Related papers: Exact solutions to the quantum many-body problem u…
Renormalization group methods can be applied to the nuclear many-body problem using the approach proposed by Shankar. We start with the two-body low momentum interaction V_{low k} and use the RG flow from the particle-hole channels to…
Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional Hubbard model as an example to demonstrate its…
Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most…
We introduce a new computational method to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a…
The second-order reduced density matrix method (the RDM method) has performed well in determining energies and properties of atomic and molecular systems, achieving coupled-cluster singles and doubles with perturbative triples (CC SD(T))…
We study the quantum evolution of many-body Fermi gases in three dimensions, in arbitrarily large domains. We consider both particles with non-relativistic and with relativistic dispersion. We focus on the high-density regime, in the…
Non-Hermitian (NH) quantum systems have emerged as a powerful framework for describing open quantum systems, non-equilibrium dynamics, and engineered quantum optical materials. However, solving the ground-state properties of NH systems is…
The two-body problem with a central interaction on simply connected constant curvature spaces of an arbitrary dimension is considered. The explicit expression for the quantum two-body Hamiltonian via a radial differential operator and…
We study the many-body theory of graphene Dirac quasiparticles interacting via the long-range Coulomb potential, taking as a starting point the ladder approximation to different vertex functions. We test in this way the low-energy behavior…
Constrained mechanical multibody systems arise in many important applications like robotics, vehicle and machinery dynamics and biomechanics of locomotion of humans. These systems are described by the Euler-Lagrange equations which are…
We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs (thermal) state. The classical analog of this problem, known as learning graphical models or Boltzmann machines, is a well-studied…
In this paper, we provide the two-body exact solutions of two dimensional (2D) Schr\"{o}dinger equation with isotropic $\pm 1/r^3$ interactions. Analytic quantum defect theory are constructed base on these solutions and are applied to…
Free classical particles have well-defined momentum and position, while free quantum particles have well-defined momentum but a position fully delocalized over the sample volume. We develop a many-body formalism based on wave-packet…
We extend the conforming virtual element method to the numerical resolution of eigenvalue problems with potential terms on a polytopal mesh. An important application is that of the Schrodinger equation with a pseudopotential term. This…
We analyze the properties of particles trapped in three-dimensional potentials formed from superimposed Gaussian beams, fully taking into account effects of potential anharmonicity and non-separability. Although these effects are negligible…
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or…
The canonical ADM equations are solved in terms of the conformal factor in the instantaneous York gauge. A simple derivation is given for the solution of the two body problem. A geometrical characterization is given for the apparent…
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
Within the hyperspherical harmonics approach the three-body problem is reduced to a motion of one effective particle in a "strongly deformed" field, which is described in coupled-channel formalism. This method is especially suited to…
The stationary Schr\"odinger equation can be cast in the form $H \rho = E \rho$, where $H$ is the system's Hamiltonian and $\rho$ is the system's density matrix. We explore the merits of this form of the stationary Schr\"odinger equation,…