On a numerical exact solution to the many-body problem in one dimension

The Hamiltonian matrix for up to 30 particles has been diagonalised for three different interactions in a plane wave base, among them a hard-core potential. Restriction was made to the spin-polarised case in one space dimension. In the present feasibility study much weight is placed on the questions of convergence, numerical stability and efficiency. Some selected results on binding energies, excitation spectra, momentum distributions and spatial correlation functions are presented and discussed.     

On a new formulation of the many-body problem in general relativity

A generalized Riemannian geometry is studied where the metric tensor is replaced by a matrix g of metrics. In this context new geometric quantities arise, which are trivial in ordinary Riemannian geometry. An application of this formalism to many-body alignments in general relativity is proposed, where the sub-constituents of the overall gravitational field are described by the components of g. The mutual gravitational interactions between the individual particles are encoded in specific tensors. In particular, very specific approximation schemes for Einstein’s field equations may be considered, which exclusively approximate those terms in the field equations which are due to interactions. The Newtonian limit as well as the first post-Newtonian approximation of the presented formalism is studied in order to display the interpretability of the presented formalism in terms of many-body alignments and in order to deduce a physical interpretation of the new geometric quantities.     

Geometrical derivation of a new ground state formula for the n-electron Friedel resonance model

The n-electron ground state of the Friedel resonance model can be written as a single Slater determinant of n s-electrons plus d-electron-s-hole companion. This new formula is derived geometrically in the Hilbert space. The derivation uses the fact that a n-electron Slater determinant, built from N band states, corresponds to a n-dimensional subspace in the N-dimensional Hilbert space. Received: 4 November 1997 / Accepted: 19 November 1997     

The pion-nucleus many-body problem

Low energy pion-nucleus elastic scattering is discussed within the framework of many-body theory. In these considerations exchange of virtual ρ ad π mesons, as well as the π meson, are found to play an important role, producing effects like the Ericson-Ericson Lorentz-Lorenz effect. By inclusion of interactions in channels other than the pionic one, the pion-nucleus problem is brought into the context of other nuclear many-body problems, and various relations to the nucleon problem made use of .Some of the necessary parameters here are drawn from pionic atom work. With these and our deduced interactions the theoretically predicted cross-sections are found to be in good agreement with the experimental work.     

A translationally invariant RPA-calculation for16O on the basis of an algebraic solution of the many-body oscillator problem

The solution of the many-body oscillator problem is used as a basis for a RPA-calculation of¹⁶O. The calculation is performed in a LS-coupling scheme with an interaction containing central, spin-orbit and tensor forces. The main differences with conventional RPA-calculations occur for the transition probabilities.     

A new method in the theory of many-body scattering

New coupled equations for the transition (T) and reactance (K) operators for N-channel, many-body, rearrangement scattering are derived. The key to the new method is the channel coupling array W, which links the various rearrangement channels together. By specializing W to the class of channel permuting arrays, it is shown that the (N−1)st iterate of the kernel of the coupled equations is connected.     

A functional approach to the many-body nuclear problem: the MEC

Summary We show how a functional approach to the nuclear many-body problem can provide a unified scheme to deal with the many facets of the problem and to establish well-defined procedures of approximation. We consider, in particular, the perturbative and the mean-field (loop expansion) approximations to an exact effective bosonic Lagrangian, discussing how well-known computational schemes (hole-line expansion, RPA, etc.) may be obtained as subsets of definite orders in these expansions. An application to the calculation of the longitudinal electromagnetic response function, with the simpleNπ interaction, is finally presented. We show how the pion dynamic and the short-range correlations cooperate to obtain a better agreement with experimental data. Presented by R. Cenni.     

"甲虫和橡胶带"问题新解

给出“甲虫和橡胶带”问题的一种简便的新解法.     

A new solution to the problem of an acoustically transparent body

The method of active impedance matching is applied to the well-known problem of an acoustically transparent body. Two laws of active force control, by velocity and by pressure, are obtained for solving the problem.     

Effective-field theory and the nuclear many-body problem

We review many-body calculations of the equation of state of dilute neutron matter in the context of effective-field theories of the nucleon-nucleon interaction.     

The many-body problem within the Lee model

The structure of a field theoretical many-body problem is studied within the (non-static) Lee model. The explicit solvability of the renormalization problem allows the investigation of renormalization corrections in many-particle systems. Herefore, the renormalized equations are worked out for the N-V scattering and for the binding-energy problem of “N-V matter” — these cases taken in analogy to nucleon-nucleon scattering and nuclear matter. The N-V matter equations are obtained from a cluster expansion suitably defined for the field theoretical case. The ansatz for the correlated wave functions is chosen in such a way as to generate a two-hole-line expansion of the binding energy. The renormalized form of this field theoretical extension of Brueckner theory is discussed in detail revealing the medium effects on renormalization.     

A classical solution for many-body forces of directly interacting particles

The first class constraint conditions of relativistic direct interaction dynamics have been solved. Their solution expresses the many-body interactions in terms of the two-body interactions in perturbation expansion. The n-body interaction is of order g smaller than the (n-1)-body interaction. The expressions are considerably simpler than those obtained previously.     

An integro-differential equation approach to the many-body problem

An integro-differential equation in two variables which includes two-body correlations, has been derived for a many-body system of identical particles. This equation has been obtained by means of a complete expansion in terms of the hyperspherical harmonic potential basis. It is proved that this equation is identical to the Faddeev equation for a system of three bosons. The implications of this result for many-body systems are discussed.     

New nomographic solutions in the newtonian many-body problem

The problem of the existence of concentric central configurations, geometrically presented by regular n- and 2n-sided polygons nested in one another, is investigated. The necessary and sufficient conditions for the existence of these central configurations are derived using computer algebra.     

Monte Carlo method for the many-body scattering problem

The non-relativistic many-body scattering problem is cast in a form suitable for treatment by Monte Carlo methods. The formulation is based on resonant standing waves of the compound system, similar to those used in the R-matrix theory of nuclear reactions. Integral expressions are derived from which the scattering matrix elements at low energies can be evaluated. The method is demonstrated by application to simple one- and two-channel one-dimensional scattering problems.     

A new integrable one-dimensional completely degenerate many-body system

We introduce and solve a new completely integrable N-body system in one dimension. It is shown that this system is completely degenerate in the sense that it has 2N − 1 independent integrals of motion which determine its trajectories uniquely.     

Manipulating many-body quantum states via single-photon resonance

For an atomic Bose-Hubbard dimer quantum control via multiphoton processes have been investigated widely. We here explore how to manipulate the many-body quantum states via single-photon resonance by treating the periodic driving as a weak perturbation. The transition probabilities up to second-order approximation are given as functions of the driving parameters, which are considerable only for the single-photon resonance case. Due to some transition matrix elements vanishing, the first-order quantum transition obeys a selection rule. The non-forbidden transitions involve states of different entanglement entropies and all (part) of the forbidden transitions relate to the entropy balances between two states for odd (even) number of particles. The results provide a new route for manipulating many-body quantum states and entanglement entropies, and controlling the atomic tunnelings of the Bose-Hubbard dimer.     

Exact stochastic mean-field approach to the fermionic many-body problem

We investigate a reformulation of the dynamics of interacting fermion systems in terms of a stochastic extension of time-dependent Hartree-Fock equations. From a path-integral representation of the evolution operator, we show that the exact N-body state can be interpreted as a coherent average over Slater determinants evolving in a random mean-field. The imaginary time propagation is also presented and gives a similar scheme which converges to the exact ground state. In addition, the growth of statistical errors is examined to show the stability of this stochastic formulation.