arXiv subjects

F. Mazzanti

Publications and source records attributed to F. Mazzanti.

35 records · Page 2Linked to original sources

arXiv2009

High-order Time Expansion Path Integral Ground State

The feasibility of path integral Monte Carlo ground state calculations with very few beads using a high-order short-time Green's function expansion is discussed. An explicit expression of the evolution operator which provides dramatic enhancements in the quality of ground-state wave-functions is examined. The efficiency of the method makes possible to remove the trial wave function and thus obtain completely model-independent results still with a very small number of beads. If a single iteration of the method is used to improve a given model wave function, the result is invariably a shadow-type wave function, whose precise content is provided by the high-order algorithm employed.

cond-mat.other↗

arXiv2007

Off-diagonal Ground State Properties of a 1D Gas of Fermi Hard Rods

A variational Monte Carlo calculation of the one-body density matrix and momentum distribution of a system of Fermi hard rods (HR) is presented and compared with the same quantities for its bosonic counterpart. The calculation is exact within statistical errors since we sample the exact ground state wave function, whose analytical expression is known. The numerical results are in good agreement with known asymptotic expansions valid for Luttinger liquids. We find that the difference between the absolute value of the bosonic and fermionic density matrices becomes marginally small as the density increases. In this same regime, the corresponding momentum distributions merge into a common profile that is independent of the statistics. Non-analytical contributions to the one--body density matrix are also discussed and found to be less relevant with increasing density.

cond-mat.stat-mech↗

arXiv2007

Ground-State Properties of a One-Dimensional System of Hard Rods

A quantum Monte Carlo simulation of a system of hard rods in one dimension is presented and discussed. The calculation is exact since the analytical form of the wavefunction is known, and is in excellent agreement with predictions obtained from asymptotic expansions valid at large distances. The analysis of the static structure factor and the pair distribution function indicates that a solid-like and a gas-like phases exist at high and low densities, respectively. The one-body density matrix decays following a power-law at large distances and produces a divergence in the low density momentum distribution at k=0 which can be identified as a quasi-condensate.

cond-mat.other↗

arXiv2004

Ground state properties of a dilute homogeneous Bose gas of hard disks in two dimensions

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 $x$.

cond-mat.stat-mech↗

arXiv2004

Energy and Structure of Hard-Sphere Bose Gases in three and two dimensions

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 $x=ρa^d$ where $ρ$, $a$ 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.

cond-mat.stat-mech↗

arXiv2004

High momentum response of liquid 3He

A final-state-effects formalism suitable to analyze the high-momentum response of Fermi liquids is presented and used to study the dynamic structure function of liquid $^3$He. The theory, developed as a natural extension of the Gersch-Rodriguez formalism, incorporates the Fermi statistics explicitely through a new additive term which depends on the semi-diagonal two-body density matrix. The use of a realistic momentum distribution, calculated using the diffusion Monte Carlo method, and the inclusion of this additive correction allows for a good agreement with available deep-inelastic neutron scattering data.

cond-mat.stat-mech↗

arXiv2003

Energy and structure of dilute hard- and soft-sphere gases

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.

cond-mat.soft↗

arXiv2001

Finite Temperatur Dynamic Susceptibility of the Free Bose Gas

A detailed calculation of the real part of the finite temperature dynamic susceptibility of the free Bose gas is presented. After a short discussion on the different ways in which it can be calculated for temperatures above and below the Bose--Einstein transition temperature, its main properties and its evolution with $q$ and $T$ are analyzed. Finally, expressions for the lowest order energy weighted sum rules are also derived and studied.

cond-mat.stat-mech↗

arXiv2000

High-momentum dynamic structure function of liquid 3He-4He mixtures: a microscopic approach

The high-momentum dynamic structure function of liquid 3He-4He mixtures has been studied introducing final state effects. Corrections to the impulse approximation have been included using a generalized Gersch-Rodriguez theory that properly takes into account the Fermi statistics of 3He atoms. The microscopic inputs, as the momentum distributions and the two-body density matrices, correspond to a variational (fermi)-hypernetted chain calculation. The agreement with experimental data obtained at $q=23.1$ Å$^{-1}$ is not completely satisfactory, the comparison being difficult due to inconsistencies present in the scattering measurements. The significant differences between the experimental determinations of the 4He condensate fraction and the 3He kinetic energy, and the theoretical results, still remain unsolved.

cond-mat.stat-mech↗

arXiv2000

Finite temperature dynamic structure function of the free Bose gas

A detailed calculation of the finite temperature dynamic structure function of the free Bose gas is presented and discussed. After a short derivation of the expressions describing the exact response $S(q,ω;T)$ and the Impulse Approximation (IA) $S_{IA}(q,ω;t)$, their main properties and their evolution with q and T are analyzed. The lowest order energy weighted sum rules of both $S(q,ω;T)$ and $S_{IA}(q,ω;T)$ are also derived and commented. Finally, the $q\to\infty$ asymptotic behavior is analyzed and discussed in terms of scaling laws.

cond-mat↗

arXiv2000

Final State Effects in the high q response of $^3$He-$^4$He mixtures

A modified Gersch-Rodriguez formalism describing the leading Final State Effects in the high momentum transfer response of low concentration $^3$He-$^4$He mixtures is presented and discussed. The leading corrections to the Impulse Approximation are expressed in terms of the interatomic potentials and the semidiagonal two-body density matrices of both the mixture and its boson-boson approximation, in which the $^3$He atoms are replaced by bosons of the same mass and at the same partial density. Numerical calculations of the Final State Effects functions of $^3$He and $^4$He are finally presented and discussed.

cond-mat.soft↗

arXiv2000

Coherent and Incoherent Dynamic Structure Function of the Free Fermi Gas

A detailed calculation of the coherent and incoherent dynamic structure functions of the free Fermi gas, starting from their expressions in terms of the one- and semi-diagonal two-body density matrices, is derived and discussed. Their behavior and evolution with the momentum transfer is analyzed, and particular attention is devoted to the contributions that both functions present at negative energies. Finally, an analysis of the energy weighted sum rules satisfied by both responses is also performed. Despite of the simplicity of the model, some of the conclusions can be extended to realistic systems.

cond-mat.soft↗

arXiv2000

Finite Temperature Dynamic Structure Function of the Free Fermi Gas

A detailed discussion of the coherent and incoherent dynamic structure function of the free Fermi gas at finite temperature is presented. Their behavior and evolution with the momentum transfer and the temperature is analyzed, while particular attention is paid to the way in which their relative contribution changes with respect to the $\tilde{T}=0$ case. The influence of thermal effects on the lowest order sum rules of the coherent and incoherent responses is also discussed. Finally, the scaling properties of the responses at high momentum transfer as a function of the temperature are also analyzed.

cond-mat.soft↗

arXiv1997

Description of recent large-$q$ neutron inclusive scattering data from liquid $^4$He

We report dynamical calculations for large-$q$ structure functions of liquid $^4$He at $T$=1.6 and 2.3 K and compare those with recent MARI data. We extend those calculations far beyond the experimental range $q\le 29\Ain$ in order to study the approach of the response to its asymptotic limit for a system with interactions having a strong short-range repulsion. We find only small deviations from theoretical $1/q$ behavior, valid for smooth $V$. We repeat an extraction by Glyde et al of cumulant coefficients from data. We argue that fits determine the single atom momentum distribution, but express doubt as to the extraction of meaningful Final State Interaction parameters.

cond-mat↗

arXiv1995

A microscopic approach to the response of $^{\bf 3}$He -$^{\bf 4}$He mixtures

Correlated Basis Function perturbation theory is used to evaluate the zero temperature response $S(q,ω)$ of $^3$He-$^4$He mixtures for inelastic neutron scattering, at momentum transfers $q$ ranging from $1.1$ to $1.7 Å^{-1}$. 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 $S_{αβ}(q,ω)$, 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 $S_{34}(q,ω)$ results to be of comparable importance to $S_{33}(q,ω)$ in the particle-hole sector and to $S_{44}(q,ω)$ 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.

cond-mat↗

arXiv1995

Final state effects on superfluid $^{\bf 4}$He in the deep inelastic regime

A study of Final State Effects (FSE) on the dynamic structure function of superfluid $^4$He in the Gersch--Rodriguez formalism is presented. The main ingredients needed in the calculation are the momentum distribution and the semidiagonal two--body density matrix. The influence of these ground state quantities on the FSE is analyzed. A variational form of $ρ_2$ is used, even though simpler forms turn out to give accurate results if properly chosen. Comparison to the experimental response at high momentum transfer is performed. The predicted response is quite sensitive to slight variations on the value of the condensate fraction, the best agreement with experiment being obtained with $n_0=0.082$. Sum rules of the FSE broadening function are also derived and commented. Finally, it is shown that Gersch--Rodriguez theory produces results as accurate as those coming from other more recent FSE theories.

cond-mat↗

arXiv1993

Dynamic Structure Function in 3he-4he Mixtures

Relevant features of the dynamic structure function $S(q,ω)$ in $^3$He-$^4$He mixtures at zero temperature are investigated starting from known properties of the ground state. Sum rules are used to fix rigorous constraints to the different contributions to $S(q,ω)$, coming from $^3$He and $^4$He elementary excitations, as well as to explore the role of the cross term $S^{(3,4)}(q,ω)$. Both the low-$q$ (phonon-roton $^4$He excitations and 1p-1h $^3$He excitations) and high-$q$ (deep inelastic scattering) ranges are discussed.

cond-mat↗