Quantum-Information Theoretic Properties of Nuclei and Trapped Bose Gases

Fermionic (atomic nuclei) and bosonic (correlated atoms in a trap) systems are studied from an information-theoretic point of view. Shannon and Onicescu information measures are calculated for the above systems comparing correlated and uncorrelated cases as functions of the strength of short range correlations. One-body and two-body density and momentum distributions are employed. Thus the effect of short-range correlations on the information content is evaluated. The magnitude of distinguishability of the correlated and uncorrelated densities is also discussed employing suitable measures of distance of states i.e. the well known Kullback-Leibler relative entropy and the recently proposed Jensen-Shannon divergence entropy. It is seen that the same information-theoretic properties hold for quantum many-body systems obeying different statistics (fermions and bosons).Comment: 24 pages, 9 figures, 1 tabl

Test of a Jastrow-type wavefunction for a trapped few-body system in one dimension

For a system with interacting quantum mechanical particles in a one-dimensional harmonic oscillator, a trial wavefunction with simple structure based on the solution of the corresponding two-particle system is suggested and tested numerically. With the inclusion of a scaling parameter for the distance between particles, at least for the very small systems tested here the ansatz gives a very good estimate of the ground state energy, with the error being of the order of ~1% of the gap to the first excited state

Effects of state dependent correlations on nucleon density and momentum distributions

The proton momentum and density distributions of closed shell nuclei are calculated within a model treating short--range correlations up to first order in the cluster expansion. The validity of the model is verified by comparing the results obtained with purely scalar correlations with those produced by finite nuclei Fermi Hypernetted Chain calculations. State dependent correlations are used to calculate momentum and density distributions of 12C, 16O, 40Ca, and 48Ca, and the effects of their tensor components are studied.Comment: 16 pages, latex, 8 figures, accepted for publication in Phys. Rev.

Mott Transitions and d-wave Superconductivity in Half-Filled-Band Hubbard Model on Square Lattice with Geometric Frustration

Mechanisms of Mott transitions and dx2-y2-wave superconductivity (SC) are studied in the half-filled-band Hubbard model on square lattices with a diagonal hopping term (t'), using an optimization (or correlated) variational Monte Carlo method. In the trial wave functions, a doublon-holon binding effect is introduced in addition to the onsite Gutzwiller projection. We mainly treat a d-wave singlet state and a projected Fermi sea. In both wave functions, first-order Mott transitions without direct relevance to magnetic orders take place at U=Uc approximately of the bandwidth for arbitrary t'/t. These transitions originate in the binding or unbinding of a doublon to a holon. d-wave SC appears in a narrow range immediately below Uc. The robust d-wave superconducting correlation are necessarily accompanied by enhanced antiferromagnetic correlation; the strength of SC becomes weak, as t'/t increases.Comment: 18 pages, 30 figure

Jastrow-type calculations of one-nucleon removal reactions on open ss-dd shell nuclei

Single-particle overlap functions and spectroscopic factors are calculated on the basis of Jastrow-type one-body density matrices of open-shell nuclei constructed by using a factor cluster expansion. The calculations use the relationship between the overlap functions corresponding to bound states of the $(A-1)$-particle system and the one-body density matrix for the ground state of the $A$-particle system. In this work we extend our previous analyses of reactions on closed-shell nuclei by using the resulting overlap functions for the description of the cross sections of $(p,d)$ reactions on the open $s$-$d$ shell nuclei $^{24}$Mg, $^{28}$Si and $^{32}$S and of $^{32}$S$(e,e^{\prime}p)$ reaction. The relative role of both shell structure and short-range correlations incorporated in the correlation approach on the spectroscopic factors and the reaction cross sections is pointed out.Comment: 11 pages, 5 figures, to be published in Phys. Rev.

Two-proton overlap functions in the Jastrow correlation method and cross section of the 16^{16}O(e,e′pp)14(e,e^{\prime}pp)^{14}Cg.s._{\rm g.s.} reaction

Using the relationship between the two-particle overlap functions (TOF's) and the two-body density matrix (TDM), the TOF's for the $^{16}$O$(e,e^{\prime}pp)^{14}$C$_{\rm g.s.}$ reaction are calculated on the basis of a TDM obtained within the Jastrow correlation method. The main contributions of the removal of $^1S_0$ and $^3P_1$ $pp$ pairs from $^{16}$O are considered in the calculation of the cross section of the $^{16}$O$(e,e^{\prime}pp)^{14}$C$_{\rm g.s.}$ reaction using the Jastrow TOF's which include short-range correlations (SRC). The results are compared with the cross sections calculated with different theoretical treatments of the TOF's.Comment: 10 pages, 8 figures, ReVTeX

Bose-Einstein condensation of correlated atoms in a trap

The Bose-Einstein condensation of correlated atoms in a trap is studied by examining the effect of inter-particle correlations to one-body properties of atomic systems at zero temperature using a simplified formula for the correlated two body density distribution. Analytical expressions for the density distribution and rms radius of the atomic systems are derived using four different expressions of Jastrow type correlation function. In one case, in addition, the one-body density matrix, momentum distribution and kinetic energy are calculated analytically, while the natural orbitals and natural occupation numbers are also predicted in this case. Simple approximate expressions for the mean square radius and kinetic energy are also given.Comment: 14 pages, 19 figures, 1 Table, RevTe

Variational state based on the Bethe ansatz solution and a correlated singlet liquid state in the one-dimensional t-J model

The one-dimensional t-J model is investigated by the variational Monte Carlo method. A variational wave function based on the Bethe ansatz solution is newly proposed, where the spin-charge separation is realized, and a long-range correlation factor of Jastrow-type is included. In most regions of the phase diagram, this wave function provides an excellent description of the ground-state properties characterized as a Tomonaga-Luttinger liquid; Both of the amplitude and exponent of correlation functions are correctly reproduced. For the spin-gap phase, another trial state of correlated singlet pairs with a Jastrow factor is introduced. This wave function shows generalized Luther-Emery liquid behavior, exhibiting enhanced superconducting correlations and exponential decay of the spin correlation function. Using these two variational wave functions, the whole phase diagram is determined. In addition, relations between the correlation exponent and variational parameters in the trial functions are derived.Comment: REVTeX 3.0, 27 pages. 7 figures available upon request ([email protected]). To be published in Phys. Rev. B 5

Optimization of Gutzwiller Wavefunctions in Quantum Monte Carlo

Gutzwiller functions are popular variational wavefunctions for correlated electrons in Hubbard models. Following the variational principle, we are interested in the Gutzwiller parameters that minimize e.g. the expectation value of the energy. Rewriting the expectation value as a rational function in the Gutzwiller parameters, we find a very efficient way for performing that minimization. The method can be used to optimize general Gutzwiller-type wavefunctions both, in variational and in fixed-node diffusion Monte Carlo.Comment: 9 pages RevTeX with 10 eps figure

Antisymmetrized Green's function approach to (e,e′)(e,e') reactions with a realistic nuclear density

A completely antisymmetrized Green's function approach to the inclusive quasielastic $(e,e')$ scattering, including a realistic one-body density, is presented. The single particle Green's function is expanded in terms of the eigenfunctions of the nonhermitian optical potential. This allows one to treat final state interactions consistently in the inclusive and in the exclusive reactions. Nuclear correlations are included in the one-body density. Numerical results for the response functions of $^{16}$O and $^{40}$Ca are presented and discussed.Comment: 45 pages, 3 figure