117,602 research outputs found
Aging properties of the voter model with long-range interactions
No full textWe investigate the aging properties of the one-dimensional voter model with long-range interactions in its ordering kinetics. In this system, an agent, S-i = +/- 1, positioned at a lattice vertex i, copies the state of another one located at a distance r, selected randomly with a probability P(r) proportional to r(-alpha). Employing both analytical and numerical methods, we compute the two-time correlation function G (r; t, s) (t >= s) between the state of a variable S-i at time s and that of another one, at distance r, at time t. At time t, the memory of an agent of its former state at time s, expressed by the autocorrelation function A(t, s) = G(r = 0; t, s), decays algebraically for alpha > 1 as [L(t)/L(s)](-lambda), where Lis a time-increasing coherence length and lambda is the Fisher-Huse exponent. We find lambda = 1 for alpha > 2, and lambda = 1/(alpha - 1) for 1 < alpha <= 2 . For alpha <= 1, instead, there is an exponential decay, as in the mean field. Then, in contrast with what is known for the related Ising model, here we find that lambda increases upon decreasing alpha. The space-dependent correlation G (r; t, s) obeys a scaling symmetry G (r; t, s) = g [r/L(s); L(t)/L(s)] for alpha > 2. Similarly, for 1 < alpha <= 2, one has G (r; t, s) = g [r/L(t); L(t)/L(s)], where the length L regulating two-time correlations now differs from the coherence length as L proportional to L-delta, with delta = 1 + 2 (2 - alpha)
Remarks on SUq (2) fermions
No full textIn this paper, we show that several applications of SUq(2) fermions to statistical mechanics and quantum field theory, previously discussed in literature, are based on a wrong statement about the connection between deformed and undeformed fermion operators. Then we exclude various classes of ansatz and we put some constraints about the form of such relation
Coarsening and metastability of the long-range voter model in three dimensions
No full textWe study analytically the ordering kinetics and the final metastable states in the three-dimensional long-range voter model where N agents described by a boolean spin variable S-i can be found in two states (or opinion) +/- 1. The kinetics is such that each agent copies the opinion of another at distance r chosen with probability P(r) proportional to r(-alpha) (a > 0). In the thermodynamic limit N ->infinity the system approaches a correlated metastable state without consensus, namely without full spin alignment. In such states the equal-time correlation function C(r) = < SiSj > (where r is the i-j distance) decrease algebraically in a slow, non-integrable way. Specifically, we find C(r) similar to r(-1), or C(r)similar to r(6-a), or C(r)similar to r(-a) for a >5, 3< a <= 5 and 0 <= <= a <= 3, respectively. In a finite system metastability is escaped after a time of order N and full ordering is eventually achieved. The dynamics leading to metastability is of the coarsening type, with an ever increasing correlation length L(t) (for N ->infinity). We find L(t)similar to t1/2 for a <= 5 L(t)similar to t5{2\al}}4<\al \le 53\le \al \le 40\le \al < 3$ there is not macroscopic coarsening because stationarity is reached in a microscopic time. Such results allow us to conjecture the behavior of the model for generic space dimension
Quantum black holes as classical space factories
No full textSpace and matter may both be manifestations of a single fundamental quantum dynamics, as it may become evident during black-hole evaporation. Inspired by the fact that quantum electrodynamics underlies the classical theory of elasticity, that in turn has a natural and well-known geometric description in terms of curvature and torsion, related to topological defects, here we move some necessary steps to find the map from such fundamental quantum level to the emergent level of classical space and quantum matter. We proceed by adapting the boson transformation method of standard quantum field theory to the quantum gravity fundamental scenario and successfully obtain the emergence of curvature and torsion, our main focus here. In doing so, we have been able to overcome difficult issues of interpretation, related to the Goldstone modes for rotational symmetry. In fact, we have been able to apply the boson transformation method to disclinations, to relate them to the spin structure and to give an heuristic derivation of the matter field equation on curved space. We also improve results of previous work on the emergence of geometric tensors from elasticity theory, as the non-Abelian contributions to the torsion and curvature tensors, postulated in those papers, here emerge naturally. More work is necessary to identify the type of gravity theories one can obtain in this way
General properties of the response function in a class of solvable non-equilibrium models
No full textWe study the non-equilibrium response function R i j ( t , t ′ ) , namely the variation of the local magnetization ⟨ S i ( t ) ⟩ on site i at time t as an effect of a perturbation applied at the earlier time t′ on site j, in a class of solvable spin models characterized by the vanishing of the so-called asymmetry. This class encompasses both systems brought out of equilibrium by the variation of a thermodynamic control parameter, as after a temperature quench, or intrinsically out of equilibrium models with violation of detailed balance. The one-dimensional Ising model and the voter model (on an arbitrary graph) are prototypical examples of these two situations which are used here as guiding examples. Defining the fluctuation-dissipation ratio X i j ( t , t ′ ) = β R i j / ( ∂ G i j / ∂ t ′ ) , where G i j ( t , t ′ ) = ⟨ S i ( t ) S j ( t ′ ) ⟩ is the spin-spin correlation function and β is a parameter regulating the strength of the perturbation (corresponding to the inverse temperature when detailed balance holds), we show that, in the quite general case of a kinetics obeying dynamical scaling, on equal sites this quantity has a universal form X i i ( t , t ′ ) = ( t + t ′ ) / ( 2 t ) , whereas lim t → ∞ X i j ( t , t ′ ) = 1 / 2 for any ij couple. The specific case of voter models with long-range interactions is thoroughly discussed
Neutrino Mixing and Oscillations in Quantum Field Theory: A Comprehensive Introduction
No full textWe review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits giving a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula, which in the relativistic limit reproduces the Pontecorvo oscillation formula and illustrates some of the contradictions arising in the quantum mechanics approximation. We show that the gauge theory structure underlies the neutrino mixing phenomenon and that there exists entanglement between mixed neutrinos. The flavor vacuum is found to be an entangled generalized coherent state of SU(2). We also discuss flavor energy uncertainty relations, which impose a lower bound on the precision of neutrino energy measurements, and we show that the flavor vacuum inescapably emerges in certain classes of models with dynamical symmetry breaking
Quantum black holes, partition of integers and self-similarity
No full textIn this paper, we take the view that the area of a black hole's event horizon is quantized, A = l(P)(2)(4 ln 2)N, and the associated degrees of freedom are finite in number and of fermionic nature. We then investigate general aspects of the entropy, S-BH, our main focus being black hole self-similarity. We first find a two-to-one map between the black hole's configurations and the ordered partitions of the integer N. Hence, we construct from there a composition law between the subparts making the whole configuration space. This gives meaning to black hole self-similarity, entirely within a single description, as a phenomenon stemming from the well-known self-similarity of the ordered partitions of N. Finally, we compare the above to the well-known results on the subleading (quantum) corrections, which necessarily require different (quantum) statistical weights for the various configurations
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