arXiv subjects

M. P. Tosi

Publications and source records attributed to M. P. Tosi.

At least 55 records · Page 3Linked to original sources

arXiv2004

Analytic theory of correlation energy and spin polarization in the 2D electron gas

We present an analytic theory of the pair distribution function and the ground-state energy in a two-dimensional (2D) electron gas with an arbitrary degree of spin polarization. Our approach involves the solution of a zero-energy scattering Schrödinger equation with an effective potential which includes a Fermi term from exchange and kinetic energy and a Bose-like term from Jastrow-Feenberg correlations. The form of the latter is assessed from an analysis of data on a 2D gas of charged bosons. We obtain excellent agreement with data from quantum Monte Carlo studies of the 2D electron gas. In particular, our results for the correlation energy show a quantum phase transition occurring at coupling strength $r_s\approx 24$ from the paramagnetic to the fully spin-polarized fluid.

cond-mat.str-el↗

arXiv2004

Matter-wave interferometry in periodic and quasi-periodic arrays

We calculate within a Bose-Hubbard tight-binding model the matter-wave flow driven by a constant force through a Bose-Einstein condensate of Rb 87 atoms in various types of quasi-onedimensional arrays of potential wells. Interference patterns are obtained when beam splitting is induced by creating energy minigaps either through period doubling or through quasi-periodicity governed by the Fibonacci series. The generation of such condensate modulations by means of optical-laser structures is also discussed.

cond-mat.soft↗

arXiv2004

Collisional oscillations of trapped boson-fermion mixtures approaching collapse

We study the collective modes of a confined gaseous cloud of bosons and fermions with mutual attractive interactions at zero temperature. The cloud consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a spherical harmonic trap and the coupling between the two species is varied by increasing either the magnitude of the interspecies s-wave scattering length or the number of bosons. The mode frequencies are obtained in the collisional regime by solving the equations of generalized hydrodynamics and are compared with the spectra calculated in the collisionless regime within a random-phase approximation. We find that, as the mixture is driven towards the collapse instability, the frequencies of the modes of fermionic origin show a blue shift which can become very significant for large numbers of bosons. Instead the modes of bosonic origin show a softening, which becomes most pronounced in the very proximity of collapse. Explicit illustrations of these trends are given for the monopolar spectra, but similar trends are found for the dipolar and quadrupolar spectra except for the surface (n=0) modes which are essentially unaffected by the interactions.

cond-mat.soft↗

arXiv2003

Collective oscillations of a confined Bose gas at finite temperature in the random-phase approximation

We present a theory for the linear dynamics of a weakly interacting Bose gas confined inside a harmonic trap at finite temperature. The theory treats the motions of the condensate and of the non-condensate on an equal footing within a generalized random-phase approximation, which ({\it i}) extends the second-order Beliaev-Popov approach by allowing for the dynamical coupling between fluctuations in the thermal cloud, and ({\it ii}) reduces to an earlier random-phase scheme when the anomalous density fluctuations are omitted. Numerical calculations of the low-lying spectra in the case of isotropic confinement show that the present theory obeys with high accuracy the generalized Kohn theorem for the dipolar excitations and demonstrate that combined normal and anomalous density fluctuations play an important role in the monopolar excitations of the condensate. Mean-field theory is instead found to yield accurate results for the quadrupolar modes of the condensate. Although the restriction to spherical confinement prevents quantitative comparisons with measured spectra, it appears that the non-mean field effects that we examine may be relevant to explain the features exhibited by the breathing mode as a function of temperature in the experiments carried out at JILA on a gas of $^{87}$Rb atoms.

cond-mat.stat-mech↗

arXiv2003

Transition to hydrodynamics in colliding fermion clouds

We study the transition from the collisionless to the hydrodynamic regime in a two-component spin-polarized mixture of 40K atoms by exciting its dipolar oscillation modes inside harmonic traps. The time evolution of the mixture is described by the Vlasov-Landau equations and numerically solved with a fully three-dimensional concurrent code. We observe a master/slave behaviour of the oscillation frequencies depending on the dipolar mode that is excited. Regardless of the initial conditions, the transition to hydrodynamics is found to shift to lower values of the collision rate as temperature decreases.

cond-mat↗

arXiv2003

Density profile of a strictly two-dimensional Bose gas at finite temperature

We study a Bose-condensed gas at finite temperature, in which the particles of the condensate and of the thermal cloud are constrained to move in a plane under radial harmonic confinement and interact via strictly two-dimensional collisions. The coupling parameters are obtained from a calculation of the many-body T-matrix and decreases as temperature increases through a dependence on the chemical potential and on the occupancy of excited states. We discuss the consequences on the condensate fraction and on the density profiles of the condensed and thermal components as functions of temperature, within a simplified form of the two-fluid model.

cond-mat.soft↗

arXiv2003

Correlation energy of a two-dimensional electron gas from static and dynamic exchange-correlation kernels

We calculate the correlation energy of a two-dimensional homogeneous electron gas using several available approximations for the exchange-correlation kernel $f_{\rm xc}(q,ω)$ entering the linear dielectric response of the system. As in the previous work of Lein {\it et al.} [Phys. Rev. B {\bf 67}, 13431 (2000)] on the three-dimensional electron gas, we give attention to the relative roles of the wave number and frequency dependence of the kernel and analyze the correlation energy in terms of contributions from the $(q, iω)$ plane. We find that consistency of the kernel with the electron-pair distribution function is important and in this case the nonlocality of the kernel in time is of minor importance, as far as the correlation energy is concerned. We also show that, and explain why, the popular Adiabatic Local Density Approximation performs much better in the two-dimensional case than in the three-dimensional one.

cond-mat.mes-hall↗

arXiv2003

Transmittivity of a Bose-Einstein condensate on a lattice: interference from period doubling and the effect of disorder

We evaluate the particle current flowing in steady state through a Bose-Einstein condensate subject to a constant force in a quasi-onedimensional lattice and to attractive interactions from fermionic atoms that are localized in various configurations inside the lattice wells. The system is treated within a Bose-Hubbard tight binding model by an out-of-equilibrium Green's function approach. A new band gap opens up when the lattice period is doubled by locating the fermions in alternate wells and yields an interference pattern in the transmittivity on varying the intensity of the driving force. The positions of the transmittivity minima are determined by matching the period of Bloch oscillations and the time for tunnelling across the band gap. Massive disorder in the distribution of the fermions will wash out the interference pattern, but the same period doubling of the lattice can be experimentally realized in a four-beam set-up. We report illustrative numerical results for a mixture of 87Rb and 40K atoms in an optical lattice created by laser beams with a wavelength of 763 nm.

cond-mat.stat-mech↗

arXiv2003

Collective excitations in trapped boson-fermion mixtures: from demixing to collapse

We calculate the spectrum of low-lying collective excitations in a gaseous cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas over a range of the boson-fermion coupling strength extending from strongly repulsive to strongly attractive. Increasing boson-fermion repulsions drive the system towards spatial separation of its components (``demixing''), whereas boson-fermion attractions drive it towards implosion (``collapse''). The dynamics of the system is treated in the experimentally relevant collisionless regime by means of a Random-Phase approximation and the behavior of a mesoscopic cloud under isotropic harmonic confinement is contrasted with that of a macroscopic mixture at given average particle densities. In the latter case the locations of both the demixing and the collapse phase transitions are sharply defined by the same stability condition, which is determined by the softening of an eigenmode of either fermionic or bosonic origin. In contrast, the transitions to either demixing or collapse in a mesoscopic cloud at fixed confinement and particle numbers are spread out over a range of boson-fermion coupling strength, and some initial decrease of the frequencies of a set of collective modes is followed by hardening as evidenced by blue shifts of most eigenmodes. The spectral hardening can serve as a signal of the impending transition and is most evident when the number of bosons in the cloud is relatively large. We propose physical interpretations for these dynamical behaviors with the help of suitably defined partial compressibilities for the gaseous cloud under confinement.

cond-mat↗

arXiv2003

Analytic theory of ground-state properties of a three-dimensional electron gas at varying spin polarization

We present an analytic theory of the spin-resolved pair distribution functions $g_{σσ'}(r)$ and the ground-state energy of an electron gas with an arbitrary degree of spin polarization. We first use the Hohenberg-Kohn variational principle and the von Weizsäcker-Herring ideal kinetic energy functional to derive a zero-energy scattering Schrödinger equation for $\sqrt{g_{σσ'}(r)}$. The solution of this equation is implemented within a Fermi-hypernetted-chain approximation which embodies the Hartree-Fock limit and is shown to satisfy an important set of sum rules. We present numerical results for the ground-state energy at selected values of the spin polarization and for $g_{σσ'}(r)$ in both a paramagnetic and a fully spin-polarized electron gas, in comparison with the available data from Quantum Monte Carlo studies over a wide range of electron density.

cond-mat.str-el↗

arXiv2003

Free expansion of two-dimensional condensates with a vortex

We study the free expansion of a pancake-shaped Bose-condensed gas, which is initially trapped under harmonic confinement and containing a vortex at its centre. In the case of a radial expansion holding fixed the axial confinement we consider various models for the interactions, depending on the thickness of the condensate relative to the value of the scattering length. We are thus able to evaluate different scattering regimes ranging from quasi-three-dimensional (Q3D) to strictly two-dimensional (2D). We find that as the system goes from Q3D to 2D the expansion rate of the condensate increases whereas that of the vortex core decreases. In the Q3D scattering regime we also examine a fully free expansion in 3D and find oscillatory behaviour for the vortex core radius: an initial fast expansion of the vortex core is followed by a slowing down. Such a nonuniform expansion rate of the vortex core may be taken into account in designing new experiments.

cond-mat↗

arXiv2003

Collective dynamics of fermion clouds in cigar-shaped traps

The propagation of zero sound in a spin-polarized Fermi gas under harmonic confinement is studied as a function of the mean-field interactions with a second Fermi gas. A local-density treatment is compared with the numerical solution of the Vlasov-Landau equations for the propagation of density distortions in a trapped two-component Fermi gas at temperature T=0.2 Tf. The response of the gas to the sudden creation of a sharp hole at its centre is also studied numerically.

cond-mat.stat-mech↗

arXiv2003

Collective excitations of a trapped boson-fermion mixture across demixing

We calculate the spectrum of low-lying collective excitations in a mesoscopic cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a function of the boson-fermion repulsions. The cloud is under isotropic harmonic confinement and its dynamics is treated in the collisional regime by using the equations of generalized hydrodynamics with inclusion of surface effects. For large numbers of bosons we find that, as the cloud moves towards spatial separation (demixing) with increasing boson-fermion coupling, the frequencies of a set of collective modes show a softening followed by a sharp upturn. This behavior permits a clear identification of the quantum phase transition. We propose a physical interpretation for the dynamical transition point in a confined mixture, leading to a simple analytical expression for its location.

cond-mat↗

arXiv2002

Pair densities at contact in the quantum electron gas

The value of the pair distribution function g(r) at contact (r = 0) in a quantum electron gas is determined by the scattering events between pairs of electrons with antiparallel spins. The theoretical results for g(0) as a function of the coupling strength r_s in the paramagnetic electron gas in dimensionality D=2 and 3, that have been obtained from the solution of the two-body scattering problem with a variety of effective scattering potentials embodying many-body effects, are compared with the results of many-body calculations in the ladder approximation and with quantum Monte Carlo data.

cond-mat.str-el↗

arXiv2002

Self-consistent scattering theory of the pair distribution function in charged Bose fluids

We use a density functional theoretical approach to calculate the pair distribution function and the effective interactions in homogeneous fluids of spinless charged bosons. The scheme involves the self-consistent solution of a two-particle scattering problem with an effective scattering potential which embodies many-body effects and is adjusted to the compressibility sum rule. Numerical results are presented over an extensive range of density in both three and two dimensions.

cond-mat.soft↗

arXiv2002

Dynamics of trapped two-component Fermi gas: temperature dependence of the transition from collisionless to collisional regime

We develop a numerical method to study the dynamics of a two-component atomic Fermi gas trapped inside a harmonic potential at temperature T well below the Fermi temperature Tf. We examine the transition from the collisionless to the collisional regime down to T=0.2 Tf and find good qualitative agreement with the experiments of B. DeMarco and D.S. Jin [Phys. Rev. Lett. vol. 88, 040405 (2002)]. We demonstrate a twofold role of temperature on the collision rate and on the efficiency of collisions. In particular we observe an hitherto unreported effect, namely that the transition to hydrodynamic behavior is shifted towards lower collision rates as temperature decreases.

cond-mat.stat-mech↗

arXiv2002

Damping of long-wavelength collective excitations in quasi-onedimensional Fermi liquids

The imaginary part of the exchange-correlation kernel in the longitudinal current-current response function of a quasi-onedimensional Fermi liquid is evaluated by an approximate decoupling in the equation of motion for the current density, which accounts for processes of excitation of two particle-hole pairs. The two-pair spectrum determines the intrinsic damping rate of long-wavelength collective density fluctuations, which is calculated and contrasted with a result previously obtained for a clean Luttinger liquid.

cond-mat.str-el↗

arXiv2002

Spin-density functional approach to thermodynamic and structural consistence in the charge and spin response of an electron gas

We use spin-density functional theory to obtain novel expressions for the charge and spin local-field factors of an electron gas in terms of its electron-pair structure factors. These expressions (i) satisfy the compressibility and spin susceptibility sum rules; (ii) keep account of kinetic correlations by means of an integration over the coupling strength; and (iii) provide a practical self-consistent scheme for evaluating linear response and liquid structure. Numerical illustrations are given for the dielectric response of the paramagnetic electron gas in both three and two dimensions.

cond-mat.str-el↗