Integral equations for four identical particles with separable two-particle interactions

The problem of four identical spinless particles with separable two-particle interactions is considered. The integral equations of motion for four particles in the bound states and in the continuum states with two non-ihteracting subsystems in the initial channel are formulated. The angular-momentum reduction of the obtained equations is given.     

Four-body Yakubovsky differential equations for identical particles

The differential equations for Yakubovsky components of the four-body wave functions are derived. An asymptotic form of these components is described. A symmetrized form of the Yakubovsky differential equations for four identical particles is given and its angular analysis is performed. Bound-state calculations are presented for various potentials.     

Quantum Boltzmann equations for binary interactions between identical particles

The inhomogeneous master equation obtained in a previous paper (by Van Vliet) is employed to obtain as first-moment equation two quantum mechanical Boltzmann equations (diagonal) for systems of weakly interacting identical particles. The interactions considered are of a binary nature: fermion-fermion or boson-boson. The resulting equations have the same structure as before. The total Boltzmann equation (diagonal and nondiagonal part) is also derived.     

Integral equations for the scattering of N identical particles

Integral equations are obtained for the scattering of N identical particles using a form of the N-particle scattering equations derived previously. The equations couple together only transition operators between physical two cluster channels, the breakup amplitudes being expressed in terms of quadratures over two-cluster amplitudes. The kernel of the equations becomes connected after a single iteration. The number of coupled equations for identical particles is $\text{1}\text{2}\text{N}\text{or}\text{1}\text{2}\text{(N?1)}$ when N is even or odd respectively.     

One-dimensional integral equations for a system of three identical particles in the boundary condition model and the possibility of changing the off-shell behaviour of the two-particle T-matrix

It is shown that in the framework of the boundary condition model (BCM) for the two-particle interaction the Schrödinger equation for the system of three identical bosons can be reduced to the one-dimensional integral equation in an exact way. The method used for obtaining such an equation is based on a special consideration of the two-particle off-shell wave functions. The binding energy of the simple three-particle system is calculated. It is indicated that by means of the equation obtained it is possible to change the off-shell behaviour of the two-particle (-matrix and therefore to simulate three-particle effects.     

Solutions of singular integral equations from gas dynamics and plasma physics

In this paper we give the explicit form of the solutions of the singular integral equations associated with some models of gas dynamics and plasma physics which are extensively investigated in the existing literature. In particular, we deal with equations on infinite and semi-infinite contours, where the data are assumed to be meromorphic functions. In this context we rederive some published results and present some new results which show how our method can be successfully used to obtain the explicit form of the solutions in much more general cases than those found in the literature.     

Quantum counterfactuality with identical particles

Quantum self-interference enables the counterfactual transmission of information, whereby the transmitted bits involve no particles traveling through the channel. In this work, we show how counterfactuality can be realized even when the self-interference is replaced by interference between identical particles. Interestingly, the facet of indistinguishability called forth here is associated with first-order coherence, and is different from the usual notion of indistinguishability associated with ...     

Unitarity and the inhomogeneous equations method for identical particle scattering

A K-matrix solution to the coupled, inhomogeneous equations describing the scattering of a particle by a system of identical particles is developed. It is shown that K is a sum of two terms, one arising from the homogeneous solution and one from the particular integral. The former is a direct contribution, i.e., with no exchange, while the latter is a pure exchange contribution. Thus, as in the previously studied case of the T matrix arising from this system of equations, the direct and exchange portions of K are additive, and can be computed separately. A unitary S matrix is obtained from K in the usual way: S = (1 + iK)(1 − iK)⁻¹. The problem of how to calculate K when an apparent two-channel problem is actually a two-particle problem with the channels referring to the identical particle labels is also solved.     

On wave properties of identical particles

A generalization of de Finetti's theorem is used to show that certain quantities which usually are interpreted as evidence for the wave aspect of quantum phenomena may be explained from a statistical dependence induced by the indistinguishability of the particles under consideration.     

Quantum interference of charged identical particles

We present the results of a computer simulation study of charged-particle interferometry, combining features of both the Aharonov-Bohm and Hanbury Brown-Twiss experiment. In contrast to a previous theoretical analysis of this experiment, we find that the Aharonov-Bohm effect is also present in the cross-correlated two-particle intensity. A simple, time-independent scattering theory that leads to conclusions that are in concert with the simulation data is given.     

Symmetric integral equations derived from the Faddeev equations

A way is shown to transform the Faddeev equations of the atomic three-body problem into a set of integral equations with symmetric kernel. The method is treated in more detail for total angular momentumJ=0 and applied to calculating the binding energy of theH ^? ion.     

Stark-interaction stabilization of the excited state of identical particles

It has been shown in the Markov approximation of the quantum stochastic differential equation approach, with decay of the symmetric W state as an example, that the collective spontaneous decay of an ensemble of identical particles can be suppressed almost completely due to the Stark interaction of the particles with the vacuum electromagnetic field, which results in stabilization of the excited state of the atomic ensemble with a certain number of particles.     

Generalized self-consistent integral equations for magnetic impurities

The simplest system of integral equations resulting from self-consistent perturbation techniques applied to a generalized Anderson-model is known to give rise to certain mathematical pathologies. In the local moment limit, it is shown that the system improperly takes account of the physical situation of two competing scattering channels. A generalized system, free of this defect, is derived. It differs from dispersion relations by unusual nonlinear terms, and also from parquet-equations.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

The integral equations for the average stochastic scattering matrix

The integral equations describing the dependence of the average scattering matrix on the distribution of resonance parameters are derived for the large numbers of the levels and channels. In particular, the case of statistically nonequivalent channels is considered.The authors are grateful to Prof. V.M. Strutinsky for useful discussions.     

Kernel approximation for solving few-body integral equations

This paper investigates an approximate method for solving integral equations that arise in few-body problems. The method is to replace the kernel by a degenerate kernel defined on a finite dimensional subspace of piecewise Lagrange polynomials. Numerical accuracy of the method is tested by solving the two-body Lippmann-Schwinger equation with non-separable potentials, and the three-body Amado-Lovelace equation with separable two-body potentials.     

An affinity theorem for integral imaging equations

It is shown that any integral imaging equation whose solutions are known can be used to generate a class of solvable integral equations via an affinity transformation.     

Finite-temperature Bose-Einstein distribution functions of identical particles

We study the evolution properties of propagating identical particles produced at a finite temperature in a randomly distributed environment. The lower bound on the spacetime size of the multiparticle production region and the correlation chaoticity are derived.     

Reduction of the Bethe-Salpeter equation for the amplitude of the scattering of spin-1 particles to a set of integral equations for invariant functions

Physics of Atomic Nuclei - The Bethe-Salpeter equation for massive spin-1 particles is considered. The amplitude for the scattering of spin-1 particles is expanded in relativistically invariant...     

Linear integral equations and nonlinear difference-difference equations

This paper studies the dynamics of members of the two-parameter family of maps x → μx(1 ? x^v), emphasizing the evolution from snapback repeller to crisis bifurcations. The example of the square root map $\text{v =}\text{1}\text{2}$ is taken to represent the subfamily where v is fixed and taken from the range $\text{1}\text{2}\text{≤ v ≤ 1}$. A map from such a subfamily is shown to be conjugate with a map with negative Schwarzian derivative. This allows a characterization of crisis as the demise of a snapback repeller on a proper subinterval.