arXiv subjects

Pablo Serra

Publications and source records attributed to Pablo Serra.

At least 19 recordsLinked to original sources

arXiv2026

Engineering Perfect State Transfer Graphs via Givens Transformations

Perfect quantum state transfer is achievable in different settings, including linear qubit chains, bi-dimensional arrays, ladders, etc. The most studied case contemplates transferring arbitrary one-qubit pure states in systems with homogeneous interactions. These restrictions allow finding numerous examples of systems that show perfect transfer but in geometries that are not implementable or are very difficult to implement in actual experimental settings. Relaxing the homogeneity of the interactions and inspired by the $XX$ qubit chains that show perfect transmission, we present a simple scheme based on the Givens Transformations to analyse and obtain a class of qubit graphs that possess perfect quantum state transmission. We present some simple examples and show how it is possible to generalize them for longer transmission lengths.

quant-ph↗

arXiv2025

On the number of words of $N=3 \,n$ letters with a three-letter alphabet

In this paper we address the well-known problem of counting the number of $3n$-letter words that can be formed from a three-letter alphabet by decomposing it into four possible cases based on its remainder when divided by three. The solution to the problem also gives us some sums of trinomial coefficients.

math.CO↗

arXiv2025

Perfect, Pretty Good and Optimized Quantum State Transfer in Transmon qubit chains

Chains of transmon qubits are considered promising systems to implement different quantum information tasks. In particular as channels that perform high-quality quantum state transfer. We study how changing the interaction strength between the chain qubits allows us to obtain perfect or pretty good state transfer and present explicit analytic expressions for their transmission fidelity. For particular values of the interactions between the qubits, transmon chains are equivalent to generalized SSH chains and show the traditional traits observed in chains with topological states, localized states at the extremes of the chain, and eigenvalues that lie inside the spectral gap. Consequently, we study the quantum state transfer on chains with dimerized interactions, looking for chains with fast transfer times. We show that, in many cases, asking for fast transfer times results in chains with dimerized interactions that do not have topological states.

quant-ph↗

arXiv2023

The scaling law of the arrival time of spin systems that present pretty good transmission

The pretty good transmission scenario implies that the probability of sending one excitation from one extreme of a spin chain to the other can reach values arbitrarily close to the unity just by waiting a time long enough. The conditions that ensure the appearance of this scenario are known for chains with different interactions and lengths. Sufficient conditions for the presence of pretty good transmission depend on the spectrum of the Hamiltonian of the spin chain. Some works suggest that the time $t_{\varepsilon}$ at which the pretty good transmission takes place scales as $1/(|\varepsilon|)^{f(N)}$, where $\varepsilon$ is the difference between the probability that a single excitation propagates from one extreme of the chain to the other and the unity, while $f(N)$ is an unknown function of the chain length. In this paper, we show that the exponent is not a simple function of the chain length but a power law of the number of linearly independent irrational eigenvalues of the one-excitation block of the Hamiltonian that enter into the expression of the probability of transmission of one excitation. We explicitly provide examples of a chain showing that the exponent changes when the couplings between the spins change while the length remains fixed. For centrosymmetric spin chains the exponent is at most $N/2$.

quant-ph↗

arXiv2023

Semi-flexible trimers on the square lattice in the full lattice limit

Trimers are chains formed by two lattice edges, and therefore three monomers. We consider trimers placed on the square lattice, the edges belonging to the same trimer are either colinear, forming a straight rod with unitary statistical weight, or perpendicular, a statistical weight $\omega$ being associated to these angular trimers. The thermodynamic properties of this model are studied in the full lattice limit, where all lattice sites are occupied by monomers belonging to trimers. In particular, we use transfer matrix techniques to estimate the entropy of the system as a function of $\omega$. The entropy $s(\omega)$ is a maximum at $\omega=1$ and our results are compared to earlier studies in the literature for straight trimers ($\omega=0$), angular trimers ($\omega \to \infty$) and for mixtures of equiprobable straight and angular trimers ($\omega=1$).

cond-mat.stat-mech↗

arXiv2022

Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer

We construct the exact solution for a family of one-half spin chains explicitly. The spin chains Hamiltonian corresponds to an isotropic Heisenberg Hamiltonian, with staggered exchange couplings that take only two different values. We work out the exact solutions in the one-excitation subspace. Regarding the problem of quantum state transfer, we use the solution and some theorems concerning the approximation of irrational numbers, to show the appearance of conclusive pretty good transmission for chains with particular lengths. We present numerical evidence that pretty good transmission is achieved by chains whose length is not a power of two. The set of spin chains that shows pretty good transmission is a subset of the family with an exact solution. Using perturbation theory, we thoroughly analyze the case when one of the exchange coupling strengths is orders of magnitude larger than the other. This strong coupling limit allows us to study, in a simple way, the appearance of pretty good transmission. The use of analytical closed expressions for the eigenvalues, eigenvectors, and transmission probabilities allows us to obtain the precise asymptotic behavior of the time where the pretty good transmission is observed. Moreover, we show that this time scales as a power law whose exponent is an increasing function of the chain length. We also discuss the crossover behavior obtained for the pretty good transmission time between the regimes of strong coupling limit and the one observed when the exchange couplings are of the same order of magnitude.

quant-ph↗

arXiv2021

Understanding the propagation of excitations in quantum spin chains with different kind of interactions

The dynamical behaviour of the quantum state of different quantum spin chains, with designed site dependent interaction strengths, is analyzed when the initial state belongs to the one excitation subspace. It is shown that the inhomogeneous chains are able to transfer excitations with near perfect fidelity. This behaviour is found for two very different spin chain Hamiltonians. The first one is the ferromagnetic Heisenberg Hamiltonian with nearest neighbor interactions, the second one describes a chain with long range anisotropic interactions which are ferromagnetic in the $z$ direction and antiferromagnetic in the $(x,y)$ plane. It is shown that both designed chains have in common a partially ordered spectrum and well localized eigenvectors. This physical trait unifies the description of both kind of systems.

quant-ph↗

arXiv2021

Pretty good quantum state transfer on isotropic and anisotropic Heisenberg spin chains with tailored site dependent exchange couplings

Using a global optimization algorithm we obtain spin chains with site-dependent exchange coefficients which allow almost perfect quantum state transfer between the extremes of the chains without any further time-dependent external control. We consider chains with isotropic and anisotropic Heisenberg Hamiltonian with up to 100 spins. The method allow us to choose the arrival of the transferred state by changing the range available to the exchange coupling strengths. We consider short transferred times, in particular shorter than those achievable with known time-dependent control schemes. The chains obtained with the optimization method show some remarkable and interesting traits as, for instance, the scaling of the magnitude of the exchange couplings needed to achieve near perfect state transfer with the length of the chain and the arrival time. This scaling makes it possible to decide if the chain with site-dependent coefficients can be implemented in an actual system according to the range of interactions allowed in it. We compare the robustness of the transmission protocol against static disorder on the exchange coefficients using different figures of merit, which allow us to conclude that the isotropic Heisenberg chain is the best option when compared with anisotropic chains. This comparison is relevant since the method allow us to start with chains that all achieve near perfect quantum state transfer, regime that was not available previously in these chains without time-dependent external control.

quant-ph↗

arXiv2019

Convexity properties of superpositions of degenerate bipartite eigenstates

The entanglement content of superpositions of pairs of degenerate eigenstates of a bipartite system are considered in the case that both are also eigenstates of the $z$ component of the total angular momentum. It is shown that the von Neumann entropy of the state that is obtained tracing out one of the parts of the system has a definite convexity (concavity) as a function of the superposition parameter and that its convexity (concavity) can be predicted using a quantity of information that measures the entropy shared by the states at the extremes of the superposition. Several examples of two particle system, whose eigenfunctions and density matrices can be obtained exactly, are analyzed thoroughly.

quant-ph↗

arXiv2018

Phase transitions, order by disorder and finite entropy in the Ising antiferromagnetic bilayer honeycomb lattice

We present an analytical and numerical study of the Ising model on a bilayer honeycomb lattice including interlayer frustration and coupling with an external magnetic field. First, we discuss the exact $T=0$ phase diagram, where we find finite entropy phases for different magnetisations. Then, we study the magnetic properties of the system at finite temperature using complementary analytical techniques (Bethe lattice), and two types of Monte-Carlo algorithms (Metropolis and Wang-Landau). We characterize the phase transitions and discuss the phase diagrams. The system presents a rich phenomenology: there are first and second order transitions, low-temperature phases with extensive degeneracy, and order-by-disorder state selection.

cond-mat.stat-mech↗

arXiv2018

Simultaneous Orientational and Conformational Molecular Dynamics in Solid (1,1,2)-Trichloroethane

The molecular dynamics in the ambient-pressure solid phase of (1,1,2)-trichloroethane is studied by means of broadband dielectric spectroscopy and molecular dynamics simulations. The dielectric spectra of polycrystalline samples obtained by crystallization from the liquid phase exhibit, besides a space-charge relaxation associated with accumulation of charges at crystalline domain boundaries, two loss features arising from dipolar molecular relaxations. The most prominent and slower of the two loss features is identified as a configurational leap of the molecules which involves a simultaneous change in spatial orientation and structural conformation, namely between two isomeric forms (gauche$^+$ and gauche$^-$) of opposite chirality. In this peculiar dynamic process, the positions of the three chlorine atoms in the crystal lattice remain unchanged, while those of the carbon and hydrogen atoms are modified. This dynamic process is responsible for the disorder observed in an earlier x-ray diffraction study and confirmed by our simulation, which is present only at temperatures relatively close to the melting point, starting 40 K below. The onset of the disorder is visible as an anomaly in the temperature dependence of the dc conductivity of the sample at exactly the same temperature. While the slower relaxation dynamics (combined isomerization/reorientation) becomes increasingly more intense on approaching the melting point, the faster dynamics exhibits significantly lower but constant dielectric strength. Based on our molecular dynamics simulations, we assign the faster relaxation to large fluctuations of the molecular dipole moments, partly due to large-angle librations of the chloroethane species.

physics.chem-ph↗

arXiv2017

Dynamic heterogeneity in an orientational glass

Family of compounds CBr$_n$Cl$_{4-n}$ has been proven helpful in unraveling microscopic mechanisms responsible of glassy behavior. Some of the family members show translational ordered phases with minimal disorder which appears to reveal glassy features, thus deserving special attention in the search for universal glass anomalies. In this work, we studied CBrCl$_3$ dynamics by performing extensive molecular dynamics simulations. Molecules of this compound perform reorientational discrete jumps, where the atoms exchange equivalent positions among each other revealing a cage-orientational jump motion fully comparable to the cage-rototranslational jump motion in supercooled liquids. Correlation times were calculated from rotational autocorrelation functions showing good agreement with previous reported dielectric results. From mean waiting and persistence times calculated directly from trajectory results, we are able to explain which microscopic mechanisms lead to characteristic times associated with $α$ and $β$-relaxation times measured experimentally. We found that two nonequivalent groups of molecules have a longer characteristic time than the other two nonequivalent groups, both of them belonging to the asymmetric unit of the monoclinic (C2/c) lattice.

cond-mat.soft↗

arXiv2017

Exact wave functions and entropies of the one dimensional Regularized Calogero model

The divergence in the interaction term of the Calogero model can be prevented introducing a cutoff length parameter, this modification leads to a quasi-exactly solvable model whose eigenfunctions can be written in terms of Heun's polynomials. It is shown both, analytical and numerically. that the reduced density matrix obtained tracing out one particle from the two-particle density operator can be obtained exactly as well as its entanglement spectrum. The number of non-zero eigenvalues in these cases is finite. Besides, it is shown that taking the limit in which the cutoff distance goes to zero, the reduced density matrix and finite entanglement spectrum of the Calogero model is retrieved. The entanglement Rényi entropy is also studied to characterize the physical traits of the model. It is found that the quasi-exactly solvable character of the model is put into evidence by the entanglement entropies when they are calculated numerically over the parameter space of the model.

quant-ph↗

arXiv2016

Detecting dimensional crossover and finite Hilbert space through entanglement entropies

The information content of the two-particle one- and two-dimensional Calogero model is studied using the von Neumann and Rényi entropies. The one-dimensional model is shown to have non-monotonic entropies with finite values in the large interaction strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confinement in the two-dimensional case we show that the one-dimensional behavior is eventually reached when the anisotropy increases. The crossover from two to one dimensions is demonstrated using the harmonic approximation and it is shown that the von Neumann divergence only occurs in the isotropic case. The Rényi entropies are used to highlight the structure of the model spectrum. In particular, it is shown that these entropies have a non-monotonic and non-analytical behavior in the neighborhood of the interaction strength parameter values where the Hilbert space and, consequently, the spectrum of the reduced density matrix are both finite.

quant-ph↗

arXiv2016

Localization of the valence electron of endohedrally confined hydrogen, lithium and sodium in fullerene cages

The localization of the valence electron of $H$, $Li$ and $Na$ atoms enclosed by three different fullerene molecules is studied. The structure of the fullerene molecules is used to calculate the equilibrium position of the endohedrally atom as the minimum of the classical $(N+1)$-body Lennard-Jones potential. Once the position of the guest atom is determined, the fullerene cavity is modeled by a short range attractive shell according to molecule symmetry, and the enclosed atom is modeled by an effective one-electron potential. In order to examine whether the endohedral compound is formed by a neutral atom inside a neutral fullerene molecule $X@C_{N}$ or if the valence electron of the encapsulated atom localizes in the fullerene giving rise to a state with the form $X^{+}@C_{N}^{-}$, we analyze the electronic density, the projections onto free atomic states, and the weights of partial angular waves.

physics.chem-ph↗

arXiv2016

Dynamic Heterogeneity In The Monoclinic Phase Of CCl$_4$

Carbon tetrachloride (CCl$_4$) is one of the simplest compounds having a translationally stable monoclinic phase while exhibiting a rich rotational dynamics below 226 K. Recent nuclear quadrupolar resonance (NQR) experiments revealed that the dynamics of CCl$_4$ is similar to that of the other members of the isostructural series CBr$_{n}$Cl$_{4-n}$, suggesting that the universal relaxation features of canonical glasses such as $α$- and $β$-relaxation are also present in non-glass formers. Using molecular dynamics (MD) simulations we studied the rotational dynamics in the monoclinic phase of CCl$_4$. The molecules undergo $C3$ type jump-like rotations around each one of the four C-Cl bonds. The rotational dynamics is very well described with a master equation using as the only input the rotational rates measured from the simulated trajectories. It is found that the heterogeneous dynamics emerges from faster and slower modes associated with different rotational axes, which have fixed orientations relative to the crystal and are distributed among the four non-equivalent molecules of the unit cell.

physics.chem-ph↗

arXiv2015

Exact finite reduced density matrix and von Neumann entropy for the Calogero model

The information content of continuous quantum variables systems is usually studied using a number of well known approximation methods. The approximations are made to obtain the spectrum, eigenfunctions or the reduced density matrices that are essential to calculate the entropy-like quantities that quantify the information. Even in the sparse cases where the spectrum and eigenfunctions are exactly known the entanglement spectrum, {\em i.e.} the spectrum of the reduced density matrices that characterize the problem, must be obtained in an approximate fashion. In this work, we obtain analytically a finite representation of the reduced density matrices of the fundamental state of the N-particle Calogero model for a discrete set of values of the interaction parameter. As a consequence, the exact entanglement spectrum and von Neumann entropy is worked out.

quant-ph↗

arXiv2015

Dynamic characterization of crystalline and glass phases of deuterated 1,1,2,2 Tetrachloroethane

A thorough characterization of the γ, β and glass phases of deuterated 1,1,2,2 Tetrachloroethane (C2D2Cl4) via Nuclear Quadrupole Resonance and Molecular Dynamic Simulations (MDS) is reported. The presence of molecular reorientations was experimentally observed in the glass phase and in the β phase. In the β phase, and from MDS, these reorientations are attributed to two possible movements, i.e. a $180^o$ reorientation around the C2 molecular symmetry axis and a reorientation of the molecule between non-equivalent positions. In the glass phase, the spin-lattice relaxation time T1 is of the order of 16 times lower that T1 in the crystalline phase and varies as $T^{-1}$ below 100 K in good agreement with the strong quadrupolar relaxation observed in amorphous materials and in the glassy state of molecular organic systems. The activation energy of molecular reorientations in the glass phase (19 kJ/mol) is comparable to that observed in the glassy crystal of a "molecular cousin" compound, Freon 112 (C2F2Cl4), for the secondary β-relaxation. Moreover, the on-site orientational motion of Tetrachloroethane molecules offers a new indirect evidence of the prominent role of such orientational disorder in glassy dynamics.

physics.chem-ph↗