arXiv subjects

S. L. A. de Queiroz

Publications and source records attributed to S. L. A. de Queiroz.

At least 19 recordsLinked to original sources

arXiv2021

Rare-event properties in a classical stochastic model describing the evolution of random unitary circuits

We investigate the statistics of selected rare events in a (1+1)-dimensional (classical) stochastic growth model which describes the evolution of (quantum) random unitary circuits. In such classical formulation, particles are created and/or annihilated at each step of the evolution process, according to rules which generally favor a growing cluster size. We apply a large-deviation approach based on biased Monte Carlo simulations, with suitable adaptations, to evaluate (a) the probability of ending up with a single particle at a specified final time $t_f$, and (b) the probability of having particles outside the light cone, defined by a "butterfly velocity" $v_B$, at $t_f$. Morphological features of single-particle final configurations are discussed, in connection with whether the location of such particle is inside or outside the light cone; we find that joint occurrence of both events of types (a) and (b) drives significant changes to such features, signalling a second-order phase transition.

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arXiv2020

Spin-dependent conductance statistics in systems with spin-orbit coupling

Spin-dependent partial conductances are evaluated in a tight-binding description of electron transport in the presence of spin-orbit (SO) couplings, using transfer-matrix methods. As the magnitude of SO interactions increases, the separation of spin-switching channels from non-spin-switching ones is gradually erased. Spin-polarised incident beams are produced by including a Zeeman-like term in the Hamiltonian. The exiting polarisation is shown to exhibit a maximum as a function of the intensity of SO couplings. For moderate site disorder, and both weak and strong SO interactions, no evidence is found for a decay of exiting polarisation against increasing system length. With very low site disorder and weak SO couplings a spin-filter effect takes place, as polarisation {\em increases} with increasing system length.

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arXiv2019

Dynamical aspects of spontaneous symmetry breaking in driven flow with exclusion

We present a numerical study of a two-lane version of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally-imposed particle injection ($α$) and ejection ($β$) rates, spontaneous symmetry breaking can occur. We investigate the statistics and internal structure of the stochastically-induced transitions, or "flips", which occur between opposite broken-symmetry states as the system evolves in time. From the distribution of time intervals separating successive flips, we show that the evolution of the associated characteristic times against externally-imposed rates yields information regarding the proximity to a critical point in parameter space. On short time scales, we probe for the possible existence of precursor events to a flip between opposite broken-symmetry states. We study an adaptation of domain-wall theory to mimic the density reversal process associated with a flip.

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arXiv2017

Driven flow with exclusion and spin-dependent transport in graphenelike structures

We present a simplified description for spin-dependent electronic transport in honeycomb-lattice structures with spin-orbit interactions, using generalizations of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. Mean field theory and numerical simulations are used to study currents, density profiles and current polarization in quasi- one dimensional systems with open boundaries, and externally-imposed particle injection ($α$) and ejection ($β$) rates. We investigate the influence of allowing for double site occupancy, according to Pauli's exclusion principle, on the behavior of the quantities of interest. We find that double occupancy shows strong signatures for specific combinations of rates, namely high $α$ and low $β$, but otherwise its effects are quantitatively suppressed. Comments are made on the possible relevance of the present results to experiments on suitably doped graphenelike structures.

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arXiv2016

Domain wall theory and non-stationarity in driven flow with exclusion

We study the dynamical evolution toward steady state of the stochastic non-equilibrium model known as totally asymmetric simple exclusion process, in both uniform and non-uniform (staggered) one-dimensional systems with open boundaries. Domain-wall theory and numerical simulations are used and, where pertinent, their results are compared to existing mean-field predictions and exact solutions where available. For uniform chains we find that the inclusion of fluctuations inherent to the domain-wall formulation plays a crucial role in providing good agreement with simulations, which is severely lacking in the corresponding mean-field predictions. For alternating-bond chains the domain-wall predictions for the features of the phase diagram in the parameter space of injection and ejection rates turn out to be realized only in an incipient and quantitatively approximate way. Nevertheless, significant quantitative agreement can be found between several additional domain-wall theory predictions and numerics.

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arXiv2015

Localization and spin transport in honeycomb structures with spin-orbit coupling

Transfer-matrix methods are used for a tight-binding description of electron transport in graphene-like geometries, in the presence of spin-orbit couplings. Application of finite-size scaling and phenomenological renormalization techniques shows that, for strong enough spin-orbit interactions and increasing on-site disorder, this system undergoes a metal-insulator transition characterized by the exponents $ν=2.71(8)$, $η=0.174(2)$. We show how one can extract information regarding spin polarization decay with distance from an injection edge, from the evolution of wave-function amplitudes in the transfer-matrix approach. For (relatively weak) spin-orbit coupling intensity $μ$, we obtain that the characteristic length $Λ_s$ for spin-polarization decay behaves as $Λ_s \propto μ^{-2}$.

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arXiv2015

Dynamics of driven flow with exclusion in graphene-like structures

We present a mean-field theory for the dynamics of driven flow with exclusion in graphenelike structures, and numerically check its predictions. We treat first a specific combination of bond transmissivity rates, where mean field predicts, and numerics to a large extent confirms, that the sublattice structure characteristic of honeycomb networks becomes irrelevant. Dynamics, in the various regions of the phase diagram set by open boundary injection and ejection rates, is then in general identical to that of one-dimensional systems, although some discrepancies remain between mean-field theory and numerical results, in similar ways for both geometries. However, at the critical point for which the characteristic exponent is z = 3/2 in one dimension, the mean-field value z = 2 is approached for very large systems with constant (finite) aspect ratio. We also treat a second combination of bond (and boundary) rates where, more typically, sublattice distinction persists. For the two rate combinations, in continuum or late-time limits, respectively, the coupled sets of mean-field dynamical equations become tractable with various techniques and give a two-band spectrum, gapless in the critical phase. While for the second rate combination quantitative discrepancies between mean-field theory and simulations increase for most properties and boundary rates investigated, theory still is qualitatively correct in general, and gives a fairly good quantitative account of features such as the late-time evolution of density profile differences from their steady-state values.

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arXiv2013

Driven flow with exclusion and transport in graphene-like structures

The totally asymmetric simple exclusion process (TASEP), a well-known model in its strictly one-dimensional (chain) version, is generalized to cylinder (nanotube) and ribbon (nanoribbon) geometries. A mean-field theoretical description is given for very narrow ribbons ("necklaces"), and nanotubes. For specific configurations of bond transmissivity rates, and for a variety of boundary conditions, theory predicts equivalent steady state behavior between (sublattices on) these structures and chains. This is verified by numerical simulations, to excellent accuracy, by evaluating steady-state currents. We also numerically treat ribbons of general width. We examine the adequacy of this model to the description of electronic transport in carbon nanotubes and nanoribbons, or specifically-designed quantum dot arrays.

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arXiv2013

Critical line of honeycomb-lattice anisotropic Ising antiferromagnets in a field

We use numerical transfer-matrix methods, together with finite-size scaling and conformal invariance concepts, to discuss critical properties of two-dimensional honeycomb-lattice Ising spin-1/2 magnets, with couplings which are antiferromagnetic along at least one lattice axis, in a uniform external field. We focus mainly on the shape of the phase diagram in field-temperature parameter space; in order to do so, both the order and universality class of the underlying phase transition are examined. Our results indicate that, in one particular case studied, the critical line has a horizontal section (i.e. at constant field) of finite length, starting at the zero-temperature end of the phase boundary. Other than that, we find no evidence of unusual behavior, at variance with the reentrant features predicted in earlier studies.

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arXiv2012

Current-activity versus local-current fluctuations in driven flow with exclusion

We consider fluctuations of steady-state current activity, and of its dynamic counterpart, the local current, for the one-dimensional totally asymmetric simple exclusion process. The cumulants of the integrated activity behave similarly to those of the local current, except that they do not capture the anomalous scaling behavior in the maximal-current phase and at its boundaries. This indicates that the systemwide sampling at equal times, characteristic of the instantaneous activity, overshadows the subtler effects which come about from non-equal time correlations, and are responsible for anomalous scaling. We show that apparently conflicting results concerning asymmetry (skewness) of the corresponding distributions can in fact be reconciled, and that (apart from a few well-understood exceptional cases) for both activity and local current one has positive skew deep within the low-current phase, and negative skew everywhere else.

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arXiv2012

Statistics of current activity fluctuations in asymmetric flow with exclusion

We consider steady-state current activity statistics for the one-dimensional totally asymmetric simple exclusion process (TASEP). With the help of the known operator algebra (for general open boundary conditions), as well as general probabilistic concepts (for the periodic case), we derive and evaluate closed-form expressions for the lowest three moments of the probability distribution function. These are confirmed, to excellent degree of accuracy, by numerical simulations. Further exact expressions and asymptotic approximations are provided for probability distributions and generating functions.

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arXiv2011

Scaling behavior of a square-lattice Ising model with competing interactions in a uniform field

Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor interactions, both antiferromagnetic, in a uniform external field. On the critical curve separating collinearly-ordered and paramagnetic phases, our estimates of the conformal anomaly $c$ are very close to unity, indicating the presence of continuously-varying exponents. This is confirmed by direct calculations, which also lend support to a weak-universality picture; however, small but consistent deviations from the Ising-like values $η=1/4$, $γ/ν=7/4$, $β/ν=1/8$ are found. For higher fields, on the line separating row-shifted $(2 \times 2)$ and disordered phases, we find values of the exponent $η$ very close to zero.

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arXiv2011

Universal and non-universal amplitude ratios for scaling corrections on Ising strips

We consider strips of Ising spins at criticality. For strips of width $N$ sites, subdominant (additive) finite-size corrections to scaling are assumed to be of the form $a_k/N^k$ for the free energy, and $b_k/N^k$ for inverse correlation length, with integer values of $k$. We investigate the set $\{a_k,b_k\}$ ($k \geq 2$) by exact evaluation and numerical transfer-matrix diagonalization techniques, and their changes upon varying anisotropy of couplings, spin quantum number $S$, and (finite) interaction range, in all cases for both periodic (PBC) and free (FBC) boundary conditions across the strip. We find that the coefficient ratios $b_k/a_k$ remain constant upon varying coupling anisotropy for $S=1/2$ and first-neighbor couplings, for both PBC and FBC (albeit at distinct values in either case). Such universal behavior is not maintained upon changes in $S$ or interaction range.

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arXiv2011

Smoothly-varying hopping rates in driven flow with exclusion

We consider the one-dimensional totally asymmetric simple exclusion process (TASEP) with position-dependent hopping rates. The problem is solved,in a mean field/adiabatic approximation, for a general (smooth) form of spatial rate variation. Numerical simulations of systems with hopping rates varying linearly against position (constant rate gradient), for both periodic and open boundary conditions, provide detailed confirmation of theoretical predictions, concerning steady-state average density profiles and currents, as well as open-system phase boundaries, to excellent numerical accuracy.

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arXiv2010

Finite-size scaling behavior in trapped systems

Numerical transfer-matrix methods are applied to two-dimensional Ising spin systems, in presence of a confining magnetic field which varies with distance $|{\vec x}|$ to a "trap center", proportionally to $(|{\vec x}|/\ell)^p$, $p>0$. On a strip geometry, the competition between the "trap size" $\ell$ and the strip width, $L$, is analysed in the context of a generalized finite-size scaling {\em ansatz}. In the low-field regime $\ell \gg L$, we use conformal-invariance concepts in conjunction with a linear-response approach to derive the appropriate ($p$-dependent) limit of the theory, which agrees very well with numerical results for magnetization profiles. For high fields $\ell \lesssim L$, correlation-length scaling data broadly confirms an existing picture of $p$-dependent characteristic exponents. Standard spin-1/2 and spin-1 Ising systems are considered, as well as the Blume-Capel model.

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arXiv2009

Field-driven transition in an Ising magnet with mixed interactions

Transfer-matrix methods are used, in conjunction with finite-size scaling and conformal invariance concepts, to generate an accurate phase diagram for a two-dimensional square-lattice Ising spin-1/2 magnet, with couplings which are positive along one coordinate axis, and negative along the other, in a uniform external field. Our results indicate that the critical line starts horizontally at the zero-temperature end of the phase boundary, at variance with the reentrant behavior predicted in some earlier studies. Estimates of the thermal scaling exponent are very close to the Ising value $y_T=1$ along the critical line, except near T=0 where strong crossover effects prevent a reliable analysis.

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arXiv2009

On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses

We use transfer-matrix and finite-size scaling methods to investigate the location and properties of the multicritical point of two-dimensional Ising spin glasses on square, triangular and honeycomb lattices, with both binary and Gaussian disorder distributions. For square and triangular lattices with binary disorder, the estimated position of the multicritical point is in numerical agreement with recent conjectures regarding its exact location. For the remaining four cases, our results indicate disagreement with the respective versions of the conjecture, though by very small amounts, never exceeding 0.2%. Our results for: (i) the correlation-length exponent $ν$ governing the ferro-paramagnetic transition; (ii) the critical domain-wall energy amplitude $η$; (iii) the conformal anomaly $c$; (iv) the finite-size susceptibility exponent $γ/ν$; and (v) the set of multifractal exponents $\{η_k \}$ associated to the moments of the probability distribution of spin-spin correlation functions at the multicritical point, are consistent with universality as regards lattice structure and disorder distribution, and in good agreement with existing estimates.

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arXiv2008

Non-equilibrium processes: driven lattice gases, interface dynamics, and quenched disorder effects on density profiles and currents

Properties of the one-dimensional totally asymmetric simple exclusion process (TASEP), and their connection with the dynamical scaling of moving interfaces described by a Kardar-Parisi-Zhang (KPZ) equation are investigated. With periodic boundary conditions, scaling of interface widths (the latter defined via a discrete occupation-number-to-height mapping), gives the exponents $α=0.500(5)$, $z=1.52(3)$, $β=0.33(1)$. With open boundaries, results are as follows: (i) in the maximal-current phase, the exponents are the same as for the periodic case, and in agreement with recent Bethe ansatz results; (ii) in the low-density phase, curve collapse can be found to a rather good extent, with $α=0.497(3)$, $z=1.20(5)$, $β=0.41(2)$, which is apparently at variance with the Bethe ansatz prediction $z=0$; (iii) on the coexistence line between low- and high- density phases, $α=0.99(1)$, $z=2.10(5)$, $β=0.47(2)$, in relatively good agreement with the Bethe ansatz prediction $z=2$. From a mean-field continuum formulation, a characteristic relaxation time, related to kinematic-wave propagation and having an effective exponent $z^\prime=1$, is shown to be the limiting slow process for the low density phase, which accounts for the above-mentioned discrepancy with Bethe ansatz results. For TASEP with quenched bond disorder, interface width scaling gives $α=1.05(5)$, $z=1.7(1)$, $β=0.62(7)$. From a direct analytic approach to steady-state properties of TASEP with quenched disorder, closed-form expressions for the piecewise shape of averaged density profiles are given, as well as rather restrictive bounds on currents. All these are substantiated in numerical simulations.

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