Ground-state Energy Of Systems Research Articles

Adiabatic projection: Bridging ab initio, density functional, semiempirical, and embedding approximations.

Modern electronic structure approximations routinely employ reference systems described by approximate Hamiltonians. This work introduces the adiabatic projection formalism for building formally exact corrections to such reference systems. Starting from the real Hamiltonian of a many-electron system, one constructs a reference system Hamiltonian by projecting the kinetic and electron-electron interaction operators onto "interesting" states. The reference system is corrected by density functionals for the difference between the projected and unprojected kinetic and electron-electron energies. These density functionals are constructed from adiabatic connections between the reference and real systems. The Hohenberg-Kohn theorems imply the existence of exact functionals, which can ensure that the reference system's ground-state energy and density match the real system. Adiabatic projection further generalizes Kohn-Sham density functional theory (DFT) and the generalized adiabatic connection [W. Yang, J. Chem. Phys. 109, 10107 (1998)] and recovers these methods for certain choices of projection operators. Other choices of projection operators offer new opportunities, including formally exact and systematically improvable analogues to wavefunction-in-DFT embedding, DFT+U, and semiempirical theories. Numerical results are presented for two representative choices: a projected exchange-correlation correction to small-basis-set coupled cluster theory and a projected kinetic energy density functional correcting basis set errors in DFT. The latter offers performance for dimerization energies approaching the Boys-Bernardi counterpoise correction while also correcting intramolecular basis set superposition errors.

Thermodynamics at zero temperature: Inequalities for the ground state of a quantum many-body system

We prove that for a single-component many-body system at zero temperature the inequality Eint≤PV holds, where Eint is the interaction energy, P is pressure and V is volume. This inequality is proven under rather general assumptions with the use of Anderson-type bound relating ground state energies of systems with different numbers of particles. We also consider adding impurity particles to the system and derive inequalities on the chemical potential of the impurity and binding energy of the bound state of two impurities.

The Study of the Ground State Properties of Heavy Famion System Using an Extended Kondo-Anderson Model in One Dimension

The Kondo interaction coupling, Heisenberg exchange coupling, and Coulomb interactions within d-sites, were introduced in a one dimensional Periodic Anderson Model Hamiltonian (PAMH) to further investigate the effects of interaction parameters on the ground state energy of systems with heavy fermions (HF) behavior. Periodic Anderson model PAM being one of the most successful model for studying the heavy fermions System (HFS) was used in an extended version (mixed Kondo-Anderson representation) on a system of three-electrons interacting on three-sites cluster. Exact Diagonalization technique (EDT) normally used to solve conventional PAM calculation was considered in this work for a very small cluster. Hamiltonian used to describe this model contains the usual term describing the kinetic energy of the system, on-site coulomb repulsion and a hopping integral. The Hamiltonian is acted on the different Hilbert states of the lattice system and results of the interactions were obtained in terms of hopping integral, coulomb repulsions, exchange couplings and the hybridization term. Graphs of ground state energy Eo plotted agains tthese interaction parameters were presented in a clear format. As these parameters were varied numerically through a finite range of values, the individual effects of these parameters on the system’s ground state energy were observed and discussed. Hence, the results obtained from this work shows theoretically how the tuning of the Columbic interaction within the conduction band provides information that sheds light on the underlying physics of the heavy fermions systems models. Results obtained from this work further demonstrate the reliability of the model Hamiltonians that we have harnessed and the importance of considering electron-lattice interactions as well as interactions that account for magnetic impurities for the proper description of heavy fermions material.

Using SCF metadynamics to extend density matrix embedding theory to excited states.

A new framework based on density matrix embedding theory (DMET) capable of directly targeting excited electronic states is proposed and implemented. DMET has previously been shown to be an effective method of calculating the ground state energies of systems exhibiting strong static correlation but has never been applied to calculate excited state energies. In this work, the Schmidt decomposition is applied directly on excited states, approximated by higher lying self-consistent field solutions. The DMET prescription is applied following this Schmidt decomposition allowing for a direct embedding of excited states. Initial results are obtained for a system of multiple hydrogen dimers and the lithium hydride dissociation. We analyze the nature of each part of the excited state DMET calculation and identify challenges. These challenges to the implementation of excited state DMET are discussed, and potential suggestions moving forward are recommended.

Trapped unitary two-component Fermi gases with up to ten particles

The properties of two-component Fermi gases with zero-range interactions are universal. We use an explicitly correlated Gaussian basis set expansion approach to investigate small equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement. At unitarity, we determine the ground state energy for systems with up to ten particles interacting through finite-range two-body potentials for both even and odd number of particles. We extrapolate the energies to the zero-range limit using a novel scheme that removes the linear and, in some cases, also the quadratic dependence of the ground state energies on the two-body range. Our extrapolated zero-range energies are compared with results from the literature. We also calculate the two-body Tan contact and structural properties.

Estimates for the interaction potential between two atoms

We consider a quantum system consisting of two electrons in the Coulomb field of two immovable nuclei spaced at a fixed distance, which is considered the problem parameter. We use spectral theory methods to obtain estimates of the system ground-state energy as a function of the internuclear distance. We obtain part of the results under the assumption that the Coulomb interaction constant between different atoms is small. We discuss the importance of the presented investigation for quantum chemistry.

Multipion states in lattice QCD and the charged-pion condensate

The ground-state energies of systems containing up to twelve $$\pi^+$$'s in a spatial volume V ~ (2.5 fm)^3 are computed in dynamical, mixed-action lattice QCD at a lattice spacing of ~ 0.125 fm for four different values of the light quark masses. Clean signals are seen for each ground state, allowing for a precise extraction of both the $$\pi^+\pi^+$$ scattering length and $$\pi^+\pi^+\pi^+$$-interaction from a correlated analysis of systems containing different numbers of $$\pi^+$$'s. This extraction of the $$\pi^+\pi^+$$ scattering length is consistent with than that from the $$\pi^+\pi^+$$-system alone. The large number of systems studied here significantly strengthens the arguments presented in our earlier work and unambiguously demonstrates the presence of a low energy $$\pi^+\pi^+\pi^+$$-interaction. The equation of state of a $$\pi^+$$ gas is investigated using our numerical results and the density dependence of the isospin chemical potential for these systems agrees well with the theoretica

Stochastic homogenization and random lattices

We present some variants of stochastic homogenization theory for scalar elliptic equations of the form − div [ A ( x ε , ω ) ∇ u ( x , ω ) ] = f . These variants basically consist in defining stochastic coefficients A ( x ε , ω ) from stochastic deformations (using random diffeomorphisms) of the periodic setting, as announced in [X. Blanc, C. Le Bris, P.-L. Lions, Une variante de la théorie de l'homogénéisation stochastique des opérateurs elliptiques (A variant of stochastic homogenization theory for elliptic operators), C. R. Acad. Sci. Sér. I 343 (2006) 717–727]. The settings we define are not covered by the existing theories. We also clarify the relation between this type of questions and our construction, performed in [X. Blanc, C. Le Bris, P.-L. Lions, A definition of the ground state energy for systems composed of infinitely many particles, Commun. Partial Differential Equations 28 (1–2) (2003) 439–475; X. Blanc, C. Le Bris, P.-L. Lions, The energy of some microscopic stochastic lattices, Arch. Rat. Mech. Anal. 184 (2) (2007) 303–339], of the energy of, both deterministic and stochastic, microscopic infinite sets of points in interaction.

Zero-point energies of subharmonic oscillators

We observe that ground-state energies of systems in potentials | x | α vary with α in a peculiar manner in regions α < 2 . This variation is most possibly due to a quantum effect. A class of still weaker confining potentials with logarithmic rise leads to considerably lower zero-point energies. Certain implications of the findings are indicated.

Asymptotic Behavior of the t Expansion

The asymptotic behavior of a system's ground-state energy from the t expansion of Horn and Weinstein has been suggested to have the form E1(t)=E1+∑exp (−ant+bn). In the limit of very large t, this becomes E1(t)=E1+exp (−a1t+b1). A simple analysis shows that the parameters are a1=E2−E1 and b1=ln [(E2−E1)|c2|2/|c1|2]. Functions are introduced which allow determination of a1, b1 and lower bounds to E1.

GROUND STATE ENERGY ESTIMATION OF JELLIUM SYSTEMS BY SPATIAL GRIDDING

A numerical approach to estimate the ground state energy of jellium systems is explored. In this approach, the space occupied by the system is gridded, with individual grid elements small enough that the electron density within an element is considered constant. The energy of an element is then a function (and not functional) of its electron density in a given environment and the total energy of the system is obtained by summing the contributions from all the elements. A self-consistent field procedure to optimize the grid densities is then carried out resulting in the ground state energy of the system. The method is tested for known atomic and jellium models to show its validity. This approach shows enough flexibility to handle the irregular jellium shapes.

Variational treatment for the bipolaronic system.

We reconsider the bipolaronic system by introducing the squeezed-polaron model or two-phonon coherent state, and obtain more satisfactory results than before with respect to lowering the system's ground-state energy and extending the singlet superconducting phase in the phase diagram of such a bipolaronic system. The necessity and the limit of using our variational treatment to this bipolaronic system are also discussed.

Probabilistic solutions of generalised birth and death equations and applications to field theory

The author gives probabilistic solutions to the equations describing non-relativistic quantum 'electrodynamical' systems. These solutions involve, besides the usual diffusion processes, also birth and death processes corresponding to the 'photon number' variables. Some inequalities are stated and in particular bounds to the ground-state energy of systems composed of a non-relativistic particle interacting with a field are established. The result is general and it is applied as an example to the polaron problem.

Excitations in quadrupolar-coupled systems

The method of double-time Green's functions is used to study the excitation spectrum of an isotropic spin-one system with quadrupolar coupling. It is shown that the random-phase approximation leads to a violation of a spin-one identity and thus to equivocal results. A consistent theory free from ambiguities is developed. Also, exact upper and lower bounds on the ground-state energy of systems with dipolar as well as quadrupolar coupling are derived and studied.

Standing Pion Waves in Superdense Matter

Previous results for the ground-state energies of systems of nucleons interacting with a condensed running-wave mode of ${\ensuremath{\pi}}^{\ensuremath{-}}$ mesons are extended to the case of standing-wave modes. The onset density of the condensation turns out to be the same as in the running-wave case; at higher densities the standing-wave case has a somewhat lower energy, at least in the case in which ordinary nuclear forces are not taken into account. There are reasons to believe that the effects of these nuclear forces on the condensation will be much greater for the standing-wave case than for the running-wave case. The possibilities of ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{0}$ condensation are discussed.