Asymptotic Bethe ansatz for the Sutherland–Römer model with open boundary conditions

By constructing the reflection spin-Dunkl operators, the integrable Sutherland–Römer model (SRM) with open boundary condition is established, which describes a one-dimensional, two-component, quantum many-particle system in which like particles interact with a pair potential g(g+1)/sinh²(r), while unlike particles interact with a pair potential −g(g+1)/cosh²(r). By solving the Schrödinger equation and using the properties of the hypergeometric functions and gamma functions, the two-particle scattering matrix and the reflection matrix are obtained in the framework of the asymptotic Bethe ansatz method. The Bethe ansatz equations of the system are obtained. The Hamiltonians of SRM with some other open boundary conditions are expressed explicitly. Our method can be generalized, as a example, to the boundary Calogero–Sutherland model which is also constructed by the reflection spin-Dunkl operators.     

Inclusive production at large transverse momentum in QCD

We calculate the cross section for the process quark + quark → quark (with large transverse momentum) + anything, up to order g⁶ in the cross section and in the leading-logarithm approximation. The result is suggestive of a simple ansatz for the calculation of the asymptotic behaviour of cross sections for the production of particles or jets with large transverse momenta.     

Integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons

A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an application, the integrable open-boundary conditions for the q-deformed supersymmetric U model of strongly correlated electrons are investigated. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary system is solved by means of the coordinate space Bethe ansatz technique and the Bethe ansatz equations are derived. As a sideline, it is shown that all R-matrices associated with a quantum affine superalgebra enjoy the crossing-unitarity property.     

Dark viscous fluid coupled with dark matter and future singularity

Motivated by Kerner and Man’s fermions tunneling method of dimension 4 black holes, in this paper, we further improve the analysis to investigate Hawking radiation of charged Dirac particles with spin 1/2 from general non-extremal rotating charged black holes with two parameters and a non-zero cosmological constant in minimal five-dimensional gauged supergravity. For space-times with different horizon topology and different dimensions, constructing a set of appropriate γ ^μ matrices for general covariant Dirac equation is an important technique for the fermion tunneling method. By introducing a set of appropriate matrices γ ^μ and employing the ansatz for the spin-up spinor field, we successfully recovered the tunneling probability of charged Dirac particles and the expected Hawking temperature of the black hole, which is exactly consistent with that obtained by other methods. Moreover, the fermion tunneling method can be directly applied to the other five-dimensional charged black holes, which strengthens the validity and power of the fermion tunneling method.     

A non-perturbative approach to the infrared problem in QED: Construction of charged states

A non-perturbative treatment of the infrared problem in quantum electrodynamics is presented. Starting from the local and covariant correlation functions of the Gupta-Bleuler formulation an explicit construction of the physical charged states is given. They are shown to satisfy a non-(Lorentz) covariant infrared condition, of Bloch-Nordsieck type, compatible with the Gupta-Bleuler condition (resolution of Zwanziger's paradox). The breaking of the Lorentz group in the charged sectors and its physical meaning is explained. The infrared structure of the S-matrix elements between physical charged states is shown to be that of the classical Bloch-Nordsieck factors, (proof of the Bloch-Nordsieck ansatz), and to be simply related to that calculated by using local covariant states.     

Some effects of the electrostatic interaction of water drops in the atmosphere

The electric field at the surface of two conducting spherical charged particles and their interaction force are calculated. It is shown that as particles carrying like charge approach each other, the force changes sign and becomes attractive. The case where the charge on each particle varies as the square of its radius is an exception (repulsion at any distance between the particles). Self-similar asymptotic solutions for the interaction force and energy are found for particles of identical size. For a pair of charged water drops falling simultaneously in the atmosphere, a numerical simulation shows that a drop formed by coalescence of the pair may be subject to the Rayleigh instability. Zh. Tekh. Fiz. 69, 12–17 (December 1999)     

Note on the Harmonic Approximation in the Treatment of Entanglement: N Cold Trapped Ions

We study a one-dimensional system composed of N charged bosons confined in an external harmonic potential. In the limit of a strong interaction between the particles, we apply the harmonic approximation and derive an integral representation for the purity of the one-particle reduced density matrix, enabling an easy determination of the asymptotic entanglement. Results for the dependence of the asymptotic linear entropy on N are provided and discussed in detail for the first time.     

Bethe ansatz study of two-dimensional soliton lattice melting

We study the melting of incommensurate soliton lattice using the exact Bethe ansatz solution of one-dimensional quantum sine-Gordon Hamiltonian with U(1) coupling. The elastic moduli of soliton lattice are obtained and their asymptotic behaviors are explicitly calculated both at zero and finite temperature. We have obtained the thermodynamic phase boundaries of the soliton lattice and shown that the direct commensurate-incommensurate transitions are intervened by the fluid phase for T>0 as predicted by Coppersmith et al. [Coppersmith et al., Phys. Rev. Lett. 46 (1981) 549. [1]] for n≤2.     

On classical and quantum relativistic dynamics

A canonical formalism for the relativistic classical mechanics of many particles is proposed. The evolution equations for a charged particle in an electromagnetic field are obtained and the relativistic two-body problem with an invariant interaction is treated. Along the same line a quantum formalism for the spinless relativistic particle is obtained by means of imprimitivity systems according to Mackey theory. A quantum formalism for the spin-1/2 particle is constructed and a new definition of spin1/2 in relativity is proposed. An evolution equation for the spin-1/2 particle in an external electromagnetic field is given. The Bargmann Michel, and Telegdi equation follows from this formalism as a quasiclassical approximation. Finally, a new relativistic model for hydrogenlike atoms is proposed. The spectrum predicted is in agreement with Dirac's when radiative corrections have been added.     

Diffractive scattering in the Ericson model for the S matrix

The elastic scattering of spinless charged particles on nuclei is considered within the strong-absorption model proposed by Ericson for the S matrix in the angular-momentum representation. Our analytic method for summing partial-wave amplitudes, which is based on a generalization of the Abel-Plana formula, makes it possible to take into account the contributions from the possible singularities of the S matrix in the right-hand half-plane of the complex-valued variable l. The uniform asymptotic behavior obtained in the present study for the scattering amplitude offers a fresh view on the origin of the diffraction patterns in the angular distributions of elastically scattered heavy particles. Special attention is given to Coulomb-nuclear interference (in particular, to refraction phenomena) in the case of scattering into the classically allowed region (illuminated region) and the classically forbidden region (shadow region). In contrast to other analytic results, our solutions to the diffraction problem within the Ericson model do not give grounds whatsoever to draw profound analogies either with Fresnel diffraction in optics or with the phenomenon of rainbow scattering in classical mechanics.     

Resonant tunneling of a few-body cluster through repulsive barriers

A model for quantum tunnelling of a cluster comprised of A identical particles, interacting via oscillator-type potential, through short-range repulsive barrier potentials is introduced for the first time in symmetrized-coordinate representation and numerically studied in the s-wave approximation. A constructive method for symmetrizing or antisymmetrizing the (A ? 1)-dimensional harmonic oscillator basis functions in the new symmetrized coordinates with respect to permutations of coordinates of A identical particles is described. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, their number A = 2, 3, 4 and the type of their symmetry, is analyzed. It is shown that the total transmission coefficient demonstrates the resonance behavior due to the existence of barrier quasi-stationary states, embedded in the continuum.     

Quantum mechanics of relativistic spinless particles

A relativistic one-particle, quantum theory for spin-zero particles is constructed uponL ²(x, ct), resulting in a positive definite spacetime probability density. A generalized Schrödinger equation having a Hermitian HamiltonianH onL ²(x, ct) for an arbitrary four-vector potential is derived. In this formalism the rest mass is an observable and a scalar particle is described by a wave packet that is a superposition of mass states. The requirements of macroscopic causality are shown to be satisfied by the most probable trajectory of a free tardyon and a nontrivial framework for charged and neutral particles is provided. The Klein paradox is resolved and a link to the free particle field operators of quantum field theory is established. A charged particle interacting with a static magnetic field is discussed as an example of the formalism.     

Algebraic Bethe ansatz for integrable Kondo impurities in the one-dimensional supersymmetric t-J model

An integrable Kondo problem in the one-dimensional supersymmetric t-J model is studied by means of the boundary supersymmetric quantum inverse scattering method. the boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.     

Comprehensive decay law for emission of charged particles and exotic cluster radioactivity

A general decay formula for the emission of charged particles from metastable nuclei is developed based on the basic phenomenon of resonances occurring in quantum scattering process under Coulomb-nuclear potential. It relates the half-lives of radioactive decays with the Q values of the outgoing elements with masses and charges of the nuclei involved in the decay. The relation is found to be a generalization of the Geiger–Nuttall law in α radioactivity and explains well all the known emissions of charged particles including clusters, alpha and proton.     

Statistical bootstrap of fireball decay spectra

We propose a generalized statistical bootstrap equation for the generating functional of the fireball decay spectra which includes the bootstrap of the hadronic mass spectrum. In the form of an integral representation a solution is given for some n-particle distributions as well as multiplicity moments in the case of identical particles. Within this formalism we are able to discuss decay-chain end effects and to treat quantum number conservation explicity. The general equation is approximated by a simpler bootstrap equation for the linear decay chain with quantum-number conservation. An asymptotic solution for the single particle distributions according to this equation is discussed.     

Integrable open boundary conditions for the Bariev model of three coupled XY spin chains

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading to nine classes of possible choices of boundary fields are found and the corresponding integrable boundary terms are presented explicitly. The boundary Hamiltonian is solved by using the coordinate Bethe ansatz technique and the Bethe ansatz equations are derived.     

An open-boundary integrable model of three coupled XY spin chains

The integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains are considered in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms is determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are derived.     

Hierarchy of interactions and mass relations in asymptotically free E6 model of unified interactions

The hierarchy of gauge interactions within the E₆ model is proved, and the vector and spinor field masses are obtained. The mass spectrum of the charged W-bosons is found, and the mass scale is fixed so that the mass of the lightest of them is about 70 GeV. The lepton spectroscopy is studied and a new charged lepton, with mass of order 4–8 GeV is predicted. For the low-energy phenomenology, the model may be considered as a theory of 6 flavoured quarks and 4 charged leptons, each with its neutrino. Being 4-component the neutrinos are massive except for the ν_e (m_νe = 0, exactly) and ν_μ (m_νμ ≈ 0, approximately) particles. The problem of the “superfluous” particles which as a rule accompanies the asymptotic freedom in such theories is also briefly discussed.     

Algebraic Bethe ansatz for the one-dimensional Hubbard model with chemical potential

The integrability and the algebraic Bethe ansatz approach for the one-dimensional (1D) Hubbard model with chemical potential are studied in the framework of the quantum inverse scattering method. We also investigate the hidden local gauge invariance for the model. It is found that the R-matrix only permits Abelian $\text{U(1) ⋇}{}_{\mathrm{s}}\text{U(1)}$ gauge transformations, and it is shown that the energy spectrum is gauge invariant whereas the eigenvectors and the Bethe ansatz equations are explicitly gauge dependent.