arXiv subjects
Publications and source records attributed to M. A. Santos.
The symplectic projector method is applied to derive the local physical degrees of freedom of a particle moving freely on an arbitrary surface. The dependence of the projector on the coordinates and momenta of the particle is discussed.
The analogue of temporal coherence resonance for spatial degrees of freedom is reported. Specifically, we show that spatiotemporal noise is able to optimally extract an intrinsic spatial scale in nonlinear media close to (but before) a pattern-forming instability. This effect is observed in a model of pattern-forming chemical reaction and in the Swift-Hohenberg model of fluid convection. In the latter case, the phenomenon is described analytically via an approximate approach.
Paper Withdrawn. Some aspects of the RG calculation have to be reconsidered. It will be rewritten.
The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework.
The Symplectic Projector Method is applied to discuss quantisation aspects of an extended Abelian model with a pair of gauge potentials coupled by means of a mixed Chern-Simons term. We focuss on a field content that spans an N=2-D=3 supersymmetric theory whenever scalar and fermionic matter is suitably coupled to the family of gauge potentials.
In this paper we apply the Symplectic Projectors Method to gauge theories with second class constraints in various space-time dimensions. The conclusion is that this method is equivalent to the standard quantization methods. Although it suffers from some limitations since its applicability is restricted to some simpler situation when one is not interested in full information provided by the BRST, our analysis shows that it is worthwhile to investigate this method further. Relevant reference for this thesis are hep-th/0005214, hep-th/0104154 and hep-th/0108197.
We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths ($D$). We found that $N>2$ cluster mean-field approximations must be considered to get consistent singular behavior. The $N=3,4$ approximations result in a continuous phase transition belonging to a single universality class along the $D\in (0,1)$ phase transition line. Large scale simulations of the particle density confirmed mean-field scaling behavior with logarithmic corrections. This is interpreted as numerical evidence supporting that the upper critical dimension in this model is $d_c=2$.The pair density scales in a similar way but with an additional logarithmic factor to the order parameter. At the D=0 endpoint of the transition line we found DP criticality.
Steady state properties in the absorbing phase of the $1d$ pair contact process (PCP) model are investigated. It is shown that, in typical absorbing states (reached by the system's dynamic rules), the density of isolated particles, $ρ_1$, approaches a stationary value which depends on the annihilation probability ($p$); the deviation from its 'natural' value at criticality, $ρ_1^{nat}$, follows a power law: $ρ_1^{nat}-ρ_1 \sim (p-p_c)^{β_1}$ for $p>p_c$. Monte Carlo simulations yield $β_1=0.81$. A cluster approximation is developed for this model, qualitatively confirming the numerical results and predicting $β_1=1$. The singular behavior of the isolated particles density in the inactive phase is explained using a phenomenological approach.
The basic arguments underlying the symplectic projector method are presented. By this method, local free coordinates on the constrait surface can be obtained for a broader class of constrained systems. Some interesting examples are analyzed.
The boundary conditions of the bosonic string theory in non-zero $B$-field background are equivalent to the second class constraints of a discretized version of the theory. By projecting the original canonical coordinates onto the constraint surface we derive a set of coordinates of string that are unconstrained.These coordinates represent a natural framework for the quantization of the theory.
The evolution of domain structure is investigated in a two-dimensional voter model with three states under cyclic dominance. The study focus on the dynamics of vortices, defined by the points where three states (domains) meet. We can distinguish vortices and antivortices which walk randomly and annihilate each other. The domain wall motion can create vortex-antivortex pairs at a rate which is increased by the spiral formation due to the cyclic dominance. This mechanism is contrasted with a branching annihilating random walk (BARW) in a particle antiparticle system with density dependent pair creation rate. Numerical estimates for the critical indices of the vortex density ($β=0.29(4)$) and of its fluctuation ($γ=0.34(6)$) improve an earlier Monte Carlo study [Tainaka and Itoh, Europhys. Lett. 15, 399 (1991)] of the three-state cyclic voter model in two dimensions.
We have investigated the effect of the initial condition on the spreading exponents of the one-dimensional pair contact process (PCP) and threshold transfer process (TTP).The non-order field was found to exhibit critical fluctuations, relaxing to its natural value with the same power-law as the order parameter field. We argue that this slow relaxation, which was not taken into account in earlier studies of these models, is responsible for the continuously changing survival probability exponent. High precision numerical simulations show evidence of a(slight) dependence of the location of the transition point on the initial concentration, in the case of PCP. The damage spreading (DS) point and the spreading exponents coincide with those of the ordinary critical point in both cases.
Short time Monte Carlo methods are used to study the nonequilibrium ferromagnetic phase transition in a majority vote model in two dimensions. The existance of an initial critical slip regime is verified. The measured values of dyamic exponents $z=2.170(5)$ and $θ= 0.191(2)$ are in excellent agreement with those of the kinetic Ising model universality class.