Zero-range Model Research Articles

Generation of vortex electrons in tunneling ionization of polyatomic molecules: Exact results in the zero-range potential model

Generation of vortex electrons in tunneling ionization of polyatomic molecules: Exact results in the zero-range potential model

On a Class of Solvable Stationary Non Equilibrium States for Mass Exchange Models

We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of reversible models for which the product invariant measure is known and the gradient condition is satisfied so that we can explicitly compute the transport coefficients associated to the diffusive hydrodynamic rescaling. Based on the Macroscopic Fluctuation Theory (Bertini et al. in Rev Mod Phys 87:593–636, 2015) we have that the large deviations rate functional for a stationary non equilibrium state can be computed solving a Hamilton–Jacobi equation depending only on the transport coefficients and the details of the boundary sources. Thus, we are able to identify a class of models having transport coefficients for which the Hamilton–Jacobi equation can indeed be solved. We give a complete characterization in the case of generalized zero range models and discuss several other cases. For the generalized zero range models we identify a class of discrete models that, modulo trivial extensions, coincides with the class discussed in Frassek and Giardinà (J Math Phys 63(10):103301–103335, 2022) and a class of continuous dynamics that coincides with the class in Franceschini et al. (J Math Phys 64(4): 043304–043321, 2023). Along the discussion we obtain a complete characterization of reversible misanthrope processes solving the discrete equations in Cocozza-Thivent (Z Wahrsch Verw Gebiete 70(4):509–523, 1985).

XUV Rectification Effect in the IR-Dressed Medium.

We show that the quasistatic dipole moment can be induced by a short extreme ultraviolet (XUV) pulse (XUV rectification effect) in atomic gas medium subjected to an intense infrared (IR) field (IR-dressed atoms). The general theory of the XUV rectification effect for a single IR-dressed atom is presented, which explicitly relates IR-modified polarizability of an atomic system in the XUV range with the induced quasistatic dipole moment. We illustrate general properties of the XUV rectification effect in an atomic system within the analytical zero-range potential model by presenting the dependence on the IR-field intensity and the time delay between XUV and IR pulses.

On the adiabatic approximation for the laser-dressed atom

The adiabatic approximation is analyzed for non-perturbative interaction of an atomic system with an intense low-frequency laser field. We find that the well-known adiabatic ansatz, which consists in using the DC-based Green’s and wave functions for an atom in the instantaneous AC field to calculate transition matrix elements, exceeds the level of accuracy of the adiabatic approximation and requires further theoretical revision. It is shown that the non-analyticity in the field strength of the DC-based Green’s and wave functions leads to violation of the adiabaticity constrains and the appearance of rapidly oscillating components in the transition matrix elements. We suggest an improved adiabatic approach utilizing the analytical parts in the DC-based Green’s and wave functions. We illustrate our revised adiabatic approach for analysis of atomic polarizability in two-component laser field with an intense infrared and perturbative extreme ultraviolet components within the zero-range potential model.

Finite-range bias in fitting three-body loss to the zero-range model

Three-body recombination loss in ultracold atoms is a central process for studying universal few-body systems. Here, the authors discuss a systematic error that occurs when analyzing this loss mechanism with zero-range models.

Double thresholds distort the line shapes of the PψsΛ(4338)0 resonance

Very recently, the LHCb Collaboration reported the first observation of the hidden-charm pentaquark with strangeness, ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}(4338{)}^{0}$. Considering this state is very close to the ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\overline{D}}^{0}$ and ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}{D}^{\ensuremath{-}}$ thresholds, we explore the possible bias of the Breit-Wigner parametrization, with emphasis on the effect of its coupling to the double thresholds ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\overline{D}}^{0}$ and ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}{D}^{\ensuremath{-}}$. We first use a qualitative picture based on the ``uniformization'' of the Riemann surface of the two-channel system to understand the positions of the enhancement. Then we use the Lippmann-Schwinger equation formalism (equivalent to the $K$-matrix parametrization) with two models, the zero-range model and the Flatt\'e model to investigate the $J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}$ line shapes. Our results show that the nominal peak of the ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}(4338{)}^{0}$ could arise either from the pole well above the ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}{D}^{\ensuremath{-}}$ threshold on the $(\ensuremath{-},+)$ sheet or from the pole well below the ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\overline{D}}^{0}$ threshold on the $(\ensuremath{-},\ensuremath{-})$ sheet in the two-channel system. Using the Breit-Wigner distribution to depict the above two line shapes could be misleading. We also find a novel type of line shapes with the enhancement constrained by the threshold difference. We urge the LHCb Collaboration to perform the refined experimental analysis considering the unitarity and analyticity, e.g., using the $K$-matrix parametrization. As a by-product, we obtain that the ratio of the isospin violating decay ${\mathrm{\ensuremath{\Gamma}}}_{{P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}\ensuremath{\rightarrow}J/\ensuremath{\psi}\mathrm{\ensuremath{\Sigma}}}/{\mathrm{\ensuremath{\Gamma}}}_{{P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}\ensuremath{\rightarrow}J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}}$ could be up to 10%.

Three-body recombination in a single-component Fermi gas with p -wave interaction

We study the three-body recombination of identical fermionic atoms. Using a zero-range model for the $p$-wave interaction, we show that the rate constant of three-body recombination into weakly bound $p$-wave dimers can be written as $\alpha_{\rm rec} \propto v^{5/2}R^{1/2} k_T^4 (1+ C k_T^2 l_{\rm d}^2)$ for large and positive scattering volume $v$. Here $R$ is the $p$-wave effective range, $k_T^2$ gives the average thermal kinetic energy of the colliding atoms, and $l_{\rm d}$ is the size of the $p$-wave dimer. The leading term is different from the usually stated $v^{8/3}$-scaling law, but is consistent with an earlier two-channel calculation. For the subleading term, we compute the constant $C$ by solving the relevant three-body problem perturbatively when the parameter $\gamma\equiv R/v^{1/3}$ is small. The additional $C k_T^2 l_{\rm d}^2$ term provides important corrections for the temperature and interaction dependence of $\alpha_{\rm rec}$, especially close to resonance when $k_T l_{\rm d}$ is relatively large.

Minlos–Faddeev Regularization of Zero-Range Interactions in the Three-Body Problem

To regularize the three-body problem, Minlos and Faddeev suggested a modification of zero-range model, which diminishes interaction at the triple-collision point. The analysis reveals that this regularization results in four alternatives depending on the regularization parameter $ \sigma $. Explicitly, Efimov or Thomas effects remain for $ \sigma < \sigma_c $, the additional boundary conditions of two types should be imposed at the triple-collision point for $ \sigma_c \le \sigma < \sigma_e $ and $ \sigma_e < \sigma < \sigma_r $, and the problem is regularized for $ \sigma \ge \sigma_r $. Critical values $ \sigma_c < \sigma_e < \sigma_r $ separating different alternatives are determined both for a two-component three-body system and for three identical bosons.

Constraining equation of state of nuclear matter by charge-changing cross section measurements of mirror nuclei

The nuclear symmetry energy plays a key role in determining the equation of state (EoS) of dense, neutron-rich matter, which connects the atomic nuclei with the hot and dense matter in universe, thus has been the subject of intense investigations in laboratory experiments, astronomy observations and theories. Various probes have been proposed to constrain the symmetry energy and its density dependence. Currently, the extensive data yield already a good and consistent constraint to the symmetry energy (Esym(ρ)) at saturation density, but do not yet give a consistent result of one critical EoS parameter, L, the density dependence of the symmetry energy. In this work, we report a new probe of L at saturation density. A good linear correlation is found between L and the charge changing cross section difference (Δσcc) of mirror nuclei 30Si-30S for both the Skyrme-Hartree-Fock theory (SHF) and covariant (relativistic) density functionals (CDF). We found that the pairing effect for this mirror pair is essential to get a consistent correlation between L and Δσcc in both the SHF and CDF. Here, the cross sections are calculated on the same target and at the same energy using the zero-range optical-limit Glauber model. The linearity is found to be in the same precision as those found between L and neutron skin thickness or proton radius difference.

Finite-range effects in the unitary Fermi polaron

Quantum Monte Carlo techniques are employed to study the properties of polarons in an ultracold Fermi gas, at $T=0$, and in the unitary regime using both a zero-range model and a square-well potential. For a fixed density, the potential range is varied and results are extrapolated and compared against a zero-range model. A discussion regarding the choice of an interacting potential with a finite range is presented. We compute the polaron effective mass, the polaron binding energy, and the effective coupling between them. The latter is obtained using the Landau-Pomeranchuk's weakly interacting quasiparticle model. The contact parameter is estimated by fitting the pair distribution function of atoms in different spin states.

Quantum Monte Carlo studies of a trimer scaling function with microscopic two- and three-body interactions

We present an energy scaling function to predict, in a specific range, the energy of bosonic trimers with large scattering lengths and finite range interactions, which is validated by quantum Monte Carlo calculations using microscopic Hamiltonians with two- and three-body potentials. The proposed scaling function depends on the scattering length, effective range, and a reference energy, which we chose as the trimer energy at unitarity. We obtained the scaling function as a limit cycle from the solution of the renormalized zero-range model with effective range corrections. We proposed a simple parametrization of the energy scaling function. Besides the intrinsic interest in theoretical and experimental investigations, this scaling function allows one to probe Efimov physics with only the trimer ground states, which may open opportunities to identify Efimov trimers whenever access to excited states is limited.

Long-range Rydberg molecule Rb2 : Two-electron R -matrix calculations at intermediate internuclear distances

The adiabatic potential energy curves of Rb$_2$ in the long-range Rydberg electronic states are calculated using the two-electron \textit{R}-matrix method [M. Tarana, R. \v{C}ur\'{i}k, Phys. Rev. A \textbf{93}, 012515 (2016)] for the intermediate internuclear separations between 35 a.u. and 200 a.u. The results are compared with the zero-range models to find a region of the internuclear distances where the Fermi's pseudopotential approach provides accurate energies. A finite-range potential model of the atomic perturber is used to calculate the wave functions of the Rydberg electron and their features specific for the studied range of internuclear distances are identified.

Scattering of cold He4 on He4Li6,7 and He4Na23 molecules

We predict $s-$wave elastic cross-sections $\sigma$ for low-energy atom-molecule collisions with kinetic energies up to 40 mK, for the $^4$He collision with weakly bound diatomic molecules formed by $^4$He with $^7$Li, $^6$Li and $^{23}$Na. Our scattering calculations are performed by using diatomic and triatomic molecular binding energies obtained from several available realistic models as input in a renormalized zero-range model, as well as a finite-range one-term separable potential in order to quantify the relevance of range corrections to our predictions. Of particular relevance for possible experimental realization, we show the occurrence of a zero in $\sigma$ for the collision of cold $^4$He on $^4$He$-^{23}$Na molecule below 20 mK. Also our results for the elastic collision $^4$He on $^4$He$-^{6,7}$Li molecules suggest that $\sigma$ varies considerably for the realistic models studied. As the chosen molecules are weakly bound and the scattering energies are very low, our results are interpreted on the light of the Efimov physics, which explains the model independent and robustness of our predictions, despite some sensitivity on the potential range.

Harmonically trapped four-boson system

Four identical spinless bosons with purely attractive two-body short-range interactions and repulsive three-body interactions under external spherically symmetric harmonic confinement are considered. The repulsive three-body potential prevents the formation of deeply-bound states with molecular character. The low-energy spectrum with vanishing orbital angular momentum and positive parity for infinitely large two-body $s$-wave scattering length is analyzed in detail. Using the three-body contact, states are classified as universal, quasi-universal, or strongly non-universal. Connections with the zero-range interaction model are discussed. The energy spectrum is mapped out as a function of the two-body $s$-wave scattering length $a_s$, $a_s>0$. In the weakly- to medium-strongly-interacting regime, one of the states approaches the energy obtained for a hard core interaction model. This state is identified as the energetically lowest-lying "BEC state". Structural properties are also presented.

Non-universal and universal aspects of the large scattering length limit

The momentum density, n(k) of interacting many-body Fermionic systems is studied (for k>kF) using examples of several well-known two-body interaction models. It is shown that n(k) can be approximated by a zero-range model for momenta k less than about 0.1/re, where re the effective range. If the scattering length is large and one includes the effects of a fixed value of re≠0, n(k) is almost universal for momenta k up to about 2/re. However, n(k) can not be approximated by a zero-range model for momenta k greater than about 1/(are2)1/3, where a is the scattering length, and if one wishes to maintain a sum rule that relates the energy of a two component Fermi-gas to an integral involving the density. We also show that the short separation distance, s, behavior of the pair density varies as s6.

How to initialize a second class particle?

We identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior, respectively (including zero-range, misanthrope and many other models). The initial condition is a step profile, which in some classical cases of asymmetric models, gives rise to a rarefaction fan scenario. We also point out a model with nonconcave, nonconvex hydrodynamics, where the rescaled second class particle distribution has both continuous and discrete counterparts. The results follow from a substantial generalization of Ferrari and Kipnis’ arguments (Ann. Inst. H. Poincare 31 (1995) 143–154) for the totally asymmetric simple exclusion process. The main novelty is the introduction of a signed coupling measure as initial data, which nevertheless results in a proper probability initial distribution for the site of the second class particle and makes the extension possible. We also reveal in full generality a very interesting invariance property of the one-site marginal distribution of the process underneath the second class particle which in particular proves the intrinsicality of our choice for the initial distribution. Finally, we give a lower estimate on the probability of survival of a second class particle–antiparticle pair.

Bound-free transitions in H + H– collisions

The processes of photo-detachment or ionization of stable molecules are widely investigated in modern atomic physics. But the present work deals with the calculation of the photo-detachment cross-sections in the case of negative quasi-molecules formed during collisions. The reaction H + H− + ħω → H + H + e has been taken as an example of bound-free transitions in single-active-electron quasi-molecules. For simplicity, we discuss the one-dimensional case in the frame of the zero-range potential model.

Emergent universality in the two-neutron halo structure of C22

The structure of the two-neutron halo $^{22}\mathrm{C}$ is investigated by means of a renormalized zero-range three-body model, with interactions in the $s$-wave channel, and a finite-range model with two- and three-body forces provided by the hyperspherical adiabatic expansion method. In both models the halo wave function in configuration space is obtained by using as inputs the two-body scattering lengths and the two-neutron separation energy. The halo-matter density is computed for $^{22}\mathrm{C}$ with different three-body forces and low-energy parameters, with two-neutron separation energy within the range $50\phantom{\rule{4.pt}{0ex}}\text{keV}\ensuremath{\le}{S}_{2n}\ensuremath{\le}1000$ keV. The halo-neutron density depends weakly on the neutron-$^{20}\mathrm{C}$ scattering length as long as its absolute value is larger than the neutron-neutron one. The halo-neutron density is then analyzed by means of the root-mean-square radius, the probability density, and also the geometry, taking into account the angle between the two Jacobi coordinates. The results of finite-range and zero-range two-neutron-core models are compared. The effects in the halo structure of short-range and long-range three-body forces are studied, and the emergent universal behavior of the halo-neutron density and its geometry is pointed out.

Blockage-induced condensation controlled by a local reaction.

We consider the setup of stationary zero range models and discuss the onset of condensation induced by a local blockage on the lattice. We show that the introduction of a local feedback on the hopping rates allows us to control the particle fraction in the condensed phase. This phenomenon results in a current versus blockage parameter curve characterized by two nonanalyticity points.

Core momentum distribution in two-neutron halo nuclei

The core momentum distribution of a weakly-bound neutron-neutron-core exotic nucleus is computed within a renormalized zero-range three-body model, with interactions in the s-wave channel. The halo wave-function in momentum space is obtained by using as inputs the two-body scattering lengths and the two-neutron separation energy. The core momentum densities are computed for $^{11}$Li, $^{14}$Be $^{20}$C and $^{22}$C. The model describes the experimental data for $^{11}$Li, $^{14}$Be and to some extend $^{20}$C. The recoil momentum distribution of the $^{20}$C from the breakup of $^{22}$C nucleus is computed for different two-neutron separation energies, and from the comparison with recent experimental data the two-neutron separation energy is estimated in the range $100\lesssim S_{2n}\lesssim 400$ KeV. The recoil momentum distribution depends weakly on the neutron-$^{20}$C scattering length, while the matter radius is strongly sensitive to it. The expected universality of the momentum distribution width is verified by also considering excited states for the system.