SciPost Phys. 18, 001 (2025) ·
published 6 January 2025
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A varying number of particles is one of the most relevant characteristics of systems of interest in nature and technology, ranging from the exchange of energy and matter with the surrounding environment to the change of particle number through internal dynamics such as reactions. The physico-mathematical modeling of these systems is extremely challenging, with the major difficulty being the time dependence of the number of degrees of freedom and the additional constraint that the increment or reduction of the number and species of particles must not violate basic physical laws. Theoretical models, in such a case, represent the key tool for the design of computational strategies for numerical studies that deliver trustful results. In this manuscript, we review complementary physico-mathematical approaches of varying number of particles inspired by rather different specific numerical goals. As a result of the analysis on the underlying common structure of these models, we propose a unifying master equation for general dynamical systems with varying number of particles. This equation embeds all the previous models and can potentially model a much larger range of complex systems, ranging from molecular to social agent-based dynamics.
SciPost Phys. 18, 002 (2025) ·
published 6 January 2025
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We calculate the low-temperature spectral function of the symmetric single impurity Anderson model using a recently proposed dynamical exchange-correlation (xc) field formalism. The xc field, coupled to the one-particle Green's function, is obtained through analytic analysis and numerical extrapolation based on finite clusters. In the Kondo regime, the xc field is modeled by an Ansatz that takes into account the different asymptotic behaviors in the small- and large-time regimes. The small-time xc field contributes to the Hubbard side-band, whereas the large-time to the Kondo resonance. We illustrate these features in terms of analytical and numerical calculations for small- and medium-size finite clusters, and in the thermodynamic limit. The results indicate that the xc field formalism provides a good trade-off between accuracy and complexity in solving impurity problems. Consequently, it can significantly reduce the complexity of the many-body problem faced by first-principles approaches to strongly correlated materials.
SciPost Phys. 18, 003 (2025) ·
published 6 January 2025
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Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of interest. Employing effective Hamiltonians that contain many-body correlations renders the use of perturbative many-body techniques difficult because of the overcounting of correlations. In this work, we develop a strategy to apply an extension of the many-body perturbation theory starting from an effective interaction that contains correlations beyond the mean-field level. The goal is to re-organize the many-body calculation to avoid the overcounting of correlations originating from the introduction of correlated effective Hamiltonians in the description. For this purpose, we generalize the formulation of the Rayleigh-Schrödinger perturbation theory by including free parameters adjusted to reproduce the appropriate limits. In particular, the expansion in the bare weak-coupling regime and the strong-coupling limit serves as a valuable input to fix the value of the free parameters appearing in the resulting expression. This method avoids double counting of correlations using beyond-mean-field strategies for the description of many-body systems. The ground state energy of various systems relevant for ultracold atomic, nuclear, and condensed matter physics is reproduced qualitatively beyond the domain of validity of the standard many-body perturbation theory. Finally, our method suggests interpreting the formal results obtained as an effective field theory using the proposed reorganization of the many-body calculation. The results, like ground state energies, are improved systematically by considering higher orders in the extended many-body perturbation theory while maintaining a straightforward polynomial expansion.
SciPost Phys. 18, 004 (2025) ·
published 7 January 2025
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The observed Standard Model is consistent with the existence of vector-like species with electric charge a multiple of $e/6$. The discovery of a fractionally charged particle would provide nonperturbative information about Standard Model physics, and furthermore rule out some or all of the minimal theories of unification. We discuss the phenomenology of such particles and focus particularly on current LHC constraints, for which we reinterpret various searches to bound a variety of fractionally charged representations. We emphasize that in some circumstances the collider bounds are surprisingly low or nonexistent, which highlights the discovery potential for these species which have distinctive signatures and important implications. We additionally offer pedagogical discussions of the representation theory of gauge groups with different global structures, and separately of the modern framework of Generalized Global Symmetries, either of which serves to underscore the bottom-up importance of these searches.
SciPost Phys. 18, 005 (2025) ·
published 7 January 2025
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The field theoretic wavefunction in cosmological spacetimes has received much attention as a fundamental object underlying the generation of primordial perturbations in our universe. Assuming an initial Bunch-Davies state, unitary time evolution implies an infinite set of cutting rules for the wavefunction to all orders in perturbation theory, collectively known as the cosmological optical theorem. In this work, we generalise these results to the case of Bogoliubov initial states, accounting for both parity-even and parity-odd interactions. We confirm our findings in a few explicit examples, assuming IR-finite interactions. In these examples, we preserve scale invariance by adiabatically turning on interactions in the infinite past rather than imposing a Bogoliubov state at some finite initial time. Finally, we give a prescription for computing Bogoliubov wavefunction coefficients from the corresponding Bunch-Davies coefficients for both $n$-point contact and four-point exchange diagrams.
