Related papers: Analytic Solution for the Ground State Energy of t…
We present a Kadanoff-Baym formalism to study time-dependent phenomena for systems of interacting electrons and phonons in the framework of many-body perturbation theory. The formalism takes correctly into account effects of the initial…
We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations.…
In this article, we define a new mathematical object, called a pair $D=\left(A,C\right)$ of anti-commutation matrices (ACMP) based on the anti-commutation relation $a^\dag_{i}a_{j} + a_{j}a^\dag_{i} = \delta_{ij}$ applied to the scalar…
The closed analytical expression for the electron density of states function in a rectangular lattice is derived in an elementary way in terms of complete elliptic integrals of the first kind. The lattice can be treated as a deformed square…
The weak coupling asymptotics, to order $(c/\rho)^2$, of the ground state energy of the delta-function Bose gasmis derived. Here $2c\ge 0$ is the delta-function potential amplitude and $\rho$ the density of the gas in the thermodynamic…
A one-dimensional quantum many-body system consisting of particles confined in a harmonic potential and subject to finite-range two-body and three-body inverse-square interactions is introduced. The range of the interactions is set by…
We study the quantum lattice gas model in one dimension introduced by Lesanovsky, who showed that the exact ground state and a couple of excited states can be obtained analytically. The Hamiltonian of the model depends solely on the…
The quantum mechanical ground state of a 2D $N$-electron system in a confining potential $V(x)=Kv(x)$ ($K$ is a coupling constant) and a homogeneous magnetic field $B$ is studied in the high density limit $N\to\infty$, $K\to \infty$ with…
The volume-dependence of a shallow three-particle bound state in the cubic box with a size $L$ is studied. It is shown that, in the unitary limit, the energy-level shift from the infinite-volume position is given by $\Delta E=c…
In this paper, we investigate a system of quantum electrodynamics with cutoffs. The total Hamiltonian is defined on a tensor product of a fermion Fock space and a boson Fock. It is shown that, under spatially localized conditions and…
We derive a formula that expresses the density of states of a system with continuous degrees of freedom as a function of microcanonical averages of squared gradient and Laplacian of the Hamiltonian. This result is then used to propose a…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, with the self-generated magnetic field, and, in particular, to derive relativistic Scott…
It is virtually impossible to directly solve the Schr\"odinger equation for a many-electron wave function due to the exponential growth in degrees of freedom with increasing particle number. The two-body reduced density matrix (2-RDM)…
We consider an interacting homogeneous Bose gas at zero temperature in two spatial dimensions. The properties of the system can be calculated as an expansion in powers of g, where g is the coupling constant. We calculate the ground state…
We describe a further development of the stochastic state selection method, a new Monte Carlo method we have proposed recently to make numerical calculations in large quantum spin systems. Making recursive use of the stochastic state…
A constituent quark model, which has recently been successfully applied to the study of heavy quarkonium properties such as its spectrum but also a diverse array of observables related with their electromagnetic, strong and weak decays and…
We consider energy-critical damped wave equation \begin{equation*} \partial_{tt}u-\Delta u+\alpha \partial_t u=\left|u\right|^{\frac{4}{D-2}}u \end{equation*} with radial initial data in dimensions $D\geq 4$. The equation has a nontrivial…
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground…
We review two results in which trial states for bosonic Hamiltonians were discussed. The problem of finding a trial state for a system with a hard-core potential in the Gross-Pitaevskii regime was recently solved by proving a link with the…
The one-body density matrix is derived within the Extended Thomas-Fermi approximation. This has been done starting from the Wigner-Kirkwood distribution function for a non-local single-particle potential. The links between this new approach…