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J. Abad

Publications and source records attributed to J. Abad.

11 recordsLinked to original sources
arXiv2011

Characterization of silicon thin overlayers on rutile \ce{TiO2} (110)-(1x1)

Silicon thin films for coverages ($θ$) between 0.3 and 3 monolayers have been grown on rutile \ce{TiO2}(110)-(1x1) at room temperature and studied by x-ray and ultra-violet photoelectron spectroscopies, Auger electron spectroscopy, and low energy electron diffraction (LEED). A clear evidence of a strong \ce{Si}/\ce{TiO2} interaction consistent with the high affinity of O for Si has been found. The Ti cations on the substrate are reduced, while the Si film is oxidized, yielding \ce{SiO2} and a mixture of silicon suboxides. Neutral Si atoms are observed at a coverage of 3 monolayers. At the interface region we observe the formation of cross-linking Ti-O-Si bonds. The thin Si overlayer strongly attenuates the $(1 \times 1)$ LEED pattern from the substrate. Finally, thermal annealing results in the improvement of the \ce{SiO2} stoichiometry, but the surface order is not recovered. Using ab-initio density functional theory we have obtained optimum geometrical configurations and corresponding density of states for 1/3 \le θ\le 1$ monolayers of Si adsorbed on the $1 \times 1$ two-dimensional unit cell.

cond-mat.mtrl-sci↗
arXiv2010

Thermal frequency noise in low oscillation amplitude Dynamic Scanning Force Microscopy

Thermal fluctuation of the cantilever position sets a fundamental limit for the precision of any Scanning Force Microscope. In the present work we analyse how these fluctuations limit the determination of the resonance frequency of the tip-sample system. The basic principles of frequency detection in Dynamic Scanning Force Microscopy are revised and the precise response of a typical frequency detection unit to thermal fluctuation of the cantilever is analysed in detail. A general relation for thermal frequency noise is found as a function of measurement bandwidth and cantilever oscillation. For large oscillation amplitude and low bandwidth, this relation converges to the result known from the literature, while for low oscillation amplitude and large bandwidth we find that the thermal frequency noise is equal to the width of the resonance curve and therefore stays finite, contrary to what is predicted by the relation known so far. The results presented in this work fundamentally determine the ultimate limits of Dynamic Scanning Force Microscopy.

cond-mat.mes-hall↗
arXiv2008

An algorithm to obtain global solutions of the double confluent Heun equation

A procedure is proposed to construct solutions of the double confluent Heun equation with a determinate behaviour at the singular points. The connection factors are expressed as quotients of Wronskians of the involved solutions. Asymptotic expansions are used in the computation of those Wronskians. The feasibility of the method is shown in an example, namely, the Schroedinger equation with a quasi-exactly-solvable potential.

math.CA↗
arXiv1999

Exact Solution of a Electron System Combining Two Different t-J Models

A new strongly correlated electron model is presented. This is formed by two types of sites: one where double occupancy is forbidden, as in the t-J model, and the other where double occupancy is allowed but vacancy is not allowed, as an inverse t-J model. The Hamiltonian shows nearest and next-to-nearest neighbour interactions and it is solved by means of a modified algebraic nested Bethe Ansatz. The number of sites where vacancy is not allowed, may be treated as a new parameter if the model is looked at as a t-J model with impurities. The ground and excited states are described in the thermodynamic limit.

cond-mat↗
arXiv1998

Excitations and S-matrix for su(3) spin chain combining ${3}$ and ${3^{*}}

The associated Hamiltonian for a su(3) spin chain combining ${3}$ and ${3^{*}}$ representations is calculated. The ansatz equations for this chain are obtained and solved in the thermodynamic limit, and the ground state and excitations are described. Thus, relations between the number of roots and the number of holes in each level have been found . The excited states are characterized by means of these quantum numbers. Finally, the exact S matrix for a state with two holes is found.

cond-mat↗
arXiv1997

Integrable su(3) spin chain combining different representations

The general expression for the local matrix $t(θ)$ of a quantum chain with the site space in any representation of su(3) is obtained. This is made by generalizing $t(θ)$ from the fundamental representation and imposing the fulfillment of the Yang-Baxter equation. Then, a non-homogeneous spin chain combining different representations of su(3) is solved by developing a method inspired in the nested Bethe ansatz. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations. A conjecture about the solution of a chain with the site states in different representations of su(n) is presented. The thermodynamic limit of the ground state is calculated.

cond-mat↗
arXiv1996

Integrable quantum chains combining site states in different representations of $su(3)$

The general expression for the local matrix $L(θ)$ of a quantum chain with the site space in any representation of $su(3)$ is obtained. This is made by generalizing $L(θ)$ from the fundamental representation and imposing the fulfilment of the Yang-Baxter equation. Then, a non-homogeneous spin chain combining different representations of $su(3)$ is solved by a method inspired in the nested Bethe ansatz. The solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled Bethe equations. A conjecture about the solution of a chain with the site states in different representations of $su(n)$ is presented.

cond-mat↗
arXiv1996

Integrable Models Associated to Classical Representations of U_q(\widehat{sl(n)})

We describe a representation for $U_q(\widehat{sl(n)})$, when $q$ is not a root of unity, based on the fundamental representation of $sl(n)$. As $U_q(sl(n))$ has a Hopf algebra structure with a non-commutative co-product, we look for a intertwine matrix $R$ that relates two possible definitions of that co-product. We solve cases for $n=2$ and $n=3$, and then we generalize for any $n$. We obtain the hamiltonian associated to such matrix $R$, corresponding to a multi-state chain. As the case for $n=2$ corresponds to the XXZ model with spin $1/2$, for $n>2$ we have the generalization of the XXZ model to $sl(n)$. We show the case for $n=3$ and its solution by Bethe ansatz.

cond-mat↗
arXiv1996

Bethe ansatz equations for quantum chains combining different representations of $su(3)$

The general expression for the local matrix of a quantum chain $L(θ)$ with the site space in any representation of $su(3)$ is obtained. This is made by generalizing $L(θ)$ from the fundamental representation and imposing the fulfilment of the Yang-Baxter equation. With these operators and using a generalization of the nested Bethe ansatz, the Bethe equations for a multistate quantum chain combining two arbitrary representations of $su(3)$ are obtained .

cond-mat↗
arXiv1994

Integrable Spin Chains Associated to $\widehat{sl_q(n)}$ and $\widehat{sl_{p,q}(n)}$

The Hoft structure of the central extension of the $U_q \left( \widehat{sl\left( n \right) }\right)$ algebra is considered. The intertwine matrix induces new integrable spin chain models. We show the relation of these models and the biparametric spin chain $\widehat{sl_{p,q} \left( n \right)}$ models. The cases $n=2$ are $n=3$ are discussed and for $n=2$ we obtain the model of Dasgupta and Chowdhury . The case $n=3$ is solved with nested Bethe ansatz method and it is showed the dependence of the Bethe equations in the second parameter introduced

hep-th↗