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Bound-state-like wave functions are used to determine the scattering matrix corresponding to low energy $N-d$ and $p-^3$He collisions. To this end, the coupled channel form of the integral relations derived from the Kohn variational…
Determining quantum excited states is crucial across physics and chemistry but presents significant challenges for variational methods, primarily due to the need to enforce orthogonality to lower-energy states, often requiring…
In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with respect to a probability distribution of the…
A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
The use of a single-qubit parametrized circuit as an Ansatz for the variational wave function in the calculation of the ground state energy of a quantum many-body system is demonstrated using the one-dimensional Bose-Hubbard model.…
The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy and eigenfunction of the lowest levels of a Hamiltonian. The approach is illustrated by the case of the Morse…
We consider ground state energies (GSE) of multipartite $p$-spin models. Relying on partially lifted random duality theory (pl RDT) concepts we introduce an analytical mechanism that produces easy to compute lower and upper GSE bounds for…
The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational…
We consider $N_a$ three-level atoms (or systems) interacting with a one-mode electromagnetic field in the dipolar and rotating wave approximations. The order of the quantum phase transitions is determined explicitly for each of the…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…
Using the Feynman-Pines diagram technique, the energy spectrum of localized quasi-particles interacting with polarization phonons is calculated and analyzed in the wide range of energies at the finite temperature of the system. It is…
A variational method is discussed, based on the principle of minimal variance. The method seems to be suited for gauge interacting fermions, and the simple case of quantum electrodynamics is discussed in detail. The issue of renormalization…
It is not possible to detect a vacuum fluctuation without a test particle interacting with the vacuum fluctuation in a measurable manner. In the quantum electrodynamics calculation presented here, a photon traveling through the vacuum is…
A variational model for the infra-red spectrum of VO is presented which aims to accurately predict the hyperfine structure within the VO $\mathrm{X}\,^4\Sigma^-$ electronic ground state. To give the correct electron spin splitting of the…
In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a class of states which is suitable as a variational set to find ground states in spin systems of arbitrary spatial dimension and with long-range entanglement.…
The electronic properties of semiconductor, vertical, double quantum dot systems with few electrons are investigated by means of analytic, configuration-interaction, and mean-field methods. The combined effect of a high magnetic field,…
Within unitary transformed Hamiltonian of Fr\"ohlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at $T=0$ K in a model of…
Consider $N$ bosons in a finite box $\Lambda= [0,L]^3\subset \bR^3$ interacting via a two-body nonnegative soft potential $V= \lambda \tilde V$ with $\tilde V$ fixed and $\lambda>0$ small. We will take the limit $L, N \to \infty$ by keeping…
Two-, three-, and four-boson systems are studied close to the unitary limit using potential models constructed to reproduce the minimal information given by the two-body scattering length $a$ and the two-body binding energy or virtual state…