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Living systems face both environmental complexity and limited access to free-energy resources. Survival under these conditions requires a control system that can activate, or deploy, available perception and action resources in a context specific way. We show here that when systems are described as executing active inference driven by the free-energy principle (and hence can be considered Bayesian prediction-error minimizers), their control flow systems can always be represented as tensor networks (TNs). We show how TNs as control systems can be implmented within the general framework of quantum topological neural networks, and discuss the implications of these results for modeling biological systems at multiple scales., Comment: 44 pgs

Deep Neural Networks miss a principled model of their operation. A novel framework for supervised learning based on Topological Quantum Field Theory that looks particularly well suited for implementation on quantum processors has been recently explored. We propose using this framework to understand the problem of generalisation in Deep Neural Networks. More specifically, in this approach, Deep Neural Networks are viewed as the semi-classical limit of Topological Quantum Neural Networks. A framework of this kind explains the overfitting behavior of Deep Neural Networks during the training step and the corresponding generalisation capabilities. We explore the paradigmatic case of the perceptron, which we implement as the semiclassical limit of Topological Quantum Neural Networks. We apply a novel algorithm we developed, showing that it obtains similar results to standard neural networks, but without the need for training (optimisation)., Comment: 22 pages (two columns), 9 figures. v2: Several parts rewritten, and computational results added

Our work intends to show that: (1) Quantum Neural Networks (QNN) can be mapped onto spinnetworks, with the consequence that the level of analysis of their operation can be carried out on the side of Topological Quantum Field Theories (TQFT); (2) Deep Neural Networks (DNN) are a subcase of QNN, in the sense that they emerge as the semiclassical limit of QNN; (3) A number of Machine Learning (ML) key-concepts can be rephrased by using the terminology of TQFT. Our framework provides as well a working hypothesis for understanding the generalization behavior of DNN, relating it to the topological features of the graphs structures involved., Comment: 25 pages, 10 figures

We show that a generalized version of the holographic principle can be derived from the Hamiltonian description of information flow within a quantum system that maintains a separable state. We then show that this generalized holographic principle entails a general principle of gauge invariance. When this is realized in an ambient Lorentzian space-time, gauge invariance under the Poincare group is immediately achieved. We apply this pathway to retrieve the action of gravity. The latter is cast a la Wilczek through a similar formulation derived by MacDowell and Mansouri, which involves the representation theory of the Lie groups SO(3,2) and SO(4,1)., Comment: 26 pages, 1 figure

S-wave pairing in neutron matter is studied within an extension of correlated basis function (CBF) theory to include the strong, short range spatial correlations due to realistic nuclear forces and the pairing correlations of the Bardeen, Cooper and Schrieffer (BCS) approach. The correlation operator contains central as well as tensor components. The correlated BCS scheme of Ref. [Nucl. Phys. A363 (1981) 383], developed for simple scalar correlations, is generalized to this more realistic case. The energy of the correlated pair condensed phase of neutron matter is evaluated at the two--body order of the cluster expansion, but considering the one--body density and the corresponding energy vertex corrections at the first order of the Power Series expansion. Based on these approximations, we have derived a system of Euler equations for the correlation factors and for the BCS amplitudes, resulting in correlated non linear gap equations, formally close to the standard BCS ones. These equations have been solved for the momentum independent part of several realistic potentials (Reid, Argonne v_{14} and Argonne v_{8'}) to stress the role of the tensor correlations and of the many--body effects. Simple Jastrow correlations and/or the lack of the density corrections enhance the gap with respect to uncorrelated BCS, whereas it is reduced according to the strength of the tensor interaction and following the inclusion of many--body contributions., Comment: 20 pages, 8 figures, 1 table

The application of the Correlated basis function theory and of the Fermi hypernetted chain technique, to the description of the ground state of medium-heavy nuclei is reviewed. We discuss how the formalism, originally developed for symmetric nuclear matter, should be changed in order to describe finite nuclear systems, with different number of protons and neutrons. This approach allows us to describe doubly closed shell nuclei by using microscopic nucleon-nucleon interactions. We presents results of numerical calculations done with two-nucleon interactions of Argonne type,implemented with three-body forces of Urbana type. Our results regard ground-state energies, matter, charge and momentum distributions, natural orbits, occupation numbers, quasi-hole wave functions and spectroscopic factors of 12C, 16O, 40Ca, 48Ca and 208Pb nuclei., Comment: 127 Pages, 37 figures, Accepted for publication in Physics Reports

The $^1S_0$ pairing in neutron matter has been investigated in presence of realistic two-- and three--nucleon interactions. We have adopted the Argonne $v_{8^\prime}$ NN and the Urbana IX 3N potentials. Quantum Monte Carlo theory, specifically the Auxiliary Field Diffusion Monte Carlo method, and Correlated Basis Function theory are employed in order to get quantitative and reliable estimates of the gap. They both fully take into account the medium modifications due to the interaction induced correlations. The two methods are in good agreement up to the maximum gap density and both point to a slight reduction with respect to the standard BCS value. In fact, the maximum gap is about $2.5 \text{MeV}$ at $k_F \sim 0.8 \text{fm}^{-1}$ in BCS and 2.3--$2.4 \text{MeV}$ at $k_F \sim 0.6 \text{fm}^{-1}$ in correlated matter. At higher densities the Quantum Monte Carlo gap becomes close to BCS. In general, the computed medium polarization effects are much smaller than those previously estimated within \emph{all theories}. Truncations of Argonne $v_{8^\prime}$ to simpler forms give the same gaps in BCS, provided the truncated potentials have been refitted to the same NN data set. Differences among the models appear in the correlated theories, most of the reduction being attributable to the tensor force. The three--nucleon interaction provides an additional increase of the gap of about 0.35 MeV., Comment: 4 pages, 1 figure, typeset using REVTeX

The correlated basis function theory is applied to the study of medium-heavy doubly closed shell nuclei with different wave functions for protons and neutrons and in the jj coupling scheme. State dependent correlations including tensor correlations are used. Realistic two-body interactions of Argonne and Urbana type, together with three-body interactions have been used to calculate ground state energies and density distributions of the 12C, 16O, 40Ca, 48Ca and 208Pb nuclei., Comment: Latex 10 pages, 3 Tables, 10 Figures

We extend the correlated basis functions theory (CBF) for nuclei with different number of protons and neutrons and in j-j coupling scheme. By means of the Fermi hypernetted chain integral equations, in conjunction with the single operator chain approximation (FHNC/SOC), we evaluate the ground state and the one-body densities for 40Ca, 48Ca and 208Pb nuclei. The realistic Argonne V8' two-nucleon potentials has been used. We compare the ground-state properties of these nuclei calculated by using correlation functions with and without tensor components., Comment: 4 Pages, 2 figures, Talk presented at the workshop , Cortona (It) 6-9 Oct. 2004

We study the energy per particle of symmetric nuclear matter and pure neutron matter using realistic nucleon--nucleon potentials having non central tensor and spin--orbit components, up to three times the empirical nuclear matter saturation density, $\rho_0=0.16$ fm$^{-3}$. The calculations are carried out within the frameworks of the Brueckner--Bethe--Goldstone (BBG) and Correlated Basis Functions (CBF) formalisms, in order to ascertain the accuracy of the methods. The two hole--line approximation, with the continuous choice for the single particle auxiliary potential, is adopted for the BBG approach, whereas the variational Fermi Hypernetted Chain/Single Operator Chain theory, corrected at the second order perturbative expansion level, is used in the CBF one. The energies are then compared with the available Quantum and Variational Monte Carlo results in neutron matter and with the BBG, up to the three hole--line diagrams. For neutron matter and potentials without spin--orbit components all methods, but perturbative CBF, are in reasonable agreement up to $\rho\sim$ 3 $\rho_0$. After the inclusion of the LS interactions, we still find agreement around $\rho_0$, whereas it is spoiled at larger densities. The spin--orbit potential lowers the energy of neutron matter at $\rho_0$ by $\sim$ 3--4 MeV per nucleon. In symmetric nuclear matter, the BBG and the variational results are in agreement up to $\sim$ 1.5 $\rho_0$. Beyond this density, and in contrast with neutron matter, we find good agreement only for the potential having spin--orbit components., Comment: 18 pages, 4 tables. Accepted in PLB

The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values $x\sim 0.001$. The condensate fraction in 2D is also computed and found generally lower than the 3D one at the same $x$., Comment: Submitted to PRA. 7 pages and 8 figures

The energy and structure of dilute gases of hard spheres in three dimensions is discussed, together with some aspects of the corresponding 2D systems. A variational approach in the framework of the Hypernetted Chain Equations (HNC) is used starting from a Jastrow wavefunction that is optimized to produce the best two--body correlation factor with the appropriate long range. Relevant quantities describing static properties of the system are studied as a function of the gas parameter $x=\rho a^d$ where $\rho$, $a$ and $d$ are the density, $s$--wave scattering length of the potential and dimensionality of the space, respectively. The occurrence of a maximum in the radial distribution function and in the momentum distribution is a natural effect of the correlations when $x$ increases. Some aspects of the asymptotic behavior of the functions characterizing the structure of the systems are also investigated., Comment: Proceedings of the QFS2004 conference in Trento. To appear in JLTP

The He2-SF6 trimers, in their different He isotopic combinations, are studied both in the framework of the correlated Jastrow approach and of the Correlated Hyperspherical Harmonics expansion method. The energetics and structure of the He-SF6 dimers are analyzed, and the existence of a characteristic rotational band in the excitation spectrum is discussed, as well as the isotopic differences. The binding energies and the spatial properties of the trimers, in their ground and lowest lying excited states, obtained by the Jastrow ansatz are in excellent agreement with the results of the converged CHH expansion. The introduction of the He-He correlation makes all trimers bound by largely suppressing the short range He-He repulsion. The structural properties of the trimers are qualitatively explained in terms of the shape of the interactions, Pauli principle and masses of the constituents., Comment: 17 pages, 5 figures. Submitted to PRA

The energy and structure of dilute hard- and soft-sphere Bose gases are systematically studied in the framework of several many-body approaches, as the variational correlated theory, the Bogoliubov model and the uniform limit approximation, valid in the weak interaction regime. When possible, the results are compared with the exact diffusion Monte Carlo ones. A Jastrow type correlation provides a good description of the systems, both hard- and soft-spheres, if the hypernetted chain energy functional is freely minimized and the resulting Euler equation is solved. The study of the soft-spheres potentials confirms the appearance of a dependence of the energy on the shape of the potential at gas paremeter values of $x \sim 0.001$. For quantities other than the energy, such as the radial distribution functions and the momentum distributions, the dependence appears at any value of $x$. The occurrence of a maximum in the radial distribution function, in the momentum distribution and in the excitation spectrum is a natural effect of the correlations when $x$ increases. The asymptotic behaviors of the functions characterizing the structure of the systems are also investigated. The uniform limit approach results very easy to implement and provides a good description of the soft-sphere gas. Its reliability improves when the interaction weakens., Comment: Accepted in Phys. Rev. A

We compute the distribution of quasideuterons in doubly closed shell nuclei. The ground states of $^{16}$O and $^{40}$Ca are described in $ls$ coupling using a realistic hamiltonian including the Argonne $v_{8}^\prime$ and the Urbana IX models of two-- and three--nucleon potentials, respectively. The nuclear wave function contains central and tensor correlations, and correlated basis functions theory is used to evaluate the distribution of neutron-proton pairs, having the deuteron quantum numbers, as a function of their total momentum. By computing the number of deuteron--like pairs we are able to extract the Levinger's factor and compare to both the available experimental data and the predictions of the local density approximation, based on nuclear matter estimates. The agreement with the experiments is excellent, whereas the local density approximation is shown to sizably overestimate the Levinger's factor in the region of the medium nuclei., Comment: 26 pages, 8 figures, typeset using REVTeX

Final-state interactions in the response of a many-body system to an external probe delivering large momentum are normally described using the eikonal approximation, for the trajectory of the struck particle, and the frozen approximation, for the positions of the spectators. We propose a generalization of this scheme, in which the initial momentum of the struck particle is explicitly taken into account. Numerical calculations of the nuclear matter response at 1 $< |{\bf q}| <$ 2 GeV/c show that the inclusion of this momentum dependence leads to a sizable effect in the low energy tail. Possible implications for the analysis of existing electron-nucleus scattering data are discussed., Comment: 21 pages, 4 figures

We discuss some single particle properties of $^{16}$O and $^{40}$Ca using correlated basis function theory and Fermi hypernetted chain equations with central and tensor correlations. In particular, we concentrate on one body density matrix, momentum distribution, natural orbits and quasi hole states. The correlations are variationally generated by a realistic hamiltonian containing the Argonne $v'_{8}$ two-nucleon and Urbana IX three-nucleon interactions. The correlated momentum distributions show the well known enhancement at large momenta, with a relative importance of the different correlations (Jastrow and tensor) similar to that in nuclear matter. The natural orbits and their occupation numbers are obtained by diagonalization of the density matrix. The correlated first natural orbits occupations are depleted by more than 10%, whereas the first following ones are occupied by a few percent. The spectroscopic factors of the valence states are lowered by $\sim 8-12%$ with respect to unity by central and tensor correlations, confirming that short range correlations alone are not able to explain the values extracted from $(e,e'p)$ experiments., Comment: 17 pages, 3 figures, Proceedings 5th Workshop on "e.-m. induced two-hadron emission", Lund, June 13-16, 2001

We analyze the properties of deuteron-like structures in infinite, correlated nuclear matter, described by a realistic hamiltonian containing the Urbana $v_{14}$ two-nucleon and the Urbana TNI many-body potentials. The distribution of neutron-proton pairs, carrying the deuteron quantum numbers, is obtained as a function of the total momentum by computing the overlap between the nuclear matter in its ground state and the deuteron wave functions in correlated basis functions theory. We study the differences between the S- and D-wave components of the deuteron and those of the deuteron-like pair in the nuclear medium. The total number of deuteron type pairs is computed and compared with the predictions of Levinger's quasideuteron model. The resulting Levinger's factor in nuclear matter at equilibrium densityis 11.63. We use the local density approximation to estimate the Levinger's factor for heavy nuclei, obtaining results which are consistent with the available experimental data from photoreactions., Comment: 22 pages, 7 figures, typeset using REVTeX

Within the impulse approximation the response of a many body system at large momentum tranfer can be written in a simple and transparent form, allowing to directly relate the inclusive scattering cross section to the properties of the target ground state. Although the physics assumptions underlying impulse approximation are well defined, their implementation involves ambiguities that may cause significant differences in the calculated responses. We show that, while minimal use of the impulse approximation assumptions naturally leads to write the response in terms of the target spectral function, the widely used alternative definition in terms of the momentum distribution involves a more extended use of the same assumtpions. The difference between the responses resulting from the two procedures is illustrated by two examples., Comment: 4 pages, 2 figures

We study the properties of hypernuclei containing one lambda hyperon in the framework of the correlated basis function theory with Jastrow correlations. Fermi hypernetted chain integral equations are derived and used to evaluate energies and one-body densities of lambda hypernuclei having a doubly closed shell nucleonic core in the jj coupling scheme, from Carbon to Lead. We also study hypernuclei having the least bound neutron substituted by the lambda particle. The semi-realistic Afnan and Tang nucleon-nucleon potential and Bodmer and Usmani lambda-nucleon potential are adopted. The effect of many-body forces are considered by means either of a three body lambda-nucleon-nucleon potential of the Argonne type or of a density dependent modification of the lambda-nucleon interaction, fitted to reproduce the lambda binding energy in nuclear matter. While Jastrow correlations underestimate the attractive contribution of the three body $\la$ interaction, the density dependent potential provides a good description of the lambda binding energies over all the nuclear masses range, in spite of the relative simplicity of the model.

Bose-Einstein condensates of 10$^4$ $^{85}$Rb atoms in a cylindrical trap are studied using a recently proposed modified Gross-Pitaevskii equation. The existence of a Feshbach resonance allows for widely tuning the scattering length of the atoms, and values of the peak gas parameter, $x_{pk}$, of the order of 10$^{-2}$ can be attained. We find large differences between the results of the modified Gross-Pitaevskii and of the standard Thomas-Fermi, and Gross-Pitaevskii equations in this region. The column densities at $z=0$ may differ by as much as $\sim 30%$ and the half maximum radius by $\sim 20%$. The scattering lengths estimated by fitting the half maximum radius within different approaches can differ by $\sim 40%$., Comment: 4 LaTeX pages, 2 figures

The one body density matrix, momentum distribution, natural orbits and quasi hole states of 16O and 40Ca are analyzed in the framework of the correlated basis function theory using state dependent correlations with central and tensor components. Fermi hypernetted chain integral equations and single operator chain approximation are employed to sum cluster diagrams at all orders. The optimal trial wave function is determined by means of the variational principle and the realistic Argonne v8' two-nucleon and Urbana IX three-nucleon interactions. The correlated momentum distributions are in good agreement with the available variational Monte Carlo results and show the well known enhancement at large momentum values with respect to the independent particle model. Diagonalization of the density matrix provides the natural orbits and their occupation numbers. Correlations deplete the occupation number of the first natural orbitals by more than 10%. The first following ones result instead occupied by a few percent. Jastrow correlations lower the spectroscopic factors of the valence states by a few percent (~1-3%) and an additional ~8-12% depletion is provided by tensor correlations. It is confirmed that short range correlations do not explain the spectroscopic factors extracted from (e,e'p) experiments. 2h-1p perturbative corrections in the correlated basis are expected to provide most of the remaining strength, as in nuclear matter., Comment: 25 pages, 9 figures. Submitted to Phys.Rev.C

The results of a modified Gross-Pitaevskii equation for a system of Bose hard spheres trapped in a spherical harmonic potential are analyzed to study the validity regime of the standard GP equation., Comment: 10 pages, TeX. Proceedings of CMT XXIV, Buenos Aires, 2000

We study the ground state properties of doubly closed shell nuclei $^{16}$O and $^{40}$Ca in the framework of Correlated Basis Function theory using state dependent correlations, with central and tensor components. The realistic Argonne $v_{14}$ and $v'_{8}$ two-nucleon potentials and three-nucleon potentials of the Urbana class have been adopted. By means of the Fermi Hypernetted Chain integral equations, in conjunction with the Single Operator Chain approximation, we evaluate the ground state energy, one- and two-body densities and electromagnetic and spin static responses for both nuclei. In $^{16}$O we compare our results with the available Monte Carlo and Coupled Cluster ones and find a satisfying agreement. As in the nuclear matter case with similar interactions and wave functions, the nuclei result under-bound by 2--3 MeV/A., Comment: 33 RevTeX pages + 8 figures, to appear in Phys.Rev.C

The description of the properties of liquid Helium is a challenge for any microscopic many-body theory. In this context, we study the ground state and the excitation spectrum of one $^3$He impurity in liquid $^4$He at T=0 with the aim of illustrating the power of the correlated basis function formalism in describing heavily correlated systems. The strong interatomic interaction and the large density require the theory to be pushed to a high degree of sophistication. A many-body correlation operator containing explicit two- and thre-particle correlation functions is needed to obtain a realistic ground state wave function, whereas a perturbative expansion including up to two phonon correlated states must be enforced to study the impurity excitation energies. The theory describes accurately the experimental spectrum along all the available momentum range. As empirically shown by the experiments, a marked deviation from the quadratic Landau-Pomeranchuck behavior is found and the momentum dependent effective mass of the impurity increases of $\sim50~%$ at $q\sim1.7~\AA^{-1}$ with respect to its q=0 value. Although the main emphasis is given to the Correlated Basis Function theory, we present also comparisons with other methods, as diffusion Monte Carlo, variational Monte Carlo with shadow wave functions and time dependent correlations., Comment: 16 pages, 2 figs, world-scientific latex style. Proceedings of Many Body X, Seattle, 10-15 Sept. 1999

We review the latest variational calculations of the ground state properties of doubly closed shell nuclei, from $^{12}$C to $^{208}$Pb, with semirealistic and realistic two- and three-nucleon interactions. The studies are carried on within the framework of the correlated basis function theory and integral equations technique, with state dependent correlations having central and tensor components. We report results for the ground state energy, one- and two-body densities and static structure functions. For $^{16}$O and $^{40}$Ca we use modern interactions and find that the accuracy of the method is comparable to that attained in nuclear matter with similar hamiltonians, giving nuclei underbound by $\sim$2 MeV/A. The computed Coulomb sums are in complete agreement with the latest analysis of the experimental data., Comment: 11 Latex pages, 2 ps figures. Talk delivered at the 10th International Conference on Recent Progress In Many-Body Theories, Seattle 1999. To appear in "Advances in Quantum Many-Body Theory", vol.3, World Scientific

The inclusive electromagnetic responses in the quasi-elastic region are calculated with a model which considers the terms of the cluster expansion containinga single correlation line. The validity of this model is studied by comparing, in nuclear matter, its results with those of a complete calculation. Results in finite nuclei for both one-and two-nucleon emission are presented., Comment: 9 pages, 8 Postscript figures, RevTex

The two-nucleon spectral function in nuclear matter is studied using Correlated Basis Function perturbation theory, including central and tensor correlations produceded by a realistic hamiltonian. The factorization property of the two-nucleon momentum distribution into the product of the two single nucleon distributions shows up in an analogous property of the spectral function. The correlated model yields a two-hole contribution quenched whith respect to Fermi gas model, while the peaks acquire a quasiparticle width that vanishes as the two momenta approach $k_F$. In addition, three-hole one-particle and more complicated intermediate states give rise to a background, spread out in energy and absent in the uncorrelated models. The possible connections with one- and two-nucleon emission processes are briefly discussed., Comment: 17 pages with 4 figures. elsart.sty, elsart12.sty

We study the ground state of a system of Bose hard-spheres trapped in an isotropic harmonic potential to investigate the effect of the interatomic correlations and the accuracy of the Gross-Pitaevskii equation. We compare a local density approximation, based on the energy functional derived from the low density expansion of the energy of the uniform hard sphere gas, and a correlated wave function approach which explicitly introduces the correlations induced by the potential. Both higher order terms in the low density expansion, beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of the order of percent when the number of trapped particles becomes similar to that attained in recent experiments., Comment: Revtex, 2 figures

We evaluate microscopically the excitation spectrum of the 3He impurity in liquid 4He at T=0 and compare it with the experimental curve at the equilibrium density. The adopted correlated basis perturbative scheme includes up to two independent phonons, intermediate correlated states and the correlation operator is built up with two- and three-body correlation functions. The experimental spectrum is well described by the theory along all the available momentum range. A marked deviation from the simple Landau-Pomeranchuck, quadratic behavior is found and the momentum dependent effective mass of the impurity increases of about 50% at q around 1.7 A^-1 respect to its q=0 value. No signature of roton-like structures is found., Comment: 11 RevTeX pages, 3 ps figures. Phys.Rev.B(1998) in press

The validity of a model treating the short-range correlations up to the first order is studied by calculating the charge response of an infinite system and comparing the obtained results with those of a Fermi Hypernetted Chain calculation., Comment: 6 pages, 3 Postscript figures, to be published on Phys. Rev. C

The ground state properties of N=Z doubly closed shell nuclei are studied within correlated basis function theory. A truncated version of the Urbana v14 realistic potential, with spin, isospin and tensor components, is adopted, together with state dependent correlations. Fermi hypernetted chain integral equation and single operator chain approximation are used to evaluate density, distribution function and ground state energy of 16O and 40Ca. The results favourably compare with the available, variational MonteCarlo estimates and provide a first substantial check of the accuracy of the cluster summation method for state dependent correlations. We achieve in finite nuclei at least the same level of accuracy in the treatment of non central interactions and correlations as in nuclear matter. This opens the way for a microscopic study of medium heavy nuclei ground state using present days realistic hamiltonians., Comment: 35 pages (LateX) + 3 figures. Phys.Rev.C, in press

We study microscopically the ground state properties of 16O and 40Ca nuclei within correlated basis function theory. A truncated version of the realistic Urbana v14 (U14) potential, without momentum dependent terms, is adopted with state dependent correlations having spin, isospin and tensor components. Fermi hypernetted chain integral equations and single operator chain approximation are used to evaluate one- and two-body densities and ground state energy. The results are in good agreement with the available variational MonteCarlo data, providing a first substantial check for the accuracy of the cluster expansion method with state dependent correlations. The finite nuclei treatment of non central interactions and correlations has, at least, the same level of accuracy as in infinite nuclear matter. The binding energy for the full U14+TNI interaction is computed, addressing its small momentum dependent contributions in local density approximation. The nuclei are underbound by about 1 MeV per nucleon. Further energy lowering might be achieved by a more accurate variational minimization., Comment: TeX, 10 postscript pages, XXI Int.Work.on Cond.Matt.Theories, 1997, Luso (Portugal)

We present variational calculations of the one-body density matrices and momentum distributions for ^3He-^4He mixtures in the zero temperature limit, in the framework of the correlated basis functions theory. The ground-state wave function contains two- and three-body correlations and the matrix elements are computed by (Fermi)Hypernetted Chain techniques. The dependence on the ^3He concentration (x_3) of the ^4He condensate fraction $(n_0^{(4)})$ and of the ^3He pole strength (Z_F) is studied along the P=0 isobar. At low ^3He concentration, the computed ^4He condensate fraction is not significantly affected by the ^3He statistics. Despite of the low x_3 values, Z_F is found to be quite smaller than that of the corresponding pure ^3He because of the strong ^3He-^4He correlations and of the overall, large total density \rho. A small increase of $n_0^{(4)}$ along x_3 is found, which is mainly due to the decrease of \rho respect to the pure ^4He phase., Comment: 23 pages, 7 postscript figures, Revtex

The electromagnetic inclusive transverse response of nuclear matter at saturation density is studied within the correlated basis function perturbation theory for momentum transfers q from 300 to 550 MeV/c. The correlation operator includes a Jastrow component, accounting for the short range repulsion, as well as longer range spin, tensor and isospin ones. The Schiavilla- Pandharipande-Riska model for the two-body electromagnetic currents, satisfying the continuity equation with realistic v_14 potentials, is adopted. Currents due to intermediate Delta-isobar excitations, are also included. The global contribution of the two-body currents turns out to be positive and provides an enhancement of the one-body transverse response ranging from about 20% for the lower momenta to about 10% for the higher ones. This finding is in agreement with the Green's Function Monte Carlo studies of the transverse Euclidean response in A=3,4 nuclei and contradicts previous results obtained within the Fermi gas and shell models. The tensor-isospin component of the correlation is found to be the leading responsible for such a behavior. The nuclear matter response is compared to recent experimental data on 40Ca and 56Fe., Comment: 22 RevTeX pages, 7 ps figures

We introduce a new approach to highly correlated systems which generalizes the Fermi Hypernetted Chain and Correlated Basis Function techniques. While the latter approaches can only be applied to systems for which a nonrelativistic wave function can be defined, the new approach is based on the variation of a trial hamiltonian within a path integral framework and thus can also be applied to relativistic and field theoretical problems. We derive a diagrammatic scheme for the new approach and show how a particular choice of the trial hamiltonian corresponds exactly to the use of a Jastrow correlated ansatz for the wave function in the Fermi Hypernetted Chain approach. We show how our new approach can be used to find upper bounds to ground state energies in systems which the FHNC cannot handle, including those described by an energy-dependent effective hamiltonian. We demonstrate our approach by applying it to a quantum field theoretical system of interacting pions and nucleons., Comment: 35 RevTeX pages, 7 separated ps figures available on request

Correlated Basis Function theory and Fermi Hypernetted Chain technique are extended to study medium-heavy, doubly closed shell nuclei in j-j coupling scheme, with different single particle wave functions for protons and neutrons and isospin dependent two-body correlations. Central semirealistic interactions are used. Ground state energies, one-body densities, distribution functions and momentum distributions are calculated for 12C, 16O, 40Ca, 48Ca and 208Pb nuclei. The values of the ground state energies provided by isospin dependent correlations are lower than those obtained with isospin independent correlations. In finite nuclear systems, the two--body Euler equations provide correlation functions variationally more effective than those obtained with the same technique in infinite nuclear matter., Comment: 29 Latex pages plus 6 Postscript figures

Correlated Basis Function perturbation theory is used to evaluate the zero temperature response $S(q,\omega)$ of $^3$He-$^4$He mixtures for inelastic neutron scattering, at momentum transfers $q$ ranging from $1.1$ to $1.7 \AA^{-1}$. We adopt a Jastrow correlated ground state and a basis of correlated particle-hole and phonon states. We insert correlated one particle-one hole and one-phonon states to compute the second order response. The decay of the one-phonon states into two-phonon states is accounted for in boson-boson approximation. The full response is splitted into three partial components $S_{\alpha \beta}(q,\omega)$, each of them showing a particle-hole bump and a one phonon, delta shaped peak, which stays separated from the multiphonon background. The cross term $S_{34}(q,\omega)$ results to be of comparable importance to $S_{33}(q,\omega)$ in the particle-hole sector and to $S_{44}(q,\omega)$ in the phonon one. Once the one-phonon peak has been convoluted with the experimental broadening, the computed scattering function is in semiquantitative agreement with recent experimental measurements., Comment: 26 pages, RevTex 3.0, 8 figures available upon request

The Correlated Basis Function theory (CBF) provides a theoretical framework to treat on the same ground mean-field and short-range correlations. We present, in this report, some recent results obtained using the CBF to describe the ground state properties of finite nuclear systems. Furthermore we show some results for the excited state obtained with a simplified model based on the CBF theory., Comment: 10 latex pages plus 6 uuencoded figures

A microscopic calculation of the effective mass of one $^4$He impurity in homogeneous liquid $^3$He at zero temperature is performed for an extended Jastrow--Slater wave function, including two-- and three--body dynamical correlations and also backflow correlations between the $^4$He atom and the particles in the medium. The effective mass at saturation density, $m_4^*/m_4=1.21$, is in very good agreement with the recent experimental determination by Edwards {\it et al}. The three-- particle correlations appear to give a small contribution to the effective mass and different approximations for the three--particle distribution function give almost identical results for $m_4^*/m_4$., Comment: 12 pages, RevTex 3.0, one figure available upon request, FENUPC02-94