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We consider a system of $N\gg 1$ interacting fermionic particles in three dimensions, confined in a periodic box of volume $1$, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper…
We discuss effective field theory treatments of the problem of three particles interacting via short-range forces. One case of such a system is neutron-deuteron scattering at low energies. We demonstrate that in attractive channels the…
We investigate the renormalization group theory of generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson renormalization group method. The vertex interaction is given by…
In this paper we solve one dimensional trapped SU(2) bosons with repulsive $\delta$-function interaction by means of Bethe-ansatz method. The features of ground state and low-lying excited states are studied by numerical and analytic…
We use a non-perturbative renormalization-group technique to study interacting bosons at zero temperature. Our approach reveals the instability of the Bogoliubov fixed point when $d\leq 3$ and yields the exact infrared behavior in all…
We briefly summarize the most relevant steps in the search of rigorous results about the properties of quantum systems made of three bosons interacting with zero-range forces. We also describe recent attempts to solve the unboundedness…
We revisited how Weinberg's ideas in Nuclear Physics influenced our own work and lead to a renormalization group invariant framework within the quantum mechanical few-body problem, and we also update the discussion on the relevant scales in…
We present a detailed investigation of the momentum-dependent self-energy Sigma(k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3<=D<4. Applying the functional…
We consider the heat equation with Dirichlet boundary conditions on the tubular neighborhood of a closed Riemannian submanifold. We show that, as the tube radius decreases, the semigroup of a suitably rescaled and renormalized generator can…
We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length…
The interaction of Nucleon-Nucleon (NN) has certain physical characteristics, which indicated by nucleon, and meson degrees of freedom. The main purpose of this work is calculating the ground state energies of 21 Deutron and Alfa through…
We consider systems of a small number of interacting bosons confined to harmonic potentials in one and two dimensions. By exact numerical diagonalization of the many-body Hamiltonian we determine the low lying excitation energies and the…
We investigate the topic of renormalization in the theory of weakly interacting open quantum systems. Our starting point is an open quantum system interacting with a single heat bath. For a given setup, we discuss that the stationary state…
We study a pseudogap region of the mixed boson fermion system using a recent formulation of the renormalization group technique through the set of infinitesimal unitary transformations. Renormalization of fermion energies gives rise to a…
Based on previous works, analytical calculational procedures for dealing with the strongly interacting fermions ground state are further developed through a medium dependent potential in terms of the Bethe-Peierls contact interaction model.…
We study the ground state of few bosons with repulsive dipole-dipole interaction in a quasi-one-dimensional harmonic trap by means of the exact diagonalization method. Up to three interaction regimes are found depending on the strength of…
We theoretically study the nonequilibrium thermoelectric transport properties of a strongly-correlated molecule (or quantum dot) embedded in a tunnel junction. Assuming that the coupling of the molecule to the contacts is asymmetric, we…
We consider properties of critical points in the interacting boson model, corresponding to flat-bottomed potentials as encountered in a second-order phase transition between spherical and deformed $\gamma$-unstable nuclei. We show that…
We develop a bosonization formalism that captures non-perturbatively the interaction effects on the $\mathbf{Q}=0$ continuum of excitations of nodal fermions above one dimension. Our approach is a natural extension of the classic…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…