arXiv subjects

G. M. Falco

Publications and source records attributed to G. M. Falco.

14 recordsLinked to original sources

arXiv2018

Wave function correlations and the AC conductivity of disordered wires beyond the Mott-Berezinskii law

In one-dimensional disordered wires electronic states are localized at any energy. Correlations of the states at close positive energies and the AC conductivity $σ(ω)$ in the limit of small frequency are described by the Mott-Berezinskii theory. We revisit the instanton approach to the statistics of wave functions and AC transport valid in the tails of the spectrum (large negative energies). Applying our recent results on functional determinants, we calculate exactly the integral over gaussian fluctuations around the exact two-instanton saddle point. We derive correlators of wave functions at different energies beyond the leading order in the energy difference. This allows us to calculate corrections to the Mott-Berezinskii law (the leading small frequency asymptotic behavior of $σ(ω)$) which approximate the exact result in a broad range of $ω$. We compare our results with the ones obtained for positive energies.

cond-mat.dis-nn↗

arXiv2017

On functional determinants of matrix differential operators with multiple zero modes

We generalize the method of computing functional determinants with a single excluded zero eigenvalue developed by McKane and Tarlie to differential operators with multiple zero eigenvalues. We derive general formulas for such functional determinants of $r\times r$ matrix second order differential operators $O$ with $0 < n \leqslant 2r$ linearly independent zero modes. We separately discuss the cases of the homogeneous Dirichlet boundary conditions, when the number of zero modes cannot exceed $r$, and the case of twisted boundary conditions, including the periodic and anti-periodic ones, when the number of zero modes is bounded above by $2r$. In all cases the determinants with excluded zero eigenvalues can be expressed only in terms of the $n$ zero modes and other $r-n$ or $2r-n$ (depending on the boundary conditions) solutions of the homogeneous equation $O h=0$, in the spirit of Gel'fand-Yaglom approach. In instanton calculations, the contribution of the zero modes is taken into account by introducing the so-called collective coordinates. We show that there is a remarkable cancellation of a factor (involving scalar products of zero modes) between the Jacobian of the transformation to the collective coordinates and the functional fluctuation determinant with excluded zero eigenvalues. This cancellation drastically simplifies instanton calculations when one uses our formulas.

cond-mat.dis-nn↗

arXiv2015

Instanton theory for bosons in disordered speckle potential

We study the tail of the spectrum for non-interacting bosons in a blue-detuned random speckle potential. Using an instanton approach we derive the asymptotic behavior of the density of states in d dimensions. The leading corrections resulting from fluctuations around the saddle point solution are obtained by means of the Gel'fand-Yaglom method generalized to functional determinants with zero modes. We find a good agreement with the results of numerical simulations in one dimension. The effect of weak repulsive interactions in the Lifshitz tail is also discussed.

cond-mat.dis-nn↗

arXiv2010

Cooper pairs under the action of disorder and strong magnetic field

The zero temperature phase diagram of Cooper pairs exposed to disorder and magnetic field is found to exhibit four distinct phases: a Bose and a Fermi insulating, a metallic and a superconducting phase, respectively. The results explain the giant negative magneto-resistance found experimentally in In-O, TiN, Bi and high-$T_c$ materials.

cond-mat.supr-con↗

arXiv2010

Density of states in an optical speckle potential

We study the single particle density of states of a one-dimensional speckle potential, which is correlated and non-Gaussian. We consider both the repulsive and the attractive cases. The system is controlled by a single dimensionless parameter determined by the mass of the particle, the correlation length and the average intensity of the field. Depending on the value of this parameter, the system exhibits different regimes, characterized by the localization properties of the eigenfunctions. We calculate the corresponding density of states using the statistical properties of the speckle potential. We find good agreement with the results of numerical simulations.

cond-mat.dis-nn↗

arXiv2010

Variational approach for Bose-Einstein condensates in strongly disordered traps

Recently, Nattermann and Pokrovsky [PRL 100, 060402 (2008)] have proposed a scaling approach for studying Bose-Einstein condensates in strongly disordered traps. In this paper we implement their scaling argument in the framework of the variational method for solving the time dependent Gross-Pitaevskii equation. We consider atomic gases with both short range s-wave interaction and long range anisotropic dipolar interaction. The theory is addressed to the regime of strong disorder and weak interactions where the physics is dominated by the collective pinning due to the disorder. The phenomenon of condensate fragmentation in dipolar gases is also analyzed.

cond-mat.quant-gas↗

arXiv2009

Localized states and interaction induced delocalization in Bose gases with quenched disorder

Very diluted Bose gas placed into a disordered environment falls into a fragmented localized state. At some critical density the repulsion between particles overcomes the disorder. The gas transits into a coherent superfluid state. In this article the geometrical and energetic characteristics of the localized state at zero temperature and the critical density at which the quantum phase transition from the localized to the superfluid state proceeds are found.

cond-mat.other↗

arXiv2008

Weakly interacting Bose gas in a random environment

Zero temperature properties of a dilute weakly interacting $d$-dimensional Bose gas in a random potential are studied. We calculate geometrical and energetic characteristics of the localized state of a gas confined in a large box or in a harmonic trap. Different regimes of the localized state are found depending on the ratio of two characteristic length scales of the disorder, the Larkin length and the disorder correlation length. Repulsing bosons confined in a large box with average density $n$ well below a critical value $n_c$ are trapped in deep potential wells of extension much smaller than distance between them. Tunneling between these wells is exponentially small. The ground state of such a gas is a random singlet with no long-range phase correlation For $n>n_c$ repulsion between particles overcomes the disorder and the gas transits from the localized to a coherent superfluid state. The critical density $n_c$ is calculated in terms of the disorder parameters and the interaction strength. For atoms in traps four different regimes are found, only one of it is superfluid. The theory is extended to lower (1 and 2) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose-systems.

quant-ph↗

arXiv2007

Collective Oscillations in Trapped Bose-Einstein Condensed Gases in the Presence of Weak Disorder

The influence of a weak random potential on the collective modes of a trapped interacting Bose-Einstein condensate at zero temperature is calculated in the limit when the correlation length of the disorder is smaller than the healing length of the superfluid. The problem is solved in the Thomas-Fermi limit by generalizing the superfluid hydrodynamic equations to allow for the presence of weak disorder. We find that the disorder-induced frequency-shifts of the low-energy excitations can be of the same order of magnitude as the beyond mean-field corrections in the normal interaction recently observed experimentally.

cond-mat.other↗

arXiv2007

Thermodynamics of a Bose-Einstein Condensate with Weak Disorder

We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random delta-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body T-matrix approximations. This approach permits us to include the quasi-particle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical temperature and of the temperature for the onset of superfluidity by approaching the transition points from below, i.e., from the superfluid phase. Our results lead to a phase diagram consistent with that of the finite-temperature theory of Lopatin and Vinokur which was based on the replica method, and in which the transition points were approached from above.

cond-mat.other↗

arXiv2006

Dressed-molecules in resonantly-interacting ultracold atomic Fermi gases

We present a detailed analysis of the two-channel atom-molecule effective Hamiltonian for an ultracold two-component homogeneous Fermi gas interacting near a Feshbach resonance. We particularly focus on the two-body and many-body properties of the dressed molecules in such a gas. An exact result for the many-body T-matrix of the two-channel theory is derived by both considering coupled vertex equations and the functional integral methods. The field theory incorporates exactly the two-body physics of the Feshbach scattering by means of simple analytical formulas without any fitting parameters. New interesting many-body effects are discussed in the case of narrow resonances. We give also a description of the BEC-BCS crossover above and below T_C. The effects of different approximations for the selfenergy of the dressed molecules are discussed. The single-channel results are derived as a special limit for broad resonances. Moreover, through an analytic analysis of the BEC limit, the relation between the composite boson of the single-channel model and the dressed-molecule of the two-channel model is established.

cond-mat.other↗

arXiv2004

Atom-molecule theory of broad Feshbach resonances

We derive the atom-molecule theory for an atomic gas near a broad Feshbach resonance, where the energy dependence of the atom-molecule coupling becomes crucial for understanding experimental results. We show how our many-body theory incorporates the two-atom physics exactly. In particular, we calculate the magnetic moment of a two-component gas of ^{6}Li atoms for a wide range of magnetic fields near the broad Feshbach resonance at about 834 Gauss. We find excellent agreement with the experiment of Jochim et al. [Phys. Rev. Lett. 91, 240402 (2003)].

cond-mat.stat-mech↗

arXiv2004

Crossover temperature of Bose-Einstein condensation in an atomic Fermi gas

We show that in an atomic Fermi gas near a Feshbach resonance the crossover between a Bose-Einstein condensate of diatomic molecules and a Bose-Einstein condensate of Cooper pairs occurs at positive detuning, i.e., when the molecular energy level lies in the two-atom continuum. We determine the crossover temperature as a function of the applied magnetic field and find excellent agreement with the experiment of Regal et al. [Phys. Rev. Lett. 92, 040403 (2004)] that has recently observed this crossover temperature.

cond-mat.stat-mech↗

arXiv2003

The bosonic Kondo effect

The Kondo effect is associated with the formation of a many-body ground state that contains a quantum-mechanical entanglement between a (localized) fermion and the free fermions. We show that a bosonic version of the Kondo effect can occur in degenerate atomic Fermi gases near the Feshbach resonance. We also discuss how this bosonic Kondo effect can be observed experimentally.

cond-mat.stat-mech↗