Theory of Coherent Decay in a System of Three - Particles.

Stefan Hunn

Paweł Horodecki, Kazuki Sakurai, Abhyoudai S. Shaleena +1 more

A bstract The exploration of entanglement and Bell non-locality among multi-particle quantum systems offers a profound avenue for testing and understanding the limits of quantum mechanics and local real hidden variable theories. In this work, we examine non-local correlations among three massless spin-1/2 particles generated from the three-body decay of a massive particle, utilizing a framework based on general four-fermion interactions. By analyzing several inequalities, we address the detection of deviations from quantum mechanics as well as violations of two key hidden variable theories: fully local-real and bipartite local-real theories. Our approach encompasses the standard Mermin inequality and the tight 4 × 4 × 2 inequality, providing a comprehensive framework for probing three-partite non-local correlations. Our findings provide deeper insights into the boundaries of classical and quantum theories in three-particle systems, advancing the understanding of non-locality in particle decays and its relevance to particle physics and quantum foundations.

Luciano Fonda, G. C. Ghirardi

Ulf Bissbort, Michael Buchhold, Walter Hofstetter

We present a generalized quasi-particle theory for bosonic lattice systems, which naturally contains all relevant collective modes, including the Higgs amplitude in the strongly correlated superfluid. In contrast to Bogoliubov theory, this non-perturbative method does not rely on a small condensate depletion and is valid for any interaction strength in three spatial dimensions. It is based on an expansion around the bosonic Gutzwiller ground state in terms of appropriately chosen fluctuation operators and lays the foundation for the description of real-time dynamics in terms of the natural, weakly interacting quasi-particles. Furthermore, it provides a systematic framework for efficiently calculating observables beyond the Gutzwiller approximation and for including external perturbations, as well as higher order decay and interactions in terms of quasi-particle operators. It allows for the construction of an alternative path integral approach in terms of quasi-particle coherent states.

Yakir Aharonov, J. Anandan, SHMUEL NUSSINOV

Re-considering this work.

Y. Pavlyukh, Jamal Berakdar, Ángel Rubio

Generally, the addition or removal of a single particle in a many-body system does not correspond to an exact eigenstate of the system. Thus the resulting coherent excitation evolves in time. As discussed here, the evolution at short times upon the excitation with the energy $\ensuremath{\epsilon}$ exhibits a quadratic decay [with the rate constant ${\ensuremath{\sigma}}^{2}(\ensuremath{\epsilon})$]. Later on, after some time $\ensuremath{\tau}(\ensuremath{\epsilon})$, the exponential decay sets in. It is governed by another rate constant $\ensuremath{\gamma}(\ensuremath{\epsilon})$. This behavior is generic for many realistic finite and extended systems. For a finite system it is possible to assess this behavior full numerically using an exact solution of the many-body problem. We present a simple model for the electron spectral function that links together all three aforementioned parameters and give a prescription for how the energy uncertainty ${\ensuremath{\sigma}}^{2}(\ensuremath{\epsilon})$ can be computed within the many-body perturbation theory. Our numerical results demonstrate that the model approach accurately reproduces the exact spectral function in a large range of energies even in the case of fragmented many-body states. We show that the central quantity of this study ${\ensuremath{\sigma}}^{2}(\ensuremath{\epsilon})$ can easily be computed exactly or from approximate theories and, hence, can be used for their validation. We also point out how the set in time can be tested by means of attosecond spectroscopy.