Large-distance Behavior Research Articles

Politico-Administrative Culture and Public Service Reform in Post-Independence Kazakhstan

Classical organizational management literature draws clear parallels between organizational culture and climate and effective use of power and influence as key to successful policy implementation of reforms in public sector organizations. On the other hand, the public policy literature, in particular, policy transfer as a strand within policy studies, emphasizes the role of the national context, more specifically, ‘facilitators’ and ‘constraints’ of ‘‘politico-administrative culture” within the national context, as crucial to understanding processes of transfer, convergence, and diffusion of public policy. There is a plethora of studies by Western scholars of public management who have successfully utilized these theoretical underpinnings to study the effectiveness of public service reforms in mature policy environments such as the UK, the US, Australia, New Zealand, and others. However, the public policy and comparative public management literature only offers a limited number of case studies from developing, middle-/upper-middle countries, which rely on concepts of organizational management in addition to narratives on the impact of policy learning from global doctrines, such as Weberianism, New Public Management (NPM), and New Public Governance (NPG), and national politics, on the implementation of administrative reforms in those contexts. Kazakhstan, as a resource-affluent post-Soviet country and a bastion of modernization and ‘open government’ in Central Asia or the Commonwealth of Independent States (CIS) in the post-Soviet era is a case in point. Based on ethnographic research consisting of interviews with elite academics, civil servants, and think-tank activists, as well as reviews of OECD and government strategy reports in Astana, the findings point to a potential abatement of the impact of context constraints such as large power distance and collectivist behavior by context facilitators such as those surrounding the use of ‘trilingualism’ and public diplomacy towards reforms in Kazakhstan particularly in recent years.

Brane profiles of non-supersymmetric strings

We connect the indications of 2D CFT for branes in non-supersymmetric strings to actual spacetime profiles, taking the bulk tadpole potentials into account. We find exact solutions for the uncharged branes that spread in the internal intervals of Dudas-Mourad vacua for non-tachyonic orientifolds and heterotic strings. These solutions involve suitable dressings of the uncharged branes of the nine-dimensional tadpole-free theory. Similar exact results for uncharged branes that are transverse to the internal space, or for charged branes, appear more challenging. Nevertheless, we identify their large-distance behavior, which is determined by linearized equations, and show that it is compatible with the CFT analysis in all expected cases. We also provide some hints on the leading back-reaction of the form-fields.

Effective interaction between guest charges immersed in 2D jellium

The model under study is an infinite 2D jellium of pointlike particles with elementary charge e, interacting via the logarithmic potential and in thermal equilibrium at the inverse temperature β. Two cases of the coupling constant Γ≡βe2 are considered: the Debye–Hückel limit Γ→0 and the free-fermion point Γ=2 . In the most general formulation, two guest particles, the one with charge qe (the valence q being an arbitrary integer) and the hard core of radius σ > 0 and the pointlike one with elementary charge e, are immersed in the bulk of the jellium at distance d⩾σ . Two problems are of interest: the asymptotic large-distance behavior of the excess charge density induced in the jellium and the effective interaction between the guest particles. Technically, the induced charge density and the effective interaction are expressed in terms of multi-particle correlations of the pure (translationally invariant) jellium system. It is shown that the separation form of the induced charge density onto its radial and angle parts, observed previously in the limit Γ→0 , is not reproduced at the coupling Γ=2 . Based on an exact expression for the effective interaction between guest particles at Γ=2 , oppositely ( q=0,−1,−2,… ) charged guest particles always attract one another while likely ( q=1,2,… ) charged guest particles repeal one another up to a certain distance d between them and then the mutual attraction takes place up to asymptotically large (finite) distances.

Flavor exotic triply-heavy tetraquark states in AdS/QCD potential

We study the S-wave mass spectra of flavor exotic triply-heavy tetraquark states ccbar{c}bar{q}, ccbar{b}bar{q}, bbbar{c}bar{q} and bbbar{b}bar{q}. We adopt a diquark–antidiquark scheme to solve Schrödinger equation. The calculations are carried out in a nonrelativistic quark model with a color interaction described by a potential computed in AdS/QCD. The AdS/QCD potential model consists of a central potential which reflects short distance and large distance behaviour of QCD, spin dependent term for hyperfine splitting and a constant term. We find stable state candidates in the ccbar{c}bar{q} sector whereas in the ccbar{b}bar{q}, bbbar{c}bar{q} and bbbar{b}bar{q} sectors all the states lie above corresponding S-wave meson-meson thresholds.

Asymptotically consistent analytical solutions for the non-Newtonian Sakiadis boundary layer

The Sakiadis boundary layer induced by a moving wall in a semi-infinite fluid domain is a fundamental laminar flow field relevant to high speed coating processes. This work provides an analytical solution to the boundary-layer problem for Ostwald–de Waele power law fluids via a power series expansion and extends the approach taken for Newtonian fluids [Naghshineh et al. “On the use of asymptotically motivated gauge functions to obtain convergent series solutions to nonlinear ODEs,” IMA J. of Appl. Math. 88, 43 (2023)] in which variable substitutions (which naturally determine the gauge function in the power series) are chosen to be consistent with the large distance behavior away from the wall. Contrary to prior literature, the asymptotic behavior dictates that a solution only exists in the range of power law exponents, α, lying in the range of 0.5<α≤1. An analytical solution is obtained in the range of approximately 0.74≤α<1, using a convergent power series with an asymptotically motivated gauge function. For power laws corresponding to 0.5<α<0.74, the gauge function becomes ill-defined over the full domain, and an approximate analytical solution is obtained using the method of asymptotic approximants [Barlow et al. “On the summation of divergent, truncated, and underspecified power series via asymptotic approximants,” Q. J. Mech. Appl. Math. 70, 21–48 (2017)]. The approximant requires knowledge of two physical constants, which we compute a priori using a numerical shooting method on a finite domain. The utility of the power series solution is that it can be solved on the entire semi-infinite domain and—in contrast to a numerical solution—does not require a finite domain length approximation and subsequent domain length refinement.

Imaging topological solitons: The microstructure behind the shadow

The authors study photon geodesics in the gravitational background generated by smooth horizonless topological solitons with the same large distance behaviour as neutral non-rotating black holes. They show that incoming photons experience very high redshift, inducing phenomenological horizon-like behaviors from the point of view of photon scattering. Thus, they provide a compelling case for real-world gravitational solitons and topological alternatives to black holes.

Precise determination of pair interactions from pair statistics of many-body systems in and out of equilibrium.

The determination of the pair potential v(r) that accurately yields an equilibrium state at positive temperature T with a prescribed pair correlation function g_{2}(r) or corresponding structure factor S(k) in d-dimensional Euclidean space R^{d} is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato [Phys. Rev. E 101, 032124 (2020)2470-004510.1103/PhysRevE.101.032124] conjectured that any realizable g_{2}(r) or S(k) corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised an optimization algorithm to precisely determine effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small-, intermediate- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function g_{2}(r) and structure factor S(k) so that the small intermediate- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point, (2) liquid under the Dzugutov potential, (3) nonequilibrium random sequential addition packing, and (4) a nonequilibrium hyperuniform "cloaked" uniformly randomized lattice. We found that the optimized pair potentials generate corresponding pair statistics that accurately match their corresponding targets with total L_{2}-norm errors that are an order of magnitude smaller than that of previous methods. The results of our investigation lend further support to the Zhang-Torquato conjecture. Furthermore, our algorithm will enable one to probe systems with identical pair statistics but different higher-body statistics, which will shed light on the well-known degeneracy problem of statistical mechanics.

Mediated Interaction between Ions in Quantum Degenerate Gases.

We explore the interaction between two trapped ions mediated by a surrounding quantum degenerate Bose or Fermi gas. Using perturbation theory valid for weak atom-ion interaction, we show analytically that the interaction mediated by a Bose gas has a power-law behavior for large distances whereas it has a Yukawa form for intermediate distances. For a Fermi gas, the mediated interaction is given by a power law for large density and by a Ruderman-Kittel-Kasuya-Yosida form for low density. For strong atom-ion interaction, we use a diagrammatic theory to demonstrate that the mediated interaction can be a significant addition to the bare Coulomb interaction between the ions, when an atom-ion bound state is close to threshold. Finally, we show that the induced interaction leads to substantial and observable shifts in the ion phonon frequencies.

Mobile impurity in a one-dimensional gas at finite temperatures

We consider the McGuire model of a one-dimensional gas of free fermions interacting with a single impurity. We compute the static one-body function and momentum distribution of the impurity at finite temperatures. The results involve averages over Fredholm determinants that we further analyse using the effective form factors approach. With this approach, we derive the large-distance behaviour of the one-body function, which takes the form of an averaged exponential decay. This method allows us to study an experimentally important regime of small momenta of the impurity's momentum distribution. We also consider the one-body function at short distances and compute finite temperature Tan's contact.

Density correlation functions and the spatial structure of the two-dimensional BEC-BCS crossover

The spatial structure of a two-dimensional homogeneous mixture of fermionic atoms in two hyperfine states is analyzed throughout the BEC-BCS crossover. Within the BCS-Leggett mean-field model we consider three functions: the pair wave function and the density-density correlation functions between atoms of the same and of different hyperfine states. For the correlation functions we derive analytical expressions which allow to unveil the rich spatial structure of the superfluid. Mainly, we are able to study the large-distance behavior of the three functions, which exhibits an exponential decay and a well-defined oscillatory behavior. We report closed-form expressions for the correlation lengths and mean pair radius. Differences and similarities emerge when comparing with the three dimensional case. Particularly, we find an expression for the large-distance correlation length, in terms of the chemical potential and the gap, valid in two and three dimensions, but whose dependence on the corresponding scattering lengths differ significantly.

Scaling feature of nano-scale friction based on the inverse statistical approach

Friction is known as a scaling phenomenon between rough surfaces. However, at the atomic scales, thermal fluctuations could be appreciated to scaling features. Previous studies revealed global information about the nano-friction fluctuations and showed that the fluctuations are multi-affine and correlated, and cannot be described by a white noise. In the present study, we are looking for local criteria which reveal the different features of nano-friction fluctuations and investigate whether the inverse Kolmogorov scaling is applied for the nano-friction fluctuations. If the inverse scaling is verified, we can say that kinetic energy which is converted into thermal energy, is dissipated from larger scales to smaller ones and is released at the atomic scales due to interatomic electrostatic forces. To this end, the friction force is determined using the atomic force microscope and tip dragging over the NaCl(001) surface. The minimal distance distributions for which the friction variation exceeds predefined values are studied. The results demonstrate that the dissipation distance distribution has a power-law behavior for large atomic distances as turbulence and the related exponent is determined. Furthermore, indicating the shuffled and surrogated probability distributions demonstrates that the rare friction differences are caused by the effect of both correlation and the probability distribution function. Although, it had been demonstrated that the atomic-scale friction of NaCl has a multi-scaling behavior, the current results indicate that inverse scaling is mono-fractal. It confirms that the energy loss dissipation is scaled from larger scales to the smallest atomic ones.

Two-body neutral Coulomb system in a magnetic field at rest: From hydrogen atom to positronium

A simple locally accurate uniform approximation for the nodeless wave function is constructed for a neutral system of two Coulomb charges of different masses $(\ensuremath{-}q,{m}_{1})$ and $(q,{m}_{2})$ at rest in a constant uniform magnetic field for the states of positive and negative parity, $(1{s}_{0})$ and $(2{p}_{0})$, respectively. It is shown that by keeping the mass and charge of one of the bodies fixed, all systems with different second-body masses are related. This allows one to consider the second body as infinitely massive and to take such a system as basic. Three physical systems are considered in detail: the hydrogen atom with (in)finitely massive proton (deuteron, triton) and the positronium atom $(\ensuremath{-}e,e)$. We derive the Riccati-Bloch and generalized Bloch equations, which describe the domains of small and large distances, respectively. Based on the interpolation of the small- and large-distance behavior of the logarithm of the wave function, a compact ten-parametric function is proposed. Taken as a variational trial function, it provides accuracy of not less than six significant digits (SDs) ($\ensuremath{\lesssim}{10}^{\ensuremath{-}6}$ in relative deviation) for the total energy in the whole domain of considered magnetic fields $[0\phantom{\rule{0.16em}{0ex}},\phantom{\rule{0.16em}{0ex}}{10}^{4}]$ a.u. and not less than three SDs for the quadrupole moment ${Q}_{zz}$. To get reference points, the Lagrange mesh method with 16 K mesh points was used to get from ten to six SDs in energy from small to large magnetic fields. Based on the Riccati-Bloch equation, the first 100 perturbative coefficients for the energy, in the form of rational numbers, are calculated and, using the Pad\'e-Borel resummation procedure, the energy is found with not less than ten SDs at magnetic fields $\ensuremath{\le}1\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$

Universality Classes of Hitting Probabilities of Jump Processes

Quantifying the efficiency of random target search strategies is a key question of random walk theory, with applications in various fields. If many results do exist for recurrent processes, for which the probability of eventually finding a target in infinite space-so called hitting probability-is one, much less is known in the opposite case of transient processes, for which the hitting probability is strictly less than one. Here, we determine the universality classes of the large distance behavior of the hitting probability for general d-dimensional transient jump processes, which we show are parametrized by a transience exponent that is explicitly given.

VPA: Computer program for the computation of the phase shift in atom–atom potential scattering using the Variable Phase Approach

A computer code for the computation of the phase shift in atom–atom and electron–atom potential scattering is presented. The phase shift is the central quantity required for the calculation of all types of scattering cross sections. The program uses the Variable Phase Approach (VPA). This is the only exact method for the direct calculation of the scattering phase shift. All other methods are based on examining the large distance behavior of the exact solution of the Schrödinger equation. Such methods yield the phase shift only modulo π. The absolute value of the phase shift and its variation with scattering energy is, however, needed for a full understanding of the scattering process, such as for instance in the study of shape resonances and Glory oscillations. The VPA has been sparingly used owing to the instability of the underlying equations and the consequent difficulty of writing computer code to solve them. We present a computer code for the efficient implementation of the VPA method for atom–atom scattering problems over a wide range of scattering energies. The code works for potentials which are singular and for those that are non-singular at the origin. An example of the implementation of the code is given for both an interaction potential with an attractive well and for a purely repulsive potential. Program summaryProgram title: VPA:Variable Phase ApproachCPC Library link to program files: https://dx.doi.org/10.17632/zh248d2362.1Code Ocean capsule: https://dx.doi.org/10.24433/CO.8146850.v1Licensing provisions: GNU General Public License 3 (GPL)Programming language: Fortran 90Nature of problem: To compute the quantum mechanical phase shift in an atom–atom or an electron–atom potential scattering problem. The interaction potential, dependent on a single radial coordinate, is defined by the user.Solution method: The Variable Phase Approach is used. This is the only available method for the direct calculation of the phase shift. The initial internuclear separation for the integration is chosen with the help of the analytical solution for a hard sphere core for all orbital angular momentum quantum numbers L of interest. The first-order nonlinear equation is integrated numerically with a modified LSODA19,20 program. The analytic formula for calculation of the Jacobian of the equation is also provided.Additional comments including restrictions and unusual features: Computer codes for the atom–atom interaction potential, POTENT1, and for its derivative with respect to the inter nuclear separation, DPOTENT1, must be supplied by a user. The calculation of the spherical Bessel and Neumann functions required is performed explicitly for large l angular momentum quantum numbers where the standard upward iterative generation of the functions becomes unstable.

Kernels for non interacting fermions via a Green’s function approach with applications to step potentials

The quantum correlations of N non interacting spinless fermions in their ground state can be expressed in terms of a two-point function called the kernel. Here we develop a general and compact method for computing the kernel in a general trapping potential in terms of the Green’s function for the corresponding single particle Schrödinger equation. For smooth potentials in one dimension the method allows a simple alternative derivation of the local density approximation for the density and of the sine kernel in the bulk part of the trap in the large N limit. It also recovers the density and the kernel of the so-called Airy gas at the edge. This method allows the analysis of the quantum correlations in the ground state when the potential has a singular part with a fast variation in space. For the square step barrier of height V 0 in one dimension, we derive explicit expressions for the density and for the kernel. For large Fermi energy μ > V 0 it describes the interpolation between two regions of different densities in a Fermi gas, each described by a different sine kernel. Of particular interest is the critical point of the square well potential when μ = V 0. In this critical case, while there is a macroscopic number of fermions in the lower part of the step potential, there is only a finite O(1) number of fermions on the shoulder, and moreover this number is independent of μ. In particular, the density exhibits an algebraic decay ∼1/x 2, where x is the distance from the jump. Furthermore, we show that the critical behavior around μ = V 0 exhibits universality with respect to the shape of the barrier. This is established (i) by an exact solution for a smooth barrier (the Woods–Saxon potential) and (ii) by establishing a general relation between the large distance behavior of the kernel and the scattering amplitudes of the single-particle wave-function.

Space Dimension Renormdynamics

We aim to construct a potential better suited for studying quarkonium spectroscopy. We put the Cornell potential into a more geometrical setting by smoothly interpolating between the observed small and large distance behaviour of the quarkonium potential. We construct two physical models, where the number of spatial dimensions depends on scale: one for quarkonium with Cornell potential, another for unified field theories with one compactified dimension. We construct point charge potential for different dimensions of space. The same problem is studied using operator fractal calculus. We describe the quarkonium potential in terms of the point charge potential and identify the strong coupling fine structure constant dynamics. We formulate renormdynamics of the structure constant in terms of Hamiltonian dynamics and solve the corresponding motion equations by numerical and graphical methods, we find corresponding asymptotics. Potentials of a nonlinear extension of quantum mechanics are constructed. Such potentials are ingredients of space compactification problems. Mass parameter effects are motivated and estimated.

Spatial structure of the pair wave function and the density correlation functions throughout the BEC-BCS crossover

By an exact numerical calculation of the BCS pair wavefunction and the density correlation functions both between atoms in the same and in different spin states, we extract the spatial large distance behavior of the respective functions. After different initial transients, those distributions show an algebraic dependence accompanied with their own exponential decay and a well defined periodic oscillatory behavior. While in general, in the BCS side there are long-range correlations and in the BEC region the behavior is dominated by tight pairs formation, each distribution shows its own overall behavior. We derive analytic expressions for the mean pair size and the correlation lengths of the same and different density correlation functions. The whole analysis yields a quite complete description of the spatial structure of the superfluid along the crossover.

Proof of the Absence of Long-Range Temporal Orders in Gibbs States

We address the question whether time translation symmetry can be spontaneously broken in a quantum many-body system. One way of detecting such a symmetry breaking is to examine the time-dependence of a correlation function. If the large-distance behavior of the correlation function exhibits a nontrivial time-dependence in the thermodynamic limit, the system would develop a temporal long-range order, realizing a time crystal. In an earlier publication, we sketched a proof for the absence of such time dependence in the thermal equilibrium described by the Gibbs state (Watanabe and Oshikawa in Phys Rev Lett 114:251603, 2015). Here we present a complete proof and extend the argument to a more general class of stationary states than the Gibbs states.

Diagrammatic method for tunable interactions in colloidal suspensions in rotating electric or magnetic fields.

Tunable interactions in colloids, induced by rotating electric or magnetic fields, provide a flexible and promising tool for self-assembly of soft materials, as well as for fundamental particle-resolved studies of phase transitions and other generic phenomena in condensed matter. In the case of two-dimensional systems and the in-plane rotating fields, the interactions are known to have a long-range (dipolar) attraction and an expressed three-body part at short distances, but still remain poorly understood. Here, we show that the interactions and polarization mechanisms governing the tunable interactions can be described, calculated, and analyzed in detail with the diagrammatic method we proposed. The diagrams yield a clear illustration of different polarization processes contributing to the Keesom, Debye, London, self, and external energies, classified in colloids similarly to intermolecular interactions. The real tunable interactions, obtained with the boundary element method, can be simply and accurately interpolated with the set of basis of the diagrams attributed to different physically clear polarization processes. Calculation of large-distance behavior and interpolation of the many-body interactions (and analysis of the leading mechanisms contributing to them) excellently illustrate that the diagrammatic method provides deep insights into the nature of tunable interactions. The method can be generalized for multicomponent systems, suspensions of particles with a composite structure and a complicated shape. The results provide significant advance in theoretical methods for detailed analysis of tunable interactions in colloids and, therefore, the method is of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Thermal fluctuations in crystalline membranes with long-range dipole interactions

We study the effects of long-range electrostatic interactions on the thermal fluctuations of free-standing crystalline membranes exhibiting spontaneous electric polarization directed at each point along the local normal to the surface. We show that the leading effect of dipole–dipole interactions in the long-wavelength limit consists in renormalizations of the bending rigidity and the elastic coefficients. A completely different result was obtained in the case of scalar two-point interactions decaying as R−3, where R is the distance. In the latter case, which was addressed in previous theoretical research, the energy of long-wavelength bending fluctuations is controlled by power-law interactions and it scales with the wavevector q as q3, leading to a modified large-distance behaviour of correlation functions. By contrast, in the case of dipole interactions, the q3 dependence of the bending energy vanishes. Non-local terms generated by the expansion of the electrostatic energy are suppressed in the limit of small wavevectors. This suggests that the universal scaling behaviour of elastic membranes holds even in presence of dipole interactions. At the same time, the shift of the Lamé coefficients and the bending rigidity induced by electrostatic interactions can be quantitatively important for two-dimensional materials with a permanent out-of-plane polarization.