Solving Many-Body Problems with a Quantum Microscope

Thomas Schweigler, Valentin Kasper, Sebastian Erne +5 more

Fauseweh, Benedikt

Sean S. Hodgman, R. I. Khakimov, Robert J. Lewis-Swan +2 more

In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation or annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational solution to the quantum many-body problem. Here, we demonstrate this paradigm by measuring multiparticle momentum correlations up to third order between ultracold helium atoms in an s-wave scattering halo of colliding Bose-Einstein condensates, using a quantum many-body momentum microscope. Our measurements allow us to extract a key building block of all higher-order correlations in this system-the pairing field amplitude. In addition, we demonstrate a record violation of the classical Cauchy-Schwarz inequality for correlated atom pairs and triples. Measuring multiparticle momentum correlations could provide new insights into effects such as unconventional superconductivity and many-body localization.

Yatendra Singh Jain

Basic problems of a microscopic theory of many body quantum systems and different aspects of a new approach which can help in solving them are discussed in detail. To this effect we make a critical study of the wave mechanics of two hard core quantum particles and discover its several untouched aspects, viz.: (i) the useful details of ψ_k(r) (representing the relative motion of two particles), (ii) the expectation value of hard core (HC) repulsion (), (iii) the inconsistency of the statements, r \leσand ψ_k(r \leσ)=0 (σ=HC diameter of a particle), with uncertainty principle particularly for low k values, (iv) the lower bound of allowed values of k=2q, (v) the dominance of interparticle phase correlation in low temperature phase. For the first time this study concludes that has zero value which does not agree with its non-zero value known for the last several decades. This also finds compelling reasons for a system of interacting bosons such as liquid ^4He to have (q, -q) pair condensation with allowed q, obviously controlled by V_{HC}(r), to satisfy q \geπ/d. Several important aspects of N body quantum systems like liquids ^4He and ^3He are also concluded. Free from any error [see editor's note J. Scientific Exploration 16(1), p.1 (2002)], our approach can help in developing nearly exact microscopic theories of widely different systems of interacting bosons and fermions, as demonstrated for liquids ^4He type systems [J. Scientific Exploration, 16, 77-116 (2002)]. The paper also sums up the expert observations with our response to facilitate one to have a critical assessment and better understanding of the new approach.

Hans A. Weidenmüller

Miloslav Znojil, L. Majling

For both identical and distinguishable particles and for an arbitrary polynomial approximation to the realistic two-body forces, the A-body Hamiltonian may be converted into an infinite block-three-diagonal matrix in the properly arranged, translationally invariant, oscillator basis. As a consequence, the exact Green function and all the projections of eigenstates of the microscopic Schrodinger equation become expressible in terms of the matrix continued fractions. This generalises the recent reformulation of the one-dimensional A=1 anharmonic problem by Graffi and Greechi (1975). The quick convergence of this non-perturbative method of solving the many-body bound-state problem is demonstrated for the simplest three- and four-body examples. With the core-possessing type V(r)=-r 2 +r 4 of the spin- and isospin-independent two-body interaction, only the 10 -3 error in the three-bosonic ground-state energy arises from restricting the formulae to 5*5 dimensional matrices.