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International audience; The Efimov window, or universal window, is a particular energy region in which few-body systems are loosely bound. Many characteristics of those systems are universal; their properties are largely independent of the particular interaction that produces the binding. This suggests the use of simple potential models characterized by few parameters to describe dynamical properties. Essentially, the potential parameters are set in order to reproduce a small number of data, and then the potential strength can be varied to explore the window. Among others, the Gaussian potential has been used to characterize the universal window. From calculations of the ground state and of the first excited state of three identical bosons using a Gaussian potential along the window, we determine what is called the gaussian-level function. This function is independent of the particular Gaussian potential used in this procedure. Moreover, it contains finite-range corrections which are of particular importance when theoretical predictions are compared to experimental data.

Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by a continuous-scale invariance, which is broken to a discrete one when three or more particles come into play. This symmetry induces a universal behavior for different systems, independent of the details of the underlying interaction, rooted in the smallness of the ratio $\ell/a_B \ll 1$, where the length $a_B$ is associated to the binding energy of the two-body system $E_2=\hbar^2/m a_B^2$ and $\ell$ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the on-set of system-specific non-universal effects. In this work we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which $a_B\rightarrow\infty$, and show that nuclear systems belong to this class of universality., 27 pages, 8 figures

International audience; The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the basis of the density-functional theory, are reformulated in terms of a particular many-body density, which is translational and Galilean invariant and therefore is relevant for self-bound systems. In a similar way that there is a unique relation between the one-body density and the external potential that gives rise to it, we demonstrate that there is a unique relation between that particular many-body density and a definite many-body potential. The energy is then a functional of this density, and its minimization leads to the ground-state energy of the system. As a proof of principle, the analogous of the Kohn-Sham equation is solved in the specific case of He4 atomic clusters, to put in evidence the advantages of this formulation in terms of physical insights.

Neural-network quantum states have shown great potential for the study of many-body quantum systems. In statistical machine learning, transfer learning designates protocols reusing features of a machine learning model trained for a problem to solve a possibly related but different problem. We propose to evaluate the potential of transfer learning to improve the scalability of neural-network quantum states. We devise and present physics-inspired transfer learning protocols, reusing the features of neural-network quantum states learned for the computation of the ground state of a small system for systems of larger sizes. We implement different protocols for restricted Boltzmann machines on general-purpose graphics processing units. This implementation alone yields a speedup over existing implementations on multi-core and distributed central processing units in comparable settings. We empirically and comparatively evaluate the efficiency (time) and effectiveness (accuracy) of different transfer learning protocols as we scale the system size in different models and different quantum phases. Namely, we consider both the transverse field Ising and Heisenberg XXZ models in one dimension, and also in two dimensions for the latter, with system sizes up to 128 and 8 x 8 spins. We empirically demonstrate that some of the transfer learning protocols that we have devised can be far more effective and efficient than starting from neural-network quantum states with randomly initialized parameters., 13 pages, 11 figures

Universal behavior in few-boson systems close to the unitary limit, where two bosons become unbound, has been intensively investigated in recent years both experimentally and theoretically. In this particular region, called the unitary window, details of the interparticle interactions are not important and observables, such as binding energies, can be characterized by a few parameters. With an increasing number of particles, the short-range repulsion, present in all atomic, molecular, and nuclear interactions, gradually induces deviations from the universal behavior. In the present paper, we discuss a simple way of incorporating nonuniversal behavior through one specific parameter which controls the smooth transition of the system from a universal to nonuniversal regime. Using a system of $N$ helium atoms as an example, we calculate their ground-state energies as trajectories within the unitary window and also show that the control parameters can be used to determine the energy per particle in homogeneous systems when $N\ensuremath{\rightarrow}\ensuremath{\infty}$.

Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is much larger than the range of the interaction. The binding energies of these states are described as a function of the scattering length and one three-body parameter by a transcendental equation involving a universal function of one angular variable. We provide an accurate and convenient parametrization of this function. Moreover, we discuss the effective treatment of range corrections in the universal equation and compare with a strictly perturbative scheme., 13 pages, 5 figures

International audience; The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance, which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. For example, the triton binding energy is correlated with other observables such as the doublet nucleon-deuteron scattering length or the α-particle binding energy. Moreover, the low-energy dynamics of these systems is universal; it does not depend on the details of the nuclear interaction. Instead, it depends on a few control parameters such as the (large) values of the scattering lengths and the triton binding energy. Using a potential model in order to vary the values of the scattering lengths, we study the spectrum of A=2,3,4,6 nuclei in the region between the unitary limit and the point where the scattering lengths get their physical values. In particular, we analyze how the binding energies emerge from the unitary limit forming the observed levels.

The structure of few-fermion systems having \({1/2}\) spin-isospin symmetry is studied using potential models. The strength and range of the two-body potentials are fixed to describe low energy observables in the angular momentum \({L=0}\) state and spin \({S=0,1}\) channels of the two-body system. Successively the strength of the potentials are varied in order to explore energy regions in which the two-body scattering lengths are close to the unitary limit. This study is motivated by the fact that in the nuclear system the singlet and triplet scattering lengths are both large with respect to the range of the interaction. Accordingly we expect evidence of universal behavior in the three- and four-nucleon systems that can be observed from the study of correlations between observables. In particular we concentrate in the behavior of the first excited state of the three-nucleon system as the system moves away from the unitary limit. We also analyze the dependence on the range of the three-body force of some low-energy observables in the three- and four-nucleon systems.

When the binding energy of a two-body system goes to zero the two-body system shows a continuous scaling invariance governed by the large value of the scattering length. In the case of three identical bosons, the three-body system in the same limit shows the Efimov effect and the scale invariance is broken to a discrete scale invariance. As the number of bosons increases correlations appear between the binding energy of the few- and many-body systems. We discuss some of them as the relation between the saturation properties of the infinite system and the low-energy properties of the few-boson system., 6 pages, 3 figures. Contribution to the proceedings of the XXII International Conference on Few-Body Problems in Physics (FB22) (Caen, France, July 2018)

International audience; The understanding of nuclear systems as composed of interacting nucleons has been considerably sharpened by the effective field theory (EFT) framework. The latter provides a link between the nuclear interaction and the underlying quantum chromodynamics, as the relevant degrees of freedom result, at least ideally, from a decimation process starting from fundamental quarks and gluons. Owing to chiral symmetry and the Goldstone bosons’ characters of the interchanged pions among nucleons, the properties of heavier nuclei can in principle be traced back to a restricted set of low-energy constants (LECs) to be determined in lighter systems in the framework of a systematic low-energy expansion. At smaller energy scales, in pionless EFT, the interactions simplify becoming of contact type. The low-energy expansion is organized differently, relying on the emergence of universal properties, characteristic of systems with large two-body scattering lengths. We will examine the two above schemes and discuss their relation, with the aim of devising viable power counting schemes for applications in nuclear physics.

Results obtained by the authors in recent works on the exploration of universality in systems living inside the Efimov window are critically analyzed. We discuss how to take into account finite-range corrections by introducing a finite-range parameter necessary to make comparisons to the universal predictions of the Efimov zero-range theory. Firstly we apply our analysis to two different calculations published by other authors. The first one has been used with success to describe ultracold Cs atoms close to a Feshbach resonance and the second one describes a four 4He atom system with a realistic interaction. Finally we use the finite-range parameter to analyze recombination data in experiments with ultracold 7Li atoms. The three selected cases support the introduction of the finite-range parameter as a valuable tool to extend the use of the zero-range theory to describe systems having finite-range interactions.

In chiral effective field theory the leading order (LO) nucleon-nucleon potential includes two contact terms, in the two spin channels $S=0,1$, and the one-pion-exchange potential. When the pion degrees of freedom are integrated out, as in the pionless effective field theory, the LO potential includes two contact terms only. In the three-nucleon system, the pionless theory includes a three-nucleon contact term interaction at LO whereas the chiral effective theory does not. Accordingly arbitrary differences could be observed in the LO description of three- and four-nucleon binding energies. We analyze the two theories at LO and conclude that a three-nucleon contact term is necessary at this order in both theories. In turn this implies that subleading three-nucleon contact terms should be promoted to lower orders. Furthermore this analysis shows that one single low energy constant might be sufficient to explain the large values of the singlet and triplet scattering lengths., 5 pages, 3 figures

We study small clusters of bosons, $A=2,3,4,5,6$, characterized by a resonant interaction. Firstly, we use a soft-gaussian interaction that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with LM2M2 potential, a widely used $^4$He-$^4$He interaction. We change the intensity of the potential to explore the clusters' spectra in different regions with large positive and large negative values of the two-body scattering length and we report the clusters' energies on Efimov plot, which makes the scale invariance explicit. Secondly, we repeat our calculation adding a repulsive three-body force to reproduce the trimer binding energy. In all the region explored, we have found that these systems present two states, one deep and one shallow close to the $A-1$ threshold, and scale invariance has been investigated for these states. The calculations are performed by means of Hyperspherical Harmonics basis set., Comment: Presented at the 20th International IUPAP Conference on Few-Body Problems in Physics, 20 - 25 August, 2012, Fukuoka, Japan

The universal behavior of a three-boson system close to the unitary limit is encoded in a simple dependence of many observables in terms of few parameters. For example the product of the three-body parameter $\kappa_*$ and the two-body scattering length $a$, $\kappa_* a$ depends on the angle $\xi$ defined by $E_3/E_2=\tan^2\xi$. A similar dependence is observed in the ratio $a_{AD}/a$ with $a_{AD}$ the boson-dimer scattering length. We use a two-parameter potential to determine this simple behavior and, as an application, to compute $a_{AD}$ for the case of three $^4$He atoms., Comment: presented at the 23rd European Conference on Few-Body Problems in Physics

Two-, three-, and four-boson systems are studied close to the unitary limit using potential models constructed to reproduce the minimal information given by the two-body scattering length $a$ and the two-body binding energy or virtual state energy $E_2$. The particular path used to reach the unitary limit is given by varying the potential strength. In this way the energy spectrum in the three- and four-boson systems is computed. The lowest energy states show finite-range effects absorbed in the construction of level functions that can be used to study real systems. Higher energy levels are free from finite-range effects, therefore the corresponding level functions tend to the zero-range universal function. Using this property a zero-range equation for the four-boson system is proposed and the four-boson universal function is computed., Comment: 8 pages, 4 figures

We propose to use the hyperspherical harmonics (HH) basis to solve the A-body system problem without explicit symmetrization or anti-symmetrization of the basis functions as required by the statistic of the system. Therefore, the HH basis set is expressed with respect to a given ordering of the A particles. However, after diagonalization, the eigenvectors reflect the symmetries of the Hamiltonian, and it is possible to identify the physical states having the expected symmetry under particle permutation. As an example we study the case of four particles interacting through a short-range spin-dependent interaction and the Coulomb potential.

Using potential models we analyze range corrections to the universal law dictated by the Efimov theory of three bosons. In the case of finite-range interactions we have observed that, at first order, it is necessary to supplement the theory with one finite-range parameter, $\Gamma_n^3$, for each specific $n$-level [Kievsky and Gattobigio, Phys. Rev. A {\bf 87}, 052719 (2013)]. The value of $\Gamma_n^3$ depends on the way the potentials is changed to tune the scattering length toward the unitary limit. In this work we analyze a particular path in which the length $r_B=a-a_B$, measuring the difference between the two-body scattering length $a$ and the energy scattering length $a_B$, results almost constant. Analyzing systems with very different scales, as atomic or nuclear systems, we observe that the finite-range parameter remains almost constant along the path with a numerical value of $\Gamma_0^3\approx 0.87$ for the ground state level. This observation suggests the possibility of constructing a single universal function that incorporate finite-range effects for this class of paths. The result is used to estimate the three-body parameter $\kappa_*$ in the case of real atomic systems brought to the unitary limit thought a broad Feshbach resonances. Furthermore, we show that the finite-range parameter can be put in relation with the two-body contact $C_2$ at the unitary limit., Comment: accepted Physical Review A

We calculate the dynamic polarizability of a one-dimensional Bose gas confined into a parabolic trap near the Tonks–Girardeau limit. We use the duality between the one-dimensional Bose gas with δ-interaction and the one-dimensional Fermi gas with δ''-interaction to map the strong interaction regime of the first into the weak one of the latter. The quantities which depend only on the modulus of the wavefunction can be calculated with either of the two theories; therefore, we have used the random-phase approximation in the weak coupling regime of the fermionic system to access dynamic properties in the strong coupling regime of the bosonic one.

We present a Monte Carlo simulation of two implementations of Quantum Cellular Automaton (QCA) circuits: one based on simple ground state relaxation and the other on the clocked cell scheme that has recently been proposed by Toth and Lent. We focus on the time-dependent behavior of two basic circuits, a binary wire and a majority voting gate, and assess their maximum operating speed and temperature requirements for different sets of fabrication parameters.

The Hyperspherical Harmonics basis, without a previous symmetrization step, is used to calculate binding energies of the nuclear A=6 systems using a version of the Volkov potential acting only on s-wave. The aim of this work is to illustrate the use of the nonsymmetrized basis to deal with permutational-symmetry-breaking term in the Hamiltonian, in the present case the Coulomb interaction., Presented at the 21st European Conference on Few-Body Problems in Physics, Salamanca, Spain, 30 August - 3 September 2010

We present the analysis of the $N$-boson spectrum computed using a soft two-body potential the strength of which has been varied in order to cover an extended range of positive and negative values of the two-body scattering length $a$ close to the unitary limit. The spectrum shows a tree structure of two states, one shallow and one deep, attached to the ground-state of the system with one less particle. It is governed by an unique universal function, $\Delta(\xi)$, already known in the case of three bosons. In the three-particle system the angle $\xi$, determined by the ratio of the two- and three-body binding energies $E_3/E_2=\tan^2\xi$, characterizes the Discrete Scale Invariance of the system. Extending the definition of the angle to the $N$-body system as $E_N/E_2=\tan^2\xi$, we study the $N$-boson spectrum in terms of this variable. The analysis of the results, obtained for up to $N=16$ bosons, allows us to extract a general formula for the energy levels of the system close to the unitary limit. Interestingly, a linear dependence of the universal function as a function of $N$ is observed at fixed values of $a$. We show that the finite-range nature of the calculations results in the range corrections that generate a shift of the linear relation between the scattering length $a$ and a particular form of the universal function. We also comment on the limits of applicability of the universal relations.

Universal behaviour has been found inside the window of Efimov physics for systems with $N=4,5,6$ particles. Efimov physics refers to the emergence of a number of three-body states in systems of identical bosons interacting {\it via} a short-range interaction becoming infinite at the verge of binding two particles. These Efimov states display a discrete scale invariance symmetry, with the scaling factor independent of the microscopic interaction. Their energies in the limit of zero-range interaction can be parametrized, as a function of the scattering length, by a universal function. We have found, using a particular form of finite-range scaling, that the same universal function can be used to parametrize the energies of $N\le6$ systems inside the Efimov-physics window. Moreover, we show that the same finite-scale analysis reconciles experimental measurements of three-body binding energies with the universal theory., Added the derivation of the three-body shift Added calculations with Poschl-Teller potential Added the analysis of Li7 trimer-binding energy experimental data [PRL 108, 210406 (2012)]

It is well-known that three-boson systems show the Efimov effect when the two-body scattering length $a$ is large with respect to the range of the two-body interaction. This effect is a manifestation of a discrete scaling invariance (DSI). In this work we study DSI in the $N$-body system by analysing the spectrum of $N$ identical bosons obtained with a pairwise gaussian interaction close to the unitary limit. We consider different universal ratios such as $E_N^0/E_3^0$ and $E_N^1/E_N^0$, with $E_N^i$ being the energy of the ground ($i=0$) and first-excited ($i=1$) state of the system, for $N\le16$. We discuss the extension of the Efimov radial law, derived by Efimov for $N=3$, to general $N$., 4 pages, 3 figures, presented at the 22nd European Conference on Few-Body Problems in Physics, Cracow (Poland)

In this work we investigate the structure and dynamics of small clusters of Helium atoms. We consider bound states of clusters having A = 2, 3, 4, 5, 6 atoms and continuum states in the three-atom system. Motivated by the fact that the He-He system has a very large scattering length a compared to the range r 0 of the He-He potential (r 0/a < 1/10), we propose the use of a soft-core interparticle potential. We use an attractive gaussian potential that reproduces the values of the dimer binding energy and the atomatom scattering length obtained with one of the widely used He-He interactions, the LM2M2 potential. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and a three-body potential, we show the spectrum of the four, five, and sixparticle systems and phase-shifts and inelasticities in the three-atom system. Comparisons to calculations using realistic He-He potentials are given. In addition some universal relations are explored. © 2014 Pleiades Publishing, Ltd.

We propose an experiment for the detection of quantum cellular automaton (QCA) operation in a cell made up of four silicon quantum dots. We show that correlated switching between the two pairs of dots forming the cell can be clearly detected from the locking of the Coulomb blockade current peaks through each pair. We have performed numerical simulations on the basis of capacitance values obtained from experimental results on cells fabricated with silicon-on-insulator technology. This approach is shown to allow detection of QCA switching without the need for additional charge detectors, although fabrication parameters are rather critical.

We investigate universal behavior in the recombination rate of three bosons close to threshold. Using the He-He system as a reference, we solve the three-body Schrödinger equation above the dimer threshold for different potentials having large values of the two-body scattering length a. To this aim, we use the hyperspherical adiabatic expansion and we extract the S matrix through the integral relations recently derived. The results are compared to the universal form, ¿¿67.1sin2[s0ln(¿*a)+¿], for different values of a and selected values of the three-body parameter ¿*. A good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections, which have been recently proposed [ A. Kievsky and M. Gattobigio Phys. Rev. A 87 052719 (2013)]. Furthermore, we analyze the validity of the above formula in the description of a very different system: neutron-neutron-proton recombination. Our analysis confirms the universal character of the process in systems of very different scales having a large two-body scattering length. ©2013 American Physical Society, Financial support provided by DGI of MINECO (Spain) under Contract No. FIS2011-23565.

In this work we investigate small clusters of bosons using the hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ particles interacting through a soft interparticle potential. In order to make contact with a real system, we use an attractive Gaussian potential that reproduces the values of the dimer binding energy and the atom-atom scattering length obtained with one of the most widely used ${}^{4}$He-${}^{4}$He interactions, the LM2M2 potential of Aziz and Slaman. The intensity of the potential is varied in order to explore the clusters' spectra in different regions with large positive and large negative values of the two-body scattering length. In addition, we include a repulsive three-body force to reproduce the trimer binding energy. With this model, consisting in the sum of a two- and three-body potential, we have calculated the spectrum of the four-, five-, and six-particle systems. In all the regions explored, we have found that these systems present two states, one deep and one shallow close to the $A\ensuremath{-}1$ threshold. Some universal relations between the energy levels are extracted; in particular, we have estimated the universal ratios between thresholds of the three-, four-, and five-particle continua using the two-body Gaussian potential. They agree with recent measurements and theoretical predictions.

In this work we show results for light nuclear systems and small clusters of helium atoms using the hyperspherical harmonics basis. We use the basis without previous symmetrization or antisymmetrization of the state. After the diagonalization of the Hamiltonian matrix, the eigenvectors have well defined symmetry under particle permutation and the identification of the physical states is possible. We show results for systems composed up to six particles. As an example of a fermionic system, we consider a nucleon system interacting through the Volkov potential, used many times in the literature. For the case of bosons, we consider helium atoms interacting through a potential model which does not present a strong repulsion at short distances. We have used an attractive gaussian potential to reproduce the values of the dimer binding energy, the atom-atom scattering length, and the effective range obtained with one of the most widely used He-He interaction, the LM2M2 potential. In addition, we include a repulsive hypercentral three-body force to reproduce the trimer binding energy., Presented at the Sixth Workshop on the Critical Stability of Quantum Few-Body Systems, Erice, Sicily, October 2011

We investigate universal behavior in elastic atom-dimer scattering below the dimer breakup threshold calculating the atom-dimer effective-range function $ak\cot\delta$. Using the He-He system as a reference, we solve the Schr\"odinger equation for a family of potentials having different values of the two-body scattering length $a$ and we compare our results to the universal zero-range form deduced by Efimov, $ak\cot\delta=c_1(ka)+c_2(ka)\cot[s_0\ln(\kappa_*a)+\phi(ka)]$, for selected values of the three-body parameter $\kappa_*$. Using the parametrization of the universal functions $c_1,c_2,\phi$ given in the literature, a good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections. Furthermore, we show that the same parametrization describes a very different system: nucleon-deuteron scattering below the deuteron breakup threshold. Our analysis confirms the universal character of the process, and relates the pole energy in the effective-range function of nucleon-deuteron scattering to the three-body parameter $\kappa_*$., Comment: Published version. Title changed

We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under external confinement. Such a model displays a large degeneracy of the ground state. Using a generalized Bose-Fermi mapping we find the solution for the whole set of ground-state wavefunctions of the degenerate manifold and we characterize them according to group-symmetry considerations. We find that the density profile and the momentum distribution depends on the symmetry of the solution. By combining the wavefunctions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system we propose an analytic expression for the many-body wavefunction of the inhomogeneous system which well describes the ground state at finite, large and equal interactions strengths, as validated by numerical simulations., 7 pages, 5 figures, final revised version

The use of the hyperspherical harmonic (HH) basis in the description of bound states in an A-body system composed of identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into account. This preliminary step is not strictly necessary; the direct use of the HH basis is possible, even if the basis does not have a well-defined behavior under particle permutations. In fact, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it. They have well-defined symmetry under particle permutation and identification of the physical states is possible, as shown here in specific cases. The problem related to the large degeneration of the basis is circumvented by constructing the Hamiltonian matrix as a sum of products of sparse matrices. This particular representation of the Hamiltonian is well suited for a numerical iterative diagonalization, where only the action of the matrix on a vector is needed. As an example we compute bound states for systems with A=3-6 particles interacting through a short-range central interaction. We also consider the case in which the potential is restricted to act in relative s waves with and without the inclusion of themore » Coulomb potential. This very simple model predicts results in qualitative good agreement with the experimental data and it represents the first step in a project dedicated to the use of the HH basis to describe bound and low-energy scattering states in light nuclei.« less

In this paper, we investigate small clusters of helium atoms using the hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ atoms with an interparticle potential which does not present a strong repulsion at short distances. We use an attractive Gaussian potential that reproduces the values of the dimer binding energy, the atom-atom scattering length, and the effective range obtained with one of the widely used He-He interactions, the Aziz and Slaman potential, called LM2M2. In systems with more than two atoms, we consider a repulsive three-body force that, by construction, reproduces the trimer binding energy of the LM2M2 potential. With this model, consisting of the sum of a two- and three-body potential, we have calculated the spectrum of clusters formed by four, five, and six helium atoms. We have found that these systems present two bound states, one deep and one shallow, close to the threshold fixed by the energy of the $(A\ensuremath{-}1)$-atom system. Universal relations between the energies of the excited state of the $A$-atom system and the ground-state energy of the $(A\ensuremath{-}1)$-atom system are extracted, as well as the ratio between the ground state of the $A$-atom system and the ground-state energy of the trimer.

We study the formation of Faraday waves in an elongated Bose-Einstein condensate in the presence of a one-dimensional optical lattice. The waves are parametrically excited by modulating the radial confinement of the condensate close to a transverse breathing mode of the system. For very shallow optical lattices, phonons with a well-defined wave vector propagate along the condensate, as in the absence of the lattice, and we observe the formation of a Faraday pattern. We find that by increasing the potential depth the local sound velocity decreases, and when it equals the condensate local phase velocity, the condensate develops an incoherent superposition of several modes and the parametric excitation of Faraday waves is suppressed.

The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this representation, the matrix elements between the basis elements are simple, and the potential energy is presented in a compact form, well suited for numerical implementation. The basis is neither symmetrized nor antisymmetrized, as required in the case of identical particles; however, after the diagonalization of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in it, and the identification of the physical states is possible, as it will be shown in specific cases. We have in mind applications to atomic, molecular, and nuclear few-body systems in which symmetry breaking terms are present in the Hamiltonian; their inclusion is straightforward in the present method. As an example we solve the case of three and four particles interacting through a short-range central interaction and Coulomb potential.

We investigate the momentum distribution of interacting electrons confined in a two-dimensional parabolic quantum dot for varying values of the interaction strength and for different number of electrons. We use an optimized Jastrow-type wave function for the ground state in which the Slater determinant part has been calculated using density-functional theory and evaluate the ground-state momentum distribution using the Fermi hypernetted-chain equations. We discuss the effects of interactions on the momentum distribution and reveal the existence of a shell structure in momentum space in analogy with what happens to the spatial density profile. The momentum distribution can thus be used as a further tool to investigate the effects of the interaction in parabolic quantum dots. © 2006 The American Physical Society. Fil: Gattobigio, M.. Institut de Physique de Nice; Italia Fil: Capuzzi, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina

We present an extensive comparative study of ground-state densities and pair distribution functions for electrons confined in two-dimensional parabolic quantum dots over a broad range of coupling strength and electron number. We first use spin-density-functional theory to determine spin densities that are compared with Diffusion Monte Carlo (DMC) data. This accurate knowledge of one-body properties is then used to construct and test a local approximation for the electron-pair correlations. We find very satisfactory agreement between this local scheme and the available DMC data, and provide a detailed picture of two-body correlations in a coupling-strength regime preceding the formation of Wigner-like electron ordering., Comment: 18 pages, 12 figures, submitted

We discuss specific noise phenomena in several ballistic mesoscopic structures and in networks of quantum dots or metallic dots interconnected by tunneling barriers, focusing on the techniques used for the numerical simulation and on the physical interpretation of the results.

A prototype cell for the investigation of QCA (quantum cellular automaton) functionality in silicon-on-insulator technology has been fabricated and characterized, observing interaction between the upper and the lower double dots. A simulation code, validated by comparison with the experimental results, has been used to design a modified layout that should allow demonstration of QCA operation at temperatures above 0.3 K.

A computational paradigm based on the Quantum Cellular Automaton (QCA) concept was proposed by Lent et al., offering new perspectives for the exploitation of single-electron effects in nanoelectronics. The basic logic building block is represented by a bistable cell, containing two excess electrons that can assume two different configurations. We have designed an experiment for detecting cell switching, which does not require the use of charge detectors, and that is therefore particularly well suited for nanoscale silicon-on-insulator cells, for which it would be more difficult to add nearby charge detectors. We have also developed a specifically designed Monte Carlo simulator that we have used to validate the design of the experiment.

We present the peculiar noise behavior of bistable systems of coupled quantum dots during switching between the two stable states. Shot noise of the current through different branches of the system can be suppressed and/or enhanced up to a few times the ``full'' shot-noise level. Results from Monte Carlo simulations and from an analytical model are presented.

We have studied, by means of a Monte Carlo simulation, data propagation in quantum cellular automaton circuits, comparing the performance of nonclocked and clocked implementations. Based on two choices of fabrication parameters, we have evaluated the maximum achievable clock speed for different operating temperatures, concluding that better performance can be obtained with the clocked architecture, which, however, involves significant technological difficulties. The large discrepancy existing between a simple estimate of the cell switching time, based on the RC time constant, and our results is discussed and explained by means of an intuitive argument. Two different circuits have been investigated, a binary wire and a majority voting gate, obtaining analogous results, with a slightly smaller maximum clock rate for the majority voting gate, due to the larger number of cells involved.

We present a proposal for an experiment to demonstrate QCA (Quantum Cellular Automaton) functionality for a cell fabricated with silicon-on-insulator technology. The fundamental feature of a working QCA cell consists in the anticorrelated transition of electrons in the two pairs of dots forming the cell: we show how such a phenomenon can be detected from the appearance of a “locking” effect between the Coulomb Blockade current peaks relative to each pair. The proposed approach allows the detection of QCA action without the need for additional noninvasive charge detectors probing each dot. We have performed detailed numerical simulations on the basis of interdot capacitance values obtained from experimental data and determined the range of parameters within which the effect should be detectable.

We discuss the motivation for the detailed simulation of nanotechnology devices and the challenges that it poses. Then, we present the approach to the numerical simulation of semiconductor nanostructures adopted within the project NANOTCAD, funded by the European Union within the Fifth Framework Programme, in the Future Emerging Technologies Initiative of the Information Society Technology Program. Results obtained from the initial development of a three-dimensional Poisson-Schrodinger solver are also shown.