Related papers: Lattice two-body problem with arbitrary finite ran…
A two-dimensional bistable lattice is a periodic triangular network of non-linear bi-stable rods. The energy of each rod is piecewise quadratic and has two minima. Consequently, a rod undergoes a reversible phase transition when its…
In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles on the lattice $\Z^d$, $d\ge 1$ subject to a common external potential $V(x)$ which we assume quasi-periodic…
The quest to understand three-body dynamics from first-principle QCD includes the study of non-resonant and resonant systems. The isospin $I=2$ system is of particular interest having no three-body resonance but featuring a resonance in a…
The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary…
This work reviews recent advances in the analytical treatment of the continuum spectrum of correlated few-body non-relativistic Coulomb systems. The exactly solvable two-body problem serves as an introduction to the non-separable…
We present a study of a $1+1$ dimensional heavy-light three-body system in finite volume. The heavy-light system is simulated by a coupled-channel $\phi^4$ type lattice model, and both ground state and excited states of multiparticle energy…
We consider the scattering of $n$ classical particles interacting via pair potentials, under the assumption that each pair potential is "long-range", i.e. being of order ${\cal O}(r^{-\alpha})$ for some $\alpha >0$. We define and focus on…
We consider the low energy spectrum of spin-1/2 two-dimensional triangular lattice models subject to a ferromagnetic Heisenberg interaction and a three spin chiral interaction of variable strength. Initially, we consider quasi-one…
We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be…
Three-body states are critical to the dynamics of many hadronic resonances. We show that lattice QCD calculations have reached a stage where these states can be accurately resolved. We perform a calculation over a wide range of parameters…
Low-energy scattering is well described by the effective-range expansion. In quantum mechanics, a tower of contact interactions can generate terms in this expansion after renormalization. Scattering parameters are also encoded in the…
In this paper, we investigate a family of one-dimensional multi-component quantum many-body systems. The interaction is an exchange interaction based on the familiar family of integrable systems which includes the inverse square potential.…
Finite volume multiple-particle interaction is studied in a two-dimensional complex $\phi^4$ lattice model. The existence of analytical solutions to the $\phi^4$ model in two-dimensional space and time makes it a perfect model for the…
The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Luscher. While in infinite volume, QED contributions to low-energy…
A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing…
We investigate an application of twisted boundary conditions for study of low-energy hadron-hadron interactions with L\"ushcer's finite size method. It allows us to calculate the phase shifts for elastic scattering of two hadrons at any…
Scattering and transition amplitudes with three-hadron final states play an important role in nuclear and particle physics. However, predicting such quantities using numerical Lattice QCD is very difficult, in part because of the effects of…
In this work, a multichannel Kondo lattice model is studied in the thermodynamic limit. The conduction band is described by a constant hopping amplitude between any pair of lattice sites. For this system, we have obtained the exact…
We investigate the quantum dynamics of two bosons, trapped in a two-dimensional harmonic trap, upon quenching arbitrarily their interaction strength thereby covering the entire energy spectrum. Utilizing the exact analytical solution of the…
We discuss unitarity constraints on the dynamics of a system of three interacting particles. We show how the short-range interaction that describes three-body resonances can be separated from the long-range exchange processes, in particular…