Extending canonical Monte Carlo methods II

Previously, we have presented a methodology to extend canonical Monte Carlo methods inspired on a suitable extension of the canonical fluctuation relation $C=\beta^{2}$ compatible with negative heat capacities $C<0$. Now, we improve this methodology by introducing a better treatment of finite size effects affecting the precision of a direct determination of the microcanonical caloric curve $\beta (E) =\partial S(E) /\partial E$, as well as a better implementation of MC schemes. We shall show that despite the modifications considered, the extended canonical MC methods possibility an impressive overcome of the so-called \textit{super-critical slowing down} observed close to the region of a temperature driven first-order phase transition. In this case, the dependence of the decorrelation time $\tau$ with the system size $N$ is reduced from an exponential growth to a weak power-law behavior $\tau(N)\propto N^{\alpha}$, which is shown in the particular case of the 2D seven-state Potts model where the exponent $\alpha=0.14-0.18$.Comment: Version submitted to JSTA

Equilibrium fluctuation theorems compatible with anomalous response

Previously, we have derived a generalization of the canonical fluctuation relation between heat capacity and energy fluctuations $C=\beta^{2}<\delta U^{2}>$, which is able to describe the existence of macrostates with negative heat capacities $C<0$. In this work, we extend our previous results for an equilibrium situation with several control parameters to account for the existence of states with anomalous values in other response functions. Our analysis leads to the derivation of three different equilibrium fluctuation theorems: the \textit{fundamental and the complementary fluctuation theorems}, which represent the generalization of two fluctuation identities already obtained in previous works, and the \textit{associated fluctuation theorem}, a result that has no counterpart in the framework of Boltzmann-Gibbs distributions. These results are applied to study the anomalous susceptibility of a ferromagnetic system, in particular, the case of 2D Ising model.Comment: Extended version of the paper published in JSTA

Understanding critical behavior in the framework of the extended equilibrium fluctuation theorem

Recently (arXiv:0910.2870), we have derived a fluctuation theorem for systems in thermodynamic equilibrium compatible with anomalous response functions, e.g. the existence of states with \textit{negative heat capacities} $C<0$. In this work, we show that the present approach of the fluctuation theory introduces new insights in the understanding of \textit{critical phenomena}. Specifically, the new theorem predicts that the environmental influence can radically affect critical behavior of systems, e.g. to provoke a suppression of the divergence of correlation length $\xi$ and some of its associated phenomena as spontaneous symmetry breaking. Our analysis reveals that while response functions and state equations are \emph{intrinsic properties} for a given system, critical behaviors are always \emph{relative phenomena}, that is, their existence crucially depend on the underlying environmental influence

Geometrical aspects and connections of the energy-temperature fluctuation relation

Recently, we have derived a generalization of the known canonical fluctuation relation $k_{B}C=\beta^{2}$ between heat capacity $C$ and energy fluctuations, which can account for the existence of macrostates with negative heat capacities $C<0$. In this work, we presented a panoramic overview of direct implications and connections of this fluctuation theorem with other developments of statistical mechanics, such as the extension of canonical Monte Carlo methods, the geometric formulations of fluctuation theory and the relevance of a geometric extension of the Gibbs canonical ensemble that has been recently proposed in the literature.Comment: Version accepted for publication in J. Phys. A: Math and The

Fluctuation geometry: A counterpart approach of inference geometry

Starting from an axiomatic perspective, \emph{fluctuation geometry} is developed as a counterpart approach of inference geometry. This approach is inspired on the existence of a notable analogy between the general theorems of \emph{inference theory} and the the \emph{general fluctuation theorems} associated with a parametric family of distribution functions $dp(I|\theta)=\rho(I|\theta)dI$, which describes the behavior of a set of \emph{continuous stochastic variables} driven by a set of control parameters $\theta$. In this approach, statistical properties are rephrased as purely geometric notions derived from the \emph{Riemannian structure} on the manifold $\mathcal{M}_{\theta}$ of stochastic variables $I$. Consequently, this theory arises as an alternative framework for applying the powerful methods of differential geometry for the statistical analysis. Fluctuation geometry has direct implications on statistics and physics. This geometric approach inspires a Riemannian reformulation of Einstein fluctuation theory as well as a geometric redefinition of the information entropy for a continuous distribution.Comment: Version submitted to J. Phys. A. 26 pages + 2 eps figure

Photo-ionization of planetary winds: case study HD209458b

Close-in hot Jupiters are exposed to a tremendous photon flux that ionizes the neutral escaping material from the planet leaving an observable imprint that makes them an interesting laboratory for testing theoretical models. In this work we present 3D hydrodynamic simulations with radiation transfer calculations of a close-in exoplanet in a blow-off state. We calculate the Ly-$\alpha$ absorption and compare it with observations of HD 209458b an previous simplified model results.Our results show that the hydrodynamic interaction together with a proper calculation of the photoionization proccess are able to reproduce the main features of the observed Ly-$\alpha$ absorption, in particular at the blue-shifted wings of the line. We found that the ionizing stellar flux produce an almost linear effect on the amount of absorption in the wake. Varying the planetary mass loss rate and the radiation flux, we were able to reproduce the $10\%$ absorption observed at $-100~\mathrm{km~s^{-1}}$.Comment: 9 pages, 6 figure

Constraining the History of the Sagittarius Dwarf Galaxy Using Observations of its Tidal Debris

We present a comparison of semi-analytic models of the phase-space structure of tidal debris with observations of stars associated with the Sagittarius dwarf galaxy (Sgr). We find that many features in the data can be explained by these models. The properties of stars 10-15 degrees away from the center of Sgr --- in particular, the orientation of material perpendicular to Sgr's orbit (c.f. Alard 1996) and the kink in the velocity gradient (Ibata et al 1997) --- are consistent with those expected for unbound material stripped during the most recent pericentric passage ~50 Myrs ago. The break in the slope of the surface density seen by Mateo, Olszewski & Morrison (1998) at ~ b=-35 can be understood as marking the end of this material. However, the detections beyond this point are unlikely to represent debris in a trailing streamer, torn from Sgr during the immediately preceding passage ~0.7 Gyrs ago, but are more plausibly explained by a leading streamer of material that was lost more that 1 Gyr ago and has wrapped all the way around the Galaxy. The observations reported in Majewski et al (1999) also support this hypothesis. We determine debris models with these properties on orbits that are consistent with the currently known positions and velocities of Sgr in Galactic potentials with halo components that have circular velocities v_circ=140-200 km/s. The best match to the data is obtained in models where Sgr currently has a mass of ~10^9 M_sun and has orbited the Galaxy for at least the last 1 Gyr, during which time it has reduced its mass by a factor of 2-3, or luminosity by an amount equivalent to ~10% of the total luminosity of the Galactic halo. These numbers suggest that Sgr is rapidly disrupting and unlikely to survive beyond a few more pericentric passages.Comment: 19 pages, 5 figures, accepted to Astronomical Journa

Gradual transition from insulator to semimetal of Ca1−x_{1-x}Eux_{x}B6_{6} with increasing Eu concentration

The local environment of Eu$^{2+}$ ($4f^{7}$, $S=7/2$) in Ca$_{1-x}$Eu$_{x}$B$_{6}$ ($0.003\leqslant x\leqslant 1.00$) is investigated by means of electron spin resonance (ESR). For $x\lesssim 0.003$ the spectra show resolved \textit{fine} and \textit{hyperfine} structures due to the cubic crystal \textit{electric} field and nuclear \textit{hyperfine} field, respectively. The resonances have Lorentzian line shape, indicating an \textit{insulating} environment for the Eu$^{2+}$ ions. For $0.003\lesssim x\lesssim 0.07$, as $x$ increases, the ESR lines broaden due to local distortions caused by the Eu/Ca ions substitution. For $0.07\lesssim x\lesssim 0.30$, the lines broaden further and the spectra gradually change from Lorentzian to Dysonian resonances, suggesting a coexistence of both \textit{insulating} and \textit{metallic} environments for the Eu$^{2+}$ ions. In contrast to Ca$_{1-x}$Gd$_{x}$B$_{6}$, the \textit{fine} structure is still observable up to $x\approx 0.15$. For $x\gtrsim 0.30$ the \textit{fine} and \textit{hyperfine} structures are no longer observed, the line width increases, and the line shape is purely Dysonian anticipating the \textit{semimetallic} character of EuB$_{6}$. This broadening is attributed to a spin-flip scattering relaxation process due to the exchange interaction between conduction and Eu$^{2+}$ $4f$ electrons. High field ESR measurements for $x\gtrsim 0.15$ reveal smaller and anisotropic line widths, which are attributed to magnetic polarons and Fermi surface effects, respectively.Comment: Submitted to PR

Thermodynamic fluctuation relation for temperature and energy

The present work extends the well-known thermodynamic relation $C=\beta ^{2}< \delta {E^{2}}>$ for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest and a generalized thermostat, which we define in the course of the paper. The resulting identity $=1+< \delta {E^{2}}> \partial ^{2}S(E) /\partial {E^{2}}$ can account for thermodynamic states with a negative heat capacity $C<0$; at the same time, it represents a thermodynamic fluctuation relation that imposes some restrictions on the determination of the microcanonical caloric curve $\beta (E) =\partial S(E) /\partial E$. Finally, we comment briefly on the implications of the present result for the development of new Monte Carlo methods and an apparent analogy with quantum mechanics.Comment: Version accepted for publication in J. Phys. A: Math and The

Tracing Galaxy Formation with Stellar Halos I: Methods

If the favored hierarchical cosmological model is correct, then the Milky Way system should have accreted ~100-200 luminous satellite galaxies in the past \~12 Gyr. We model this process using a hybrid semi-analytic plus N-body approach which distinguishes explicitly between the evolution of light and dark matter in accreted satellites. This distinction is essential to our ability to produce a realistic stellar halo, with mass and density profile much like that of our own Galaxy, and a surviving satellite population that matches the observed number counts and structural parameter distributions of the satellite galaxies of the Milky Way. Our model stellar halos have density profiles which typically drop off with radius faster than those of the dark matter. They are assembled from the inside out, with the majority of mass (~80%) coming from the \~15 most massive accretion events. The satellites that contribute to the stellar halo have median accretion times of ~9 Gyr in the past, while surviving satellite systems have median accretion times of ~5 Gyr in the past. This implies that stars associated with the inner halo should be quite different chemically from stars in surviving satellites and also from stars in the outer halo or those liberated in recent disruption events. We briefly discuss the expected spatial structure and phase space structure for halos formed in this manner. Searches for this type of structure offer a direct test of whether cosmology is indeed hierarchical on small scales.Comment: 22 pages, 16 figures, submitted to Ap