Short-range Contact Interaction Research Articles

Revisiting the DD* chiral interactions with the local momentum-space regularization up to the third order and the nature of Tcc+

We revisit the $DD^\ast$ interactions in chiral effective field theory up to the third order for the first time. We deal with the pion-exchanged interactions via local momentum-space regularization, in which we focus on their long-range behaviors through demanding their contributions vanish at the origin in the coordinate space. The short-range contact interactions and subleading pion-charmed meson couplings are estimated with the phenomenological resonance saturation model. The subleading pion-charmed meson couplings are much weaker than those in the pion-nucleon system, thus the $DD^\ast$ binding mechanism is very different with that of the $NN$ system. We also obtain the analytic structure of the two-pion exchange interactions in the coordinate space, and we find that its asymptotic behavior at long distance is similar to but slightly different with the $NN$ interactions. We get the same asymptotic behavior of the two-pion exchange interaction with that from HAL QCD method but appearing in the longer distance rather than $1 <r<2\text{ fm}$. The binding solution only exists in the isoscalar channel. Our calculation supports the molecular interpretation of $T_{cc}^+$.

Dynamical stability of dipolar condensate in a parametrically modulated one-dimensional optical lattice* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11764039, 11847304, 11865014, 11475027, 11305132, and 11274255), the Natural Science Foundation of Gansu Province, China (Grant No. 17JR5RA076), and Scientific Research Project of Gansu Higher Education, China (Grant No. 2016A-005).

We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.

Hidden-charm and hidden-bottom molecular pentaquarks in chiral effective field theory

The newly observed Pc(4312), Pc(4440) and Pc(4457) at the LHCb experiment are very close to the {varSigma}_coverline{D} and {varSigma}_c{overline{D}}^{ast } thresholds. In this work, we perform a systematic study and give a complete picture on the interactions between the {varSigma}_c^{left(ast right)} and {overline{D}}^{left(ast right)} systems in the framework of heavy hadron chiral effective field theory, where the short-range contact interaction, long-range one-pion-exchange contribution, and intermediate-range two-pion-exchange loop diagrams are all considered. We first investigate the three Pc states without and with considering the Λc contribution in the loop diagrams. It is difficult to simultaneously reproduce the three Pcs unless the Λc is included. The coupling between the {varSigma}_c^{left(ast right)}{overline{D}}^{left(ast right)} and {Lambda}_c{overline{D}}^{left(ast right)} channels is crucial for the formation of these Pcs. Our calculation supports the Pc(4312), Pc(4440) and Pc(4457) to be the S-wave hidden-charm {left[{varSigma}_coverline{D}right]}_{J=1/2}^{I=1/2},{left[{varSigma}_c{overline{D}}^{ast}right]}_{J=1/2}^{I=1/2} and {left[{varSigma}_c{overline{D}}^{ast}right]}_{J=3/2}^{I=1/2} molecular pentaquarks, respectively. Our calculation disfavors the spin assignment {J}^P=frac{1^{-}}{2} for Pc(4457) and {J}^P=frac{3^{-}}{2} for Pc(4440), because the excessively enhanced spin-spin interaction is unreasonable in the present case. We obtain the complete mass spectra of the {left[{varSigma}_c^{left(ast right)}{overline{D}}^{left(ast right)}right]}_J systems with the fixed low energy constants. Our result indicates the existence of the {left[{varSigma}_c^{ast }{overline{D}}^{ast}right]}_Jleft(J=frac{1}{2},frac{3}{2},frac{5}{2}right) hadronic molecules. The previously reported Pc(4380) might be a deeper bound one. Additionally, we also study the hidden-bottom {varSigma}_b^{left(ast right)}{B}^{left(ast right)} systems, and predict seven bound molecular states, which could serve as a guidance for future experiments. Furthermore, we also examine the heavy quark symmetry breaking effect in the hidden-charm and hidden-bottom systems by taking into account the mass splittings in the propagators of the intermediate states. As expected, the heavy quark symmetry in the bottom cases is better than that in the charmed sectors. We notice that the heavy quark symmetry in the {varSigma}_coverline{D} and {varSigma}_c^{ast}overline{D} systems is much worse for some fortuitous reasons. The heavy quark symmetry breaking effect is nonnegligible in predicting the effective potentials between the charmed hadrons.

Stabilization of trapless dipolar Bose-Einstein condensates by temporal modulation of the contact interaction

We theoretically study the stability of a trapless dipolar Bose-Einstein condensate (BEC) with temporal modulation of short-range contact interaction. For this aim, through both analytical and numerical methods, we solve a Gross-Pitaevskii equation with both constant and oscillatory form of short-range contact interaction along with long-range, nonlocal, dipole-dipole (DD) interaction terms. Using variational method, we discuss the stability of the trapless dipolar BEC with presence and absence of both constant and oscillatory contact interactions. We show that the oscillatory contact interaction prevents the collapse of the trapless dipolar BEC. We confirm the analytical prediction through numerical simulations. We have also studied the collective excitations in the system induced by the effective potential due to oscillating interaction.

NΩ interaction: Meson exchanges, inelastic channels, and quasibound state

Based on a baryon-baryon interaction model with meson exchanges, we investigate the origin of the strong attraction in the $N \Omega ( {}^{5}S_{2} )$ interaction, which was indicated by recent lattice QCD simulations. The long range part of the potential is constructed by the conventional mechanisms, the exchanges of the $\eta$ meson and of the correlated two mesons in the scalar-isoscalar channel, denoted by "$\sigma$" in the literature. The short range part is represented by the contact interaction. We find that the meson exchanges do not provide sufficient attraction. This means that most of the attraction is attributed to the short range contact interaction. We then evaluate the effect of the coupled channels to the $N \Omega ( {}^{5}S_{2} )$ interaction. We find that, while the $D$-wave mixing of the $N \Omega$ channel is negligible, the inelastic $\Lambda \Xi$, $\Sigma \Xi$, and $\Lambda \Xi (1530)$ channels via the $K$ meson exchange give the attraction of the $N \Omega ( {}^{5}S_{2} )$ interaction to the same level with the elastic meson exchanges. Although the elimination of these channels induces the energy dependence of the single-channel $N \Omega$ interaction, this effect is not significant. With the present model parameters fitted to reproduce the scattering length of the HAL QCD result of the nearly physical quark masses, we obtain the $N \Omega ( {}^{5}S_{2} )$ quasibound state with its eigenenergy $2611.3 - 0.7 i$ MeV, which corresponds to the binding energy $0.1$ MeV and width $1.5$ MeV for the decay to the $\Lambda \Xi$ and $\Sigma \Xi$ channels. From the analysis of the spatial structure and the compositeness, the quasibound state is shown to be the molecular state of $N\Omega$. We also construct an equivalent local potential for the $N \Omega ( {}^{5}S_{2} )$ system which is useful for various applications.

Bogoliubov theory of dipolar Bose gas in a weak random potential

We consider a dilute homogeneous Bose gas with both an isotropic short-range contact interaction and an anisotropic long-range dipole-dipole interaction in a weak random potential at low temperature in three dimensions. Within the realm of Bogoliubov theory we analyze how both condensate and superfluid depletion are depleted due to quantum and thermal fluctuations as well as disorder fluctuations.

Pairing in half-filled Landau level

Pairing of composite fermions in half-filled Landau level state is reexamined by solving the BCS gap equation with full frequency dependent current–current interactions. Our results show that there can be a continuous transition from the Halperin–Lee–Read state to a chiral odd angular momentum Cooper pair state for short-range contact interaction. This is at odds with the previously established conclusion of first order pairing transition, in which the low frequency effective interaction was assumed for the entire frequency range. We find that even if the low frequency effective interaction is repulsive, it is compensated by the high frequency regime, which is attractive. We construct the phase diagrams and show that ℓ=1 angular momentum channel is quite different from higher angular momenta ℓ≥3. Remarkably, the full frequency dependent analysis applied to the bilayer Hall system with a total filling fraction ν=12+12 is quantitatively changed from the previously established results but not qualitatively.

Stability of dipolar soliton in crossed linear and nonlinear optical lattices

Stability of a dipolar Bose-Einstein condensate (BEC) soliton in crossed linear and nonlinear optical lattices is investigated using variational approximation. The Euler-Lagrange equations for variational parameters and the effective potential are derived by means of a cylindrically symmetric Gaussian ansatz, while the equilibrium widths are determined by minimization of the effective potential. In the presence of a periodic spatial variation of short-range contact interaction, the localized bound states can exist for both attractive and repulsive dipolar interactions. And the domain of stable dipolar BEC solitons is illustrated in a phase plot of the nonlinearities. Finally, we give the evolution of the variational width for different values of the nonlinearities.

Single-particle potential from resummed ladder diagrams

A recent work on the resummation of fermionic in-medium ladder diagrams to all orders is extended by calculating the complex single-particle potential U(p, k f ) + i W(p, k f ) p > k f . The on-shell single-particle potential is constructed by means of a complex-valued in-medium loop that includes corrections from a test particle of momentum \(\vec p\) added to the filled Fermi sea. The single-particle potential U(k f , k f ) at the Fermi surface as obtained from the resummation of the combined particle and hole ladder diagrams is shown to satisfy the Hugenholtz-Van-Hove theorem. The perturbative contributions at various orders a n in the scattering length are deduced and checked against the known analytical results at order a 1 and a 2. The limit a → ∞ is studied as a special case and a strong momentum dependence of the real (and imaginary) single-particle potential is found. This feature indicates an instability against a phase transition to a state with an empty shell inside the Fermi sphere such that the density gets reduced by about 5%. The imaginary single-particle potential vanishes linearly at the Fermi surface. For comparison, the same analysis is performed for the resummed particle-particle ladder diagrams alone. In this truncation an instability for hole excitations near the Fermi surface is found at strong coupling. For the set of particle-hole ring diagrams the single-particle potential is calculated as well. Furthermore, the resummation of in-medium ladder diagrams to all orders is studied for a two-dimensional Fermi gas with a short-range two-body contact interaction.

Superconductivity and antiferromagnetism in cuprates and pnictides: Evidence of the role of Coulomb correlation

We consider the Hubbard model in terms of the perturbative diagrammatic approach (UNF⩽1) where the interaction between two electrons with antiparallel spins in the lowest order of perturbation is described by the short-range repulsive contact (on-site) interaction (U>0). We argue that in layered 2D cuprates the long-range order antiferromagnetism is driven mainly by the Van Hove singularity, whereas in the case of pnictides the antiferromagnetism exists as a result of the nesting condition. We show that when the interaction is quite strong (UNF≈1) in the case of the Van Hove singularity the electron system undergoes the antiferromagnetic phase transition with the log-range order parameter and large insulating gap. The long-range antiferromagnetism quickly disappear, as shown, with the doping away from the Van Hove singularity, but the antiferromagnetic short-range correlation persists (UNF<1) due to Coulomb repulsive interaction which is the mechanism for superconductivity in cuprates. We argue that in the case of pnictides the antiferromagnetism appears when the nesting conditions for the Fermi surface are met. Since the doping steadily changes the nesting conditions, the antiferromagnetism and superconductivity may coexist as has been observed in pnictides. We show that the proximity of the antiferromagnetism and superconductivity implies the repulsive interaction between electrons, which turns into attractive between quasiparticles as shown by the authors in the article published on the same issue as this one and entitled “Superconductivity from a Fermi Liquid: The Role of Electron-Phonon Interaction”, and the superconductivity in the nearly antiferromagnetic Fermi liquid exists as a result of the repulsive interaction.

Beyond mean-field low-lying excitations of dipolar Bose gases

We theoretically investigate various beyond mean-field effects on Bose gases at zero temperature featuring the anisotropic and long-range dipole-dipole interaction in addition to the isotropic and short-range contact interaction. Within the realm of the Bogoliubov--de Gennes theory, we consider static properties and low-lying excitations of both homogeneous and harmonically trapped dipolar bosonic gases. For the homogeneous system, the condensate depletion, the ground-state energy, the equation of state, and the speed of sound are discussed in detail. Making use of the local density approximation, we extend these results in order to study the properties of a dipolar Bose gas in a harmonic trap and in the regime of large particle numbers. After deriving the equations of motion for the general case of a triaxial trap, we analyze the influence of quantum fluctuations on important properties of the gas, such as the equilibrium configuration and the low-lying excitations in the case of a cylinder-symmetric trap. In addition to the monopole and quadrupole oscillation modes, we also discuss the radial quadrupole mode. We find that the latter acquires a quantum correction exclusively due to the dipole-dipole interaction. As a result, we identify the radial quadrupole as a reasonably accessible source for the signature of dipolar many-body effects and stress the enhancing character that dipolar interactions have for quantum fluctuations in the other oscillation modes.

Dipolar Bose-Einstein condensate in a ring or in a shell

We study properties of a trapped dipolar Bose-Einstein condensate (BEC) in a circular ring or a spherical shell using the mean-field Gross-Pitaevskii equation. In the case of the ring-shaped trap we consider different orientations of the ring with respect to the polarization direction of the dipoles. In the presence of long-range anisotropic dipolar and short-range contact interactions, the anisotropic density distribution of the dipolar BEC in both traps is discussed in detail. The stability condition of the dipolar BEC in both traps is illustrated in phase plot of dipolar and contact interactions. We also study and discuss the properties of a vortex dipolar BEC in these traps.

Strongly interacting bosons in a one-dimensional optical lattice at incommensurate densities

We investigate quantum phase transitions occurring in a system of strongly interacting ultracold bosons in a 1D optical lattice. After discussing the commensurate-incommensurate transition, we focus on the phases appearing at incommensurate filling. We find a rich phase diagram, with superfluid, supersolid and solid (kink-lattice) phases. Supersolids generally appear in theoretical studies of systems with long-range interactions; our results break this paradigm and show that they may also emerge in models including only short-range (contact) interactions, provided that quantum fluctuations are properly taken into account.

Integrability breakdown in longitudinaly trapped, one-dimensional bosonic gases

A system of identical bosons with short-range (contact) interactions is studied. Their motion is confined to one dimension by a tight lateral trapping potential and, additionally, subject to a weak harmonic confinement in the longitudinal direction. Finite delay time associated with penetration of quantum particles through each other in the course of a pairwise one-dimensional collision in the presence of the longitudinal potential makes the system non-integrable and, hence, provides a mechanism for relaxation to thermal equilibrium. To analyse this effect quantitatively in the limit of a non-degenerate gas, we develop a system of kinetic equations and solve it for small-amplitude monopole oscillations of the gas. The obtained damping rate is long enough to be neglected in a realistic cold-atom experiment, and therefore longitudinal trapping does not hinder integrable dynamics of atomic gases in the 1D regime.

Exceptional Points for Nonlinear Schroedinger Equations Describing Bose-Einstein Condensates of Ultracold Atomic Gases

The coalescence of two eigenfunctions with the same energy eigenvalue is not possible in Hermitian Hamiltonians. It is, however, a phenomenon well known from non-hermitian quantum mechanics. It can appear, e.g., for resonances in open systems, with complex energy eigenvalues. If two eigenvalues of a quantum mechanical system which depends on two or more parameters pass through such a branch point singularity at a critical set of parameters, the point in the parameter space is called an exceptional point. We will demonstrate that exceptional points occur not only for non-hermitean Hamiltonians but also in the nonlinear Schroedinger equations which describe Bose-Einstein condensates, i.e., the Gross-Pitaevskii equation for condensates with a short-range contact interaction, and with additional long-range interactions. Typically, in these condensates the exceptional points are also found to be bifurcation points in parameter space. For condensates with a gravity-like interaction between the atoms, these findings can be confirmed in an analytical way.

Cellular Particle Dynamics Simulation Of Bioprinted 3d Tissue Constructs

Previous studies have shown that under certain conditions living tissues and multicellular aggregates behave as highly visco-elastic liquids. Tissue liquidity, brought about by cellular adhesion and motility, forms the basis of the newly developed bioprinting technology, which is used to design and build 3D tissue constructs by employing computer-controlled layer-by-layer deposition of bioink (submillimeter size cell aggregate) droplets onto biopaper (biocompatible gel). In order to describe and predict the self-assembly process of bioprinted multicellular constructs we have developed a computer simulation method referred to as cellular particle dynamics (CPD). In CPD cells are modeled as an ensemble of cellular particles (CPs) that interact via short range contact interactions, characterized by an attractive (adhesive interaction) and a repulsive (excluded volume interaction) component. The time evolution of the spatial conformation of the multicellular system is determined directly by recording the trajectories of all CPs through integration of their equations of motion. The cellular level CP model parameters are related to the experimentally measurable tissue level biophysical quantities (e.g., surface tension, viscosity and shear modulus) by comparing the results from selected benchmark experiments (e.g., compression and fusion of spherical cell aggregates) with those from the corresponding CPD simulations. Here we apply the CPD method to describe and predict in silico the post-bioprinting time evolution of the formation of tubular multicellular structures (which resemble primitive blood vessels). Our CPD simulations take substantially less time and effort than the corresponding experiments and, most importantly, provide results in good agreement with the experimental ones.Work supported by the National Science Foundation [FIBR-0526854]. Computer time provided by the University of Missouri Bioinformatics Consortium.

Equilibrium Electrostatics of Responsive Polyelectrolyte Monolayers

The physical behavior of polyelectrolytes at solid-liquid interfaces presents challenges both in measurement and in interpretation. An informative, yet often overlooked, property that characterizes the equilibrium organization of these systems is their membrane or rest potential. Here a general classification scheme is presented of the relationship between the rest potential and structural response of polyelectrolyte films to salt concentration. A numerical lattice theory, adapted from the polymer community, is used to analyze the rest potential response of end-tethered polyelectrolyte layers in which electrostatics and short-range contact interactions conspire to bring about different structural states. As an experimental quantity the rest potential is a readily accessible, nonperturbing metric of the equilibrium structure of a polyelectrolyte layer. A first set of measurements is reported on monolayers of end-tethered, single-stranded DNA in monovalent (NaCl) and divalent (MgCl(2)) counterion environments. Intriguingly, in NaCl electrolyte at least two different mechanisms appear by which the DNA layers can structurally relax in response to changing salt conditions. In MgCl(2) the layers appear to collapse. The possible molecular mechanisms behind these behaviors are discussed. These studies provide insight into phenomena more generally underlying polyelectrolyte applications in the chemical, environmental, and biotechnological fields.

Stabilization of a purely dipolar quantum gas against collapse

For the first time, a purely dipolar quantum gas has been prepared experimentally. Different regimes have been explored; in some, the gas is stable, whereas in others it collapses due to the strong dipole–dipole interaction between the constituent atoms. Although the phenomenon of Bose–Einstein condensation1 is a purely statistical effect that also appears in an ideal gas, the physics of Bose–Einstein condensates (BECs) of dilute gases is considerably enriched by the presence of interactions among the atoms. In usual experiments with BECs, the only relevant interaction is the isotropic and short-range contact interaction, which is described by a single parameter, the scattering length a. In contrast, the dipole–dipole interaction between particles possessing an electric or magnetic dipole moment is of long-range character and anisotropic, which gives rise to new phenomena2,3. Most prominently, the stability of a dipolar BEC depends not only on the value of the scattering length, a, but also strongly on the geometry of the external trapping potential4,5,6,7. Here, we report on the experimental investigation of the stability of a dipolar BEC of 52Cr as a function of the scattering length and the trap aspect ratio. We find good agreement with a universal stability threshold arising from a simple theoretical model. Using a pancake-shaped trap with the dipoles oriented along the short axis of the trap, we are able to tune the scattering length to zero, stabilizing a purely dipolar quantum gas.

Folding of polymer chains with short-range binormal interactions

We study the structure of chains which have anisotropic short-range contact interactions that depend on the alignment of the binormal vectors of chain segments. This represents a crude model of hydrogen bonding or 'stacking' interactions out of the plane of curvature. The polymers are treated as ribbon-like semi-flexible chains, where the plane of the ribbon is determined by the local binormal. We show that with dipole–dipole interactions between the binormals of contacting chain segments, mean-field theory predicts a first-order transition to a binormally aligned state. We describe the onset of this transition as a function of the temperature-dependent parameters that govern the chain stiffness and the strength of the binormal interaction, as well as the binormal alignment's coupling to chain collapse. We also examine a metastable state governing the folding kinetics. Finally, we discuss the possible mesoscopic structure of the aligned phase, and application of our model to secondary structure motifs like β-sheets and α-helices, as well as composite structures like β-(amyloid) fibrils.

Weak violation of universality for polyelectrolyte chains: Variational theory and simulations

A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in $d$ dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length $N$. We find $R \simeq N^{\nu}(\log N)^{\gamma}$ where $\nu = \frac{3}{\lambda+2}$ and $\lambda$ is the exponent which characterize the long-range interaction $U \propto 1/r^{\lambda}$. The exponent $\gamma$ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings, by a direct numerical minimization of the variational energy for chains of increasing size $2^4<N<2^{15}$. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte Carlo simulation for chains of length $2^4<N<2^{10}$. The non universal behavior of the exponent $ \gamma$ previously derived within the variational method, is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in $d=3$ dimension. Particular attention is devoted to the homopolymer chain problem, when short range contact interactions are present.