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We introduce a one-dimensional stochastic system where particles perform independent diffusions and interact through pairwise coagulation events, which occur at a nontrivial rate upon collision. Under appropriate conditions on the diffusion…
The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse-graining is…
We consider various one-dimensional non-equilibrium models, namely the {\it diffusion-limited pair-annihilation and creation model} (DPAC) and its unbiased version (the Lushnikov's model), the DPAC model with particle injection (DPACI), as…
Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles…
An analytical theory, based on the perturbative treatment of the disorder and extended into a self-consistent set of equations for the dynamical density correlations, is developed and applied to the prototype one-dimensional model of…
Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrodinger equation cannot be solved analytically for more than two particles. One has to resort to approximation…
The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a…
In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…
In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation/annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational…
Constrained mechanical multibody systems arise in many important applications like robotics, vehicle and machinery dynamics and biomechanics of locomotion of humans. These systems are described by the Euler-Lagrange equations which are…
The challenging nuclear many-body problem is discussed along with classifications and qualitative descriptions of existing methods and models. We present detailed derivations of a new method where cluster correlations co-exist with an…
Many-body systems driven out of equilibrium can exhibit scaling flows of the quantum state. For a sudden quench to resonant interactions between particles we construct a new class of analytical scaling solutions for the time evolved wave…
We review recent results on many-body localization for two explicitly analyzable models of many-body quantum systems, the XY spin chain in transversal magnetic field as well as interacting systems of harmonic quantum oscillators. In both…
Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a…
In this paper we propose an ab initio method to solve quantum many-body problems of molecular dynamics where both the electronic and the nuclear degrees are represented by ensembles of trajectories and guiding waves in physical space. Both…
In this work we study self-consistent solutions in one-dimensional lattice models obtained via many-body perturbation theory. The Dyson equation is solved in a fully self-consistent manner via the algorithmic-inversion method based on the…
We present a new approach to the study of equilibrium properties in many-body quantum physics. Our method takes inspiration from Density Matrix Quantum Monte Carlo and incorporates new crucial features. First of all, the dynamics is…
Using Lindblad dynamics we study quantum spin systems with dissipative boundary dynamics that generate a stationary nonequilibrium state with a non-vanishing spin current that is locally conserved except at the boundaries. We demonstrate…
We consider two particular 1D quantum many-body systems with local interactions related to the root system $C_N$. Both models describe identical particles moving on the half-line with non-trivial boundary conditions at the origin, and they…
We derive the multiparticle-correlation expansion of the excess entropy of classical particles in the canonical ensemble using a new approach that elucidates the rationale behind each term in the expansion. This formula provides the…