here, we observe the expansion of a bundle of ultracold 1D Bose gases in a flat-bottomed optical lattice potential. By combining in situ measurements with photoassociation4,5, we follow the spatial dynamics of singly, doubly and triply occupied lattice sites. The system sheds interaction energy by dissolving some doublons and triplons. Some singlons quantum distil out of the doublon centre6,7, whereas others remain confined7. Our Gutzwiller mean-field model captures these experimental features in a physically clear way. These experiments might be used to study thermalization in systems with particle losses8, the evolution of quantum entanglement9,10 or, if applied to fermions, to prepare very low entropy states6.

Protein NMR structures refined without NOE data.

The refinement of low-quality structures is an important challenge in protein structure prediction. Many studies have been conducted on protein structure refinement; the refinement of structures derived from NMR spectroscopy has been especially intensively studied. In this study, we generated flat-bottom distance potential instead of NOE data because NOE data have ambiguity and uncertainty. The potential was derived from distance information from given structures and prevented structural dislocation during the refinement process. A simulated annealing protocol was used to minimize the potential energy of the structure. The protocol was tested on 134 NMR structures in the Protein Data Bank (PDB) that also have X-ray structures. Among them, 50 structures were used as a training set to find the optimal “width” parameter in the flat-bottom distance potential functions. In the validation set (the other 84 structures), most of the 12 quality assessment scores of the refined structures were significantly improved (total score increased from 1.215 to 2.044). Moreover, the secondary structure similarity of the refined structure was improved over that of the original structure. Finally, we demonstrate that the combination of two energy potentials, statistical torsion angle potential (STAP) and the flat-bottom distance potential, can drive the refinement of NMR structures.

Description of the shape evolution in the yrast states of 186Pt

186Pt was tested in the framework of IBM-1 and the X(3) model. The results show that 186Pt is located close to the shape phase transition point, but the B(E2) values little agree with the X(3) model. The shape evolution in the yrast states of 186Pt is also discussed in detail. TRS calculation exhibits a flat bottomed potential at low spin states, but a relatively deep minimum at high spin states. It suggests that a shape evolution from vibrational mode to rotational mode happens in 186Pt. The result is in agreement with the E-GOS calculation.

NMR Structure Refinement using Stap and Flat-Bottom Potential Without NOE Data

The low-quality structure refinement is one of important challenges in protein structure prediction. Many studies have been conducted for protein structure refinement; especially refinement of structure derived from NMR spectroscopy is accelerated. In this study, we demonstrate that statistical torsion angle potential (STAP) can drive to refine NMR structures without NOE data. Because NOE data have an ambiguity and uncertainty, we used flat-bottom potential instead of NOE data. The materials of flat-bottom potential are distance and dihedral angle derived from given structures. Instead of the NOE restraints, they prevent a structural dislocation during the refinement process. A simulated annealing protocol was used to optimize energy of structures. The protocol was tested on 134 NMR structures in Protein Data Bank (PDB) that are coexisting in X-ray structures. Among them, 50 structures of training set used to find the optimal “width” parameter in the flat-bottom potential functions. Validations of the “width” for 84 structures, most of 12 quality assessment scores of refined structure are significantly improved.

Precise shaping of laser light by an acousto-optic deflector

We present a laser beam shaping method using acousto-optic deflection of light and discuss its application to dipole trapping of ultracold atoms. By driving the acousto-optic deflector with multiple frequencies, we generate an array of overlapping diffraction-limited beams that combine to form an arbitrary-shaped smooth and continuous trapping potential. Confinement of atoms in a flat-bottomed potential formed by a laser beam with uniform intensity over its central region confers numerous advantages over the harmonic confinement intrinsic to Gaussian beam dipole traps and many other trapping schemes. We demonstrate the versatility of this beam shaping method by generating potentials with large flat-topped regions as well as intensity patterns that compensate for residual external potentials to create a uniform background to which the trapping potential of experimental interest can be added.

Decay Constants of Vector Mesons

The light vector mesons are studied within the framework of the Bethe–Salpeter equation with the vector-vector-type flat-bottom potential. The Bethe–Salpeter wavefunctions and the decay constants of the vector mesons are obtained. All the obtained results, fρ, fφ, and fK*, are in agreement with the experimental values, respectively.

Decay constants of the pseudoscalar charmonium and bottomonium

In this Letter, we investigate the structures of the pseudoscalar charmonium and bottomonium in the framework of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation with the confining effective potential (infrared modified flat bottom potential). As the current masses are very large, the dressing or renormalization for the c and b quarks are tender, however, mass poles in the timelike region are absent. The Euclidean time Fourier transformed quark propagator has no mass poles in the timelike region which naturally implements confinement. The Bethe–Salpeter wavefunctions for those mesons have the same type (Gaussian type) momentum dependence and center around zero momentum with spatial extension to about q2=1 GeV2 which happen to be the energy scale for chiral symmetry breaking, the strong interactions in the infrared region result in bound states. The decay constants for those pseudoscalar heavy quarkonia are compatible with the values of experimental extractions and theoretical calculations.

Decay constants of the pseudoscalar mesons in the framework of the coupled Schwinger–Dyson equation and Bethe–Salpeter equation

In this article, we investigate the structures of the pseudoscalar mesons ( π, K, D, D s , B and B s ) in the framework of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation with the confining effective potential (infrared modified flat bottom potential). The Schwinger–Dyson functions for the u, d and s quarks are greatly renormalized at small momentum region and the curves are steep at about q 2 = 1 GeV 2 which indicates an explicitly dynamical symmetry breaking. The Euclidean time Fourier transformed quark propagators have no mass poles in the time-like region which naturally implements confinement. As for the c and b quarks, the current masses are very large, the renormalization are more tender, however, mass poles in the time-like region are also absent. The Bethe–Salpeter wavefunctions for those mesons have the same type (Gaussian type) momentum dependence and center around small momentum which indicate that the bound states exist in the infrared region. The decay constants for those pseudoscalar mesons are compatible with the values of experimental extractions and theoretical calculations, such as lattice simulations and QCD sum rules.

Decay constants of the pion and B mesons with the Bethe–Salpeter equation

In this Letter, we investigate the under-structures of the π and B mesons in the framework of the Bethe–Salpeter equation with the confining effective potential (infrared modified flat bottom potential). In bare quark–gluon vertex approximation, we obtain the algebraic expressions for the solutions of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation. Firstly, we neglect the rainbow Schwinger–Dyson equation, take the bare quark propagator and solve the Bethe–Salpeter equation numerically alone. Although the bare quark propagator cannot embody dynamical chiral symmetry breaking and has a mass pole in the time-like region, it can give reasonable results for the values of decay constants fπ and fB compared with the values of experimental data and other theoretical calculations, such as lattice simulations and QCD sum rules. Secondly, we explore those mesons within the framework of the coupled rainbow Schwinger–Dyson equation and ladder Bethe–Salpeter equation. The Schwinger–Dyson functions for the u and d quarks are greatly renormalized at small momentum region and the curves are steep at about q2=1 GeV2 which indicates an explicitly dynamical symmetry breaking. The Euclidean time Fourier-transformed quark propagator has no mass poles in the time-like region which naturally implements confinement. As for the b quark, the current mass is very large, the renormalization is more tender, however, mass pole in the time-like region is also absent. The Bethe–Salpeter wavefunctions for both the π and B mesons have the same type (Gaussian type) momentum dependence as the corresponding wavefunctions with the bare quark propagator, however, the quantitative values are changed and the values for the decay constants fπ and fB are changed correspondingly.

Calculation of some properties of the vacuum

In this paper, we calculate the dressed quark propagator with the flat bottom potential in the framework of the rainbow Schwinger–Dyson equation, which is determined by mean field approximation of the global colour model Lagrangian. The dressed quark propagator exhibits a dynamical symmetry-breaking phenomenon and gives a constituent quark mass about 392 MeV, which is close to the value of commonly used constituent quark mass in the chiral quark model. Then based on the dressed quark propagator, we calculate some properties of the vacuum, such as quark condensate, mixed quark condensate gs⟨0|q̄Gμνσμνq|0⟩, four quark condensate ⟨0|q̄Γqq̄Γq|0⟩, tensor, π vacuum susceptibilities. The numerical results are compatible with the values of other theoretical approaches.

Dynamical symmetry breaking, confinement with flat-bottom potential

In this Letter, we calculate the dressed quark propagator with the flat bottom potential in the framework of the rainbow Schwinger–Dyson equation. Then based on the nonperturbative dressed quark propagator, we calculate the π decay constant and the quark condensate. The π decay constant is an important parameter in describing the interplay between dynamical symmetry breaking and confinement, while the quark condensate is an order parameter for dynamical chiral symmetry breaking. To implement confinement, we prove that the dressed quark propagator has no poles on the real timelike p 2 axial, the absence of Kallen–Lehmann spectral representation obviously precludes the existence of free quarks.

Calculation of Kaon Electromagnetic Form Factor in the Framework of Coupled Schwinger–Dyson and Bethe–Salpeter Formulation**The project supported by National Natural Science Foundation of China under Grant No. 19875048

The kaon electromagnetic form factor is calculated in the framework of coupled Schwinger–Dyson equation in rainbow approximation and Bethe–Salpeter equation in ladder approximation with the modified flat-bottom potential, which is the combination of the flat-bottom potential with considerations for the infrared and ultraviolet asymptotic behaviours of the effective quark-gluon coupling. All our numerical results give good fit to experimental values and other theoretical results.