arXiv subjects

R. Franco

Publications and source records attributed to R. Franco.

27 records · Page 2Linked to original sources

arXiv2007

Quantum mechanics, Bayes' theorem and the conjunction fallacy

In the present article we consider the conjunction fallacy, a well known cognitive heuristic experimentally tested in cognitive science, which occurs for intuitive judgments in situations of bounded rationality. We show that the quantum formalism can be used to describe in a very simple way this fallacy in terms of interference effect. We evidence that the quantum formalism leads quite naturally to violations of Bayes' rule when considering the probability of the conjunction of two events. Thus we suggest that in cognitive science the formalism of quantum mechanics can be used to describe a \textit{quantum regime}, the bounded-rationality regime, where the cognitive heuristics are valid.

quant-ph↗

arXiv2006

Discrete Wigner distribution for two qubits: a characterization of entanglement properties

We study the properties of the discrete Wigner distribution for two qubits introduced by Wotters. In particular, we analyze the entanglement properties within the Wigner distribution picture by considering the negativity of the Wigner function (WF) and the correlations of the marginal distribution. We show that a state is entangled if at least one among the values assumed by the corresponding discrete WF is smaller than a certain critical (negative) value. Then, based on the Partial Transposition criterion, we establish the relation between the separability of a density matrix and the non-negativity of the WF's relevant both to such a density matrix and to the partially transposed thereof. Finally, we derive a simple inequality --involving the covariance-matrix elements of a given WF-- which appears to provide a separability criterion stronger than the one based on the Local Uncertainty Relations.

quant-ph↗

arXiv2005

An algebraic approach to the study of weakly excited states for a condensate in a ring geometry

We determine the low-energy spectrum and the eigenstates for a two-bosonic mode nonlinear model by applying the Inönü-Wigner contraction method to the Hamiltonian algebra. This model is known to well represent a Bose-Einstein condensate rotating in a thin torus endowed with two angular-momentum modes as well as a condensate in a double-well potential characterized by two space modes. We consider such a model in the presence of both an attractive and a repulsive boson interaction and investigate regimes corresponding to different values of the inter-mode tunneling parameter. We show that the results ensuing from our approach are in many cases extremely satisfactory. To this end we compare our results with the ground state obtained both numerically and within a standard semiclassical approximation based on su(2) coherent states.

cond-mat.mes-hall↗

arXiv2003

Thermodynamic properties of the periodic Anderson model:X-boson treatment

We study the specific dependence of the periodic Anderson Model (PAM) in the limit of $U=\infty$ employing the X-boson treatment in two fifferent regimes of the PAM: the heavy fermion Kondo (HF-K) and the heavy fermion local magnetic regime (HF-LMM). We obtain a multiple peak structure for the specific heat in agreement with experimental results as well as the increase of the electronic effective mass at low temperatures associated with the HF-K regime. The entropy per site at low T tends to zero in the HF-K regime, corresponding to a singlet ground state, and it tends to $k_{B}ln(2)$ in the HF-LMM, corresponding to a doublet ground state at each site. The linear coefficient $γ(T)=C_{v}/T$ of the specific heat qualitatively agrees with the experimental results obtained for differents materials in the two regimes considered here.

cond-mat.str-el↗

arXiv2003

Finite band effects over the linear conductance through a quantum wire coupled with a quantum dot: X-boson treatment

We study the electronic transport through a quantum wire (QW) with a strong side coupled quantum dot (QD). We obtain a linear conductance with lateral peaks when the gate voltage, is located near the edge of the conduction band. The calculated density of states shows, that these peaks are associated with renormalized localized levels out side of the conduction band. These results are compatibles with recent experimental results.

cond-mat.mes-hall↗

arXiv2003

Phase diagram of the $CuO_{3}$ chains in $YBa_{2}Cu_{3}O_{6+X}$ and $PrBa_{2}Cu_{3}O_{6+X}$

We use a mapping of the multiband Hubbard model for $CuO_{3}$ chains in $RBa_{2}Cu_{3}0_{6+x}$ (R=Y or a rare earth) onto a $t-J$ model and the description of the charge dynamics of the latter in terms pf s spinless model, to study the electronic structure of the chains. We briefly review results for the optical conductivity and we calculate the quantum phase diagram of quarter filled chains including Coulomb repulsion up to that between next-nearest-neighbor $Cu$ atoms $V_{2}$, using the resulting effective Hamiltonian, mapped onto an XXZ chain, and the method of crossing of excitation spectra. The method gives accurate results for the boundaries of the metallic phase in this case. The inclusion of $V_{2}$ greatly enhances the region of metallic behavior of the chains.

cond-mat.supr-con↗

arXiv2002

Fano resonance in electronic transport through a quantum wire with a side-coupled quantum dot: X-boson treatment

The transport through a quantum wire with a side coupled quantum dot is studied. We use the X-boson treatment for the Anderson single impurity model in the limit of $U=\infty $. The conductance presents a minimum for values of T=0 in the crossover from mixed-valence to Kondo regime due to a destructive interference between the ballistic channel associated with the quantum wire and the quantum dot channel. We obtain the experimentally studied Fano behavior of the resonance. The conductance as a function of temperature exhibits a logarithmic and universal behavior, that agrees with recent experimental results.

cond-mat.mes-hall↗

arXiv2001

Thermodynamic potential of the Periodic Anderson Model with the X-boson method: Chain Approximation

The Periodic Anderson Model (PAM) in the $U\to\infty$ limit has been studied in a previous work employing the cumulant expansion with the hybridization as perturbation (M. S. Figueira, M. E. Foglio and G. G. Martinez, Phys. Rev. B \textbf{50}, 17933 (1994)). When the total number of electrons $N_{t}$ is calculated as a function of the chemical potential $μ$ in the ``Chain Approximation'' (CHA), there are three values of the chemical potential $μ$ for each $N_{t}$ in a small interval of $N_{t}$ at low $T$ (M. S Figueira, M. E Foglio, Physica A 208 (1994)). We have recently introduced the ``X-boson'' method, inspired in the slave boson technique of Coleman, that solves the problem of non conservation of probability (completeness) in the CHA as well as removing the spurious phase transitions that appear with the slave boson method in the mean field approximation. In the present paper we show that the X-boson method solves also the problem of the multiple roots of $N_{t}(μ)$ that appear in the CHA.

cond-mat.str-el↗

arXiv2001

X-boson cumulant approach to the periodic Anderson model

The Periodic Anderson Model (PAM) can be studied in the infinite U limit by employing the Hubbard X operators to project out the unwanted states. We have already studied this problem employing the cumulant expansion with the hybridization as perturbation, but the probability conservation of the local states (completeness) is not usually satisfied when partial expansions like the Chain Approximation (CHA) are employed. Here we treat the problem by a technique inspired in the mean field approximation of Coleman's slave-bosons method, and we obtain a description that avoids the unwanted phase transition that appears in the mean-field slave-boson method both when the chemical potential is greater than the localized level Ef at low temperatures (T) and for all parameters at intermediate T.

cond-mat.str-el↗