Related papers: Improved lower bounds for the ground-state energy …
A review is presented of the Hall-Post inequalities that give lower-bounds to the ground-state energy of quantum systems in terms of energies of smaller systems. New applications are given for systems experiencing both a static source and…
A review is first presented of the Hall--Post inequalities relating $N$-body to $(N-1)$-body energies of quantum bound states. These inequalities are then applied to delimit, in the space of coupling constants, the domain of Borromean…
We study a bound system of N identical bosons interacting by model pair potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a variational trial function and the `equivalent 2-body method', we find explicit upper and…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
We study the low-energy spectral properties of positive center-of-mass conserving two-body Hamiltonians as they arise in models of fractional quantum Hall states. Starting from the observation that positive many-body Hamiltonians must have…
I present a new approach to the many-body ground state of quantum-Hall systems. The method describes the behavior of a two-dimensional electron system at all Landau-level filling factors $\nu$, continuously as a function of magnetic field,…
The potential energy problem in an electrostatically bound two-body system is studied in the framework of a recently proposed impact model of the electrostatic force and in analogy to the potential energy in a gravitationally bound system.…
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…
We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon…
We develop an approximate second quantization method for describing the many-particle systems in the presence of bound states of particles at low energies (the kinetic energy of particles is small in comparison to the binding energy of…
We study the structure of bound states appearing in systems governed by the Coulomb and short-range interactions. We analyze the binding energies and wave functions of the bound states generated by the Coulomb plus short-range potential. We…
We derive general lower energy bounds for the ground state energy of any translationally invariant quantum lattice Hamiltonian. The bounds are given by the ground state energy of renormalized Hamiltonians on finite clusters.
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
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…
Ultracold polar molecules in multilayered systems have been experimentally realized very recently. While experiments study these systems almost exclusively through their chemical reactivity, the outlook for creating and manipulating exotic…
The development of computational resources has made it possible to determine upper bounds for atomic and molecular energies with high precision. Yet, error bounds to the computed energies have been available only as estimates. In this…
The states of a boson pair in a one-dimensional double-well potential are investigated. Properties of the ground and lowest excited states of this system are studied, including the two-particle wavefunction, momentum pair distribution and…
The lower bound masses of the ground-state relativistic three-boson system in 1+1, 2+1 and 3+1 space-time dimensions are obtained. We have considered a reduction of the ladder Bethe-Salpeter equation to the light-front in a model with…
We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a…
I present variational solutions of the many-body Schr\"odinger equation for a two-dimensional electron system in strong magnetic fields, which have, at $\nu=1$, the energy about 46% lower than the energy of the Laughlin liquid. At…