Related papers: Exact solutions to the quantum many-body problem u…
Fermionic reduced density matrices summarize the key observables in fermionic systems. In electronic systems, the two-particle reduced density matrix (2-RDM) is sufficient to determine the energy and most physical observables of interest.…
The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some…
Here we study the dynamics of many-body quantum systems using time dependent quantum Monte Carlo method where the evolution is described by ensembles of particles and guide waves. The exponential-time scaling inherent to the quantum…
Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence,connectivity and gate…
These lectures contain a theoretical introduction to the few-body problem with short-range resonant binary interactions. In the first part we discuss the effective range expansion for the two-body scattering amplitude emphasizing the role…
We map the general relativistic two-body problem onto that of a test particle moving in an effective external metric. This effective-one-body approach defines, in a non-perturbative manner, the late dynamical evolution of a coalescing…
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here…
Starting from a microscopic description of weak system-bath interactions, we derive from first principles a quantum master equation that does not rely on the well-known rotating wave approximation. This includes generic many-body systems,…
In this paper, we propose a method to describe the many-body problem of electrons in honeycomb materials via the introduction of random fields which are coupled to the electrons and have a Gaussian distribution. From a one-body approach to…
A new mathematical model for the description of three electron quantum dots in 2D space is created, and ground states of this system in external magnetic field is investigated. The Schrodinger equation for three two-dimensional electrons is…
Quantum many-body simulation provides a straightforward way to understand fundamental physics and connect with quantum information applications. However, suffering from exponentially growing Hilbert space size, characterization in terms of…
The low temperature thermodynamics of correlated 1D fermionic models with spin and charge degrees of freedom is obtained by exact diagonalization (ED) of small systems and followed by density matrix renormalization group (DMRG) calculations…
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium…
We present a general approach for the solution of the three-body problem for a general interaction, and apply it to the case of the Coulomb interaction. This approach is exact, simple and fast. It makes use of integral equations derived…
Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional…
The Bogoliubov-Born-Green-Kirkwood-Yvon or Time-Dependent Density Matrix (TDDM) hierarchy of equations for higher density matrices is truncated at the three body level in approximating the three body correlation function by a quadratic form…
Understanding quantum many-body states of correlated electrons is one main theme in modern condensed matter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, has been recently realized in ultracold optical…
We propose a neural-network variational quantum algorithm to simulate the time evolution of quantum many-body systems. Based on a modified restricted Boltzmann machine (RBM) wavefunction ansatz, the proposed algorithm can be efficiently…
A Gaussian resolution method for the computation of equilibrium density matrices rho(T) for a general multidimensional quantum problem is presented. The variational principle applied to the ``imaginary time'' Schroedinger equation provides…
The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane,…