Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order

We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, a, which is large compared to the range of the interaction, ?. The amplitude for the scattering of one boson off a bound state of the other two is computed to next-to-next-to-leading order (N²LO) in the ?/a expansion. At this order, two pieces of three-body data are required as input in order to renormalize the amplitude (for fixed a). We apply our results to a model system of three Helium-4 atoms, which are assumed to interact via the TTY potential. We generate N²LO predictions for atom-dimer scattering below the dimer breakup threshold using the bound-state energy of the shallow Helium-4 trimer and the atom-dimer scattering length as our two pieces of three-body input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N²LO phase- shift predictions will receive higher-order corrections of < 0.2 %. In contrast, the prediction of SREFT for the binding energy of the “deep” trimer of Helium-4 atoms displays poor convergence.     

Solution of Evolution Equation for Longitudinal Structure Function F L upto Next-to-Next-to-Leading Order and Its t-Evolution at Small-x

The aim of the present paper is to calculate longitudinal structure function F _L from QCD (Quantum Chromodynamics) evolution equation in next-to-next-to-leading order (NNLO) at small-x. The calculation of F _L is important for the phenomenological study of gluon distribution function inside the nucleon. Here we use Taylor Series Expansion method to solve the evolution equation for small-x and thus obtain t-evolution of F _L structure function. The calculated results are compared with H1 and ZEUS data and results of Block and Donnachie-Landshoff (DL) models.     

Ground and Low-Lying Collective States of Rotating Three-Boson System

The ground and low-lying collective states of a rotating system of N=3 bosons harmonically confined in quasi-two-dimension and interacting via repulsive finite-range Gaussian potential is studied in weakly to moderately interacting regime.The N-body Hamiltonian matrix is diagonalized in subspaces of quantized total angular momenta 0 ≤ L ≤ 4N to obtain the ground and low-lying eigenstates.Our numerical results show that breathing modes with N-body eigenenergy spacing of 2hω⊥,known to exist in strictly 2D system with zero-range(δ-function) interaction potential,may as well exist in quasi-2D system with finite-range Gaussian interaction potential.To gain an insight into the many-body states,the von Neumann entropy is calculated as a measure of quantum correlation and the conditional probability distribution is analyzed for the internal structure of the eigenstates.In the rapidly rotating regime the ground state in angular momentum subspaces L=(q/2)N(N-1) with q=2,4 is found to exhibit the anticorrelation structure suggesting that it may variationally be described by a Bose–Laughlin like state.We further observe that the first breathing mode exhibits features similar to the Bose–Laughlin state in having eigenenergy,von Neumann entropy and internal structure independent of interaction for the three-boson system considered here.On the contrary,for eigenstates lying between the Bose–Laughlin like ground state and the first breathing mode,values of eigenenergy,von Neumann entropy and internal structure are found to vary with interaction.     

Feature of Low-Lying States of a Planar Three-Boson System

The energy spectrum of the low-lying states of a system of three charged bosons confined in a two-dimensional harmonic trap is investigated as a function of the confinement strength ω₀ by means of the exact diagonalization of the Hamiltonian. The important feature of the low-lying states of three charged bosons in two-dimensional space is obtained via an analysis of the energy spectrum.     

Evolutions of Longitudinal Structure Function F L upto Next-to-Next-to-Leading Orders at Small-x

We compute the longitudinal structure function F _L of proton from its QCD (Quantum Chromodynamics) evolution equation in next-to-next-to-leading order (NNLO) approximation at small-x. Here we use Taylor series expansion method to solve the evolution equation for small-x and the obtained simple analytical expressions for F _L provide t- and x-evolution equations for the computation of the longitudinal structure function. Finally, we compare our results with the recent H1, ZEUS experimental data and results of MSTW, CT10 parameterizations and Block, Donnachie-Landshoff (DL) models. Our results are in good agreement with the data and the related fittings and parameterizations, which can also be described within the framework of perturbative QCD.     

Unified Analysis of the Structures of Three-Boson and Three-Fermion Systems

A model system of three identical particles was examined to understand the features of its structure. The low-lying states having different sets of quantum numbers and obeying different permutation symmetries were studied in a unified way, though only qualitatively. It was found that the constraints imposed by quantum-mechanical symmetry on the wave functions are embodied in inherent nodal surfaces, which affect the structures and the ways of excitation decisively. The origin of a number of rotational bands has been clarified. Features in the low-lying spectrum have been revealed. Received April 10, 1996; revised September 27, 1996; accepted for publication November 27, 1996     

Conformally Invariant Quantization at Order Three

Let (M, g) be a pseudo-Riemannian manifold and the space of densities of degree on M. Denote the space of differential operators from to of order k and S _k with = – the corresponding space of symbols. We construct (the unique) conformally invariant quantization map . This result generalizes that of Duval and Ovsienko.     

Bruhat Order in Full Symmetric Toda System

In this paper we discuss some geometrical and topological properties of the full symmetric Toda system. We show by a direct inspection that the phase transition diagram for the full symmetric Toda system in dimensions n = 3, 4 coincides with the Hasse diagram of the Bruhat order of symmetric groups S ₃ and S ₄. The method we use is based on the existence of a vast collection of invariant subvarieties of the Toda flow in orthogonal groups. We show how one can extend it to the case of general n. The resulting theorem identifies the set of singular points of dim = n Toda flow with the elements of the permutation group S _n , so that points will be connected by a trajectory, if and only if the corresponding elements are Bruhat comparable. We also show that the dimension of the submanifolds, spanned by the trajectories connecting two singular points, is equal to the length of the corresponding segment in the Hasse diagram. This is equivalent to the fact that the full symmetric Toda system is in fact a Morse–Smale system.     

On Deeply Virtual Compton Scattering at Next-to-Leading Order

Deeply virtual Compton scattering in the near forward kinematic region is the golden access to Generalized Parton Distributions. We studied the \({\mathcal{O}(\alpha_S)}\) corrections to the scattering amplitude for both spacelike and timelike kinematics relevant respectively to the leptoproduction of a real photon and to the photoproduction of a lepton pair. It turns out that these corrections are phenomenologically important and that the gluonic contributions are by no means negligible, even in the moderate energy range of JLab12 and of the COMPASS-II experiment at CERN.     

Order transition at the threshold for self-excited laser pulses

The laser-light field is shown to undergo a discontinuous order transition at the threshold for mode-locked pulses, accompanied by critical fluctuations below the transition point. These observations confirm theoretical predictions from the laser equations for a simplified model when incoherent interaction is included.     

Light Hypernuclei Based on Chiral Interactions at Next-to-Leading Order

We present predictions for the binding energies of the light hypernuclei \({^3_\Lambda{\rm H},\, ^4_\Lambda{\rm He}}\) and \({^4_\Lambda{\rm H}}\) based on Faddeev- and Yakubovsky equations in momentum space. We discuss how such results can help to test the existing hyperon–nucleon (Y N) potential models and effective field theory based Y N interactions. Especially, we show results for the chiral interactions at next-to-leading order.     

Order transition at the threshold for self-excited laser pulses

The laser-light field is shown to undergo a discontinuous order transition at the threshold for mode-locked pulses, accompanied by critical fluctuations below the transition point. These observations confirm theoretical predictions from the laser equations for a simplified model when incoherent interaction is included.     

Nonperiodic Long-Range Order for Fast-Decaying Interactions at Positive Temperatures

We present the first example of an exponentially decaying interaction which gives rise to nonperiodic long-range order at positive temperatures.     

3H at Next-to-Next-to-Next-to Leading Order of the Chiral Expansion

The chiral three-nucleon force (3NF) at next-to-next-to-next-to leading order (N³LO) is used to calculate the triton wave function and the doublet nucleon–deuteron scattering length. This allows us to fix the values of the low-energy constants which are free parameters of the theory. The obtained values of these parameters, the expectation values of the kinetic energy, two- and three-body potentials and individual contributions of different parts of 3NF are given.     

The Interfacial Profile in Two-Loop Order

The profile of interfaces separating different phases of statistical systems is investigated in the framework of renormalized field theory. The profile function is calculated analytically in the local potential approximation, using the effective potential to two loops. It can be interpreted as an intrinsic interfacial profile. The loop corrections to the leading tanh-type term turn out to be small. They yield a broadening of the interface.     

Order Parameter in Electron System: Its Fluctuations and Oscillations

Journal of Experimental and Theoretical Physics - The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is...     

Structure Model of a One-Dimensional Disordered System with Short-Range Order

An ensemble of disordered linear chains is described by a probability density distribution without making use of the laws of thermodynamical equilibrium statistics. Short-range order is present in the system, because the position of an arbitrary particle depends on the location of the nearest neighbours. The nearest neighbour distance statistics is assumed to be of the Gaussian type. All correlation functions are calculated for finite and infinite systems. The superposition approximation is found to hold rigorously. The pair correlation is of fundamental importance for the system. The radial pair distribution function is investigated thoroughly. The configurational entropy of the system is calculated and discussed.