Related papers: Matrix mechanics for actual atoms and molecules
We investigate the efficiency of the recently proposed Restricted Boltzmann Machine (RBM) representation of quantum many-body states to study both the static properties and quantum spin dynamics in the two-dimensional Heisenberg model on a…
In many physical applications, bound states and/or resonances are observed, which raises the question whether these states are elementary or composite. Here we elaborate on several methods for calculating the compositeness $X$ of bound…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
Heisenberg's matrix formulation of quantum mechanics can be generalized to relativistic systems by evolving in light-front time tau = t+z/c. The spectrum and wavefunctions of bound states, such as hadrons in quantum chromodynamics, can be…
A variational technique to describe the ground and scattering states below the break-up threshold for a three-nucleon system is developed. The method consists in expanding the wave function in terms of correlated Harmonic Hyperspherical…
We consider many-body quantum systems on a finite lattice, where the Hilbert space is the tensor product of finite-dimensional Hilbert spaces associated with each site, and where the Hamiltonian of the system is a sum of local terms. We are…
The spectra of quantum dots of different geometry (``quantum ring'', ``quantum cylinder'', ``spherical square-well'' and ``parabolic confinement'') are studied. The stochastic variational method on correlated Gaussian basis functions and a…
We consider an electronic bound state of the usual, non-relativistic, molecular Hamiltonian with Coulomb interactions, fixed nuclei, and N electrons (N>1). Near appropriate electronic collisions, we determine the regularity of the…
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…
The bootstrap is a technique recently developed to get energy eigenvalues of bound states and correlation functions. There are three crucial steps - recursive equations, positivity constraints, search space. We calculate recursive equations…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
Many-particle electron states in semiconductor quantum dots with carrier-mediated ferromagnetism are studied theoretically within the self-consistent Boltzmann equation formalism. Depending on the conditions, a quantum dot may contain there…
The Jaynes-Cummings model (JCM), one of the paradigms of quantum electrodynamics, was introduced to describe interaction between light and a fictitious two-level atom. Recently it was suggested that the JCM Hamiltonian can be invoked to…
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount…
We provide the quantum mechanics of many particles moving in twisted N-enlarged Newton-Hooke space-time. In particular, we consider the example of such noncommutative system - the set of M particles moving in Coulomb field of external…
The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property…
Advantages of using a low-energy effective theory to study bound state properties are briefly discussed, and a nonperturbative implementation of such an effective theory is described within the context of nonrelativistic quantum mechanics.…
The molecular Hubbard Hamiltonian (MHH) naturally arises for ultracold ground state polar alkali dimer molecules in optical lattices. We show that, unlike ultracold atoms, different molecules display different many-body phases due to…
We formulate a three-dimensional semi-classical model to address triple and double ionization in three-electron atoms driven by intense infrared laser pulses. During time propagation, our model fully accounts for the Coulomb singularities,…