Related papers: From bound states to the continuum
The scattering and bound states of the many-body systems, related to the short-range Dyson model, are studied. First, we show that the scattering states can be realized as coherent states and the scattering Hamiltonian can be connected to a…
Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing…
We investigate the problem of two atoms interacting via a short range s-wave potential in the presence of a deep optical lattice of arbitrary dimension $D$. Using a tight binding approach, we derive analytical results for the properties of…
Three-body systems in two dimensions with zero-range interactions are considered for general masses and interaction strengths. The problem is formulated in momentum space and the numerical solution of the Schr\"odinger equation is used to…
Absorbing-boundary-condition method and its applications to nuclear responses and breakup reactions are reported. The method facilitates calculations of the continuum states in the coordinate space of many degrees of freedom. Properties of…
I review, in a personal perspective, the history of the theory of non-relativistic bound states in QED and QCD from the Bethe-Salpeter equation to the construction of effective field theories.
To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of…
The present-day nuclear structure theory exhibits a great degree of synergy with respect to methods that are used to describe various phenomena in heavy nuclear systems. From few-body methods, through the shell model to mean-field…
We address the question of minimal requirements for the existence of quantum bound states. In particular, we demonstrate that a few-body system with zero-range momentum-independent two-body interactions is unstable against decay into…
A method to calculate reactions in quantum mechanics is outlined. It is advantageous, in particular, in problems with many open channels of various nature i.e. when energy is not low. In the method there is no need to specify reaction…
The exact treatment of nuclei starting from the constituent nucleons and the fundamental interactions among them has been a long-standing goal in nuclear physics. Above all nuclear scattering and reactions, which require the solution of the…
Transition State Theory forms the basis of computing reaction rates in chemical and other systems. Recently it has been shown how transition state theory can rigorously be realized in phase space using an explicit algorithm. The…
Bound states are dissipation-resilient states that may emerge when quantum systems are strongly coupled to reservoirs with band gaps. We analyze an exactly solvable bosonic model for bound state existence and reproduce these results by a…
In recent years, bound states in continuum (BICs) have gained significant value for practitioners in both theoretical and applied photonics. This paper focuses on devices that utilize non-homogeneous thin patterned laminae. The properties,…
The four-body bound state with two-body interactions is formulated in Three-Dimensional approach, a recently developed momentum space representation which greatly simplifies the numerical calculations of few-body systems without performing…
A first-principles description of nuclear systems along the drip lines presents a substantial theoretical and computational challenge. In this paper, we discuss the nuclear theory roadmap, some of the key theoretical approaches, and present…
We introduce a -- somewhat holographic -- dictionary between gravitational observables for scattering processes (measured at the "boundary") and adiabatic invariants for bound orbits (in the "bulk"), to all orders in the Post-Minkowskian…
Bound states in the continuum (BICs) are localized modes residing in the radiation continuum. They were first predicted for single-particle states, and became a general feature of many wave systems. In many-body quantum physics, it is still…
We study the boundary theory of the $\mathbb{Z}_N$ X-cube model using a continuum perspective, from which the exchange statistics of a subset of bulk excitations can be recovered. We discuss various gapped boundary conditions that either…
We investigate the relativistic scattering of three identical scalar bosons interacting via pair-wise interactions. Extending techniques from the non-relativistic three-body scattering theory, we provide a detailed and general prescription…