arXiv subjects

Stefan Hilbert

Publications and source records attributed to Stefan Hilbert.

60 records · Page 4Linked to original sources

arXiv2009

Nonlocal observables and lightcone-averaging in relativistic thermodynamics

The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred class of hyperplanes in spacetime. (ii) There exist different, seemingly equally plausible ways of defining heat and work in relativistic systems. These ambiguities led, for example, to various proposals for the Lorentz transformation law of temperature. Traditional 'isochronous' formulations of relativistic thermodynamics are neither theoretically satisfactory nor experimentally feasible. Here, we demonstrate how these deficiencies can be resolved by defining thermodynamic quantities with respect to the backward-lightcone of an observation event. This approach yields novel, testable predictions and allows for a straightforward-extension of thermodynamics to General Relativity. Our theoretical considerations are illustrated through three-dimensional relativistic many-body simulations.

cond-mat.stat-mech↗

arXiv2008

Strong lensing optical depths in a LCDM universe II: the influence of the stellar mass in galaxies

We investigate how strong gravitational lensing in the concordance LCDM cosmology is affected by the stellar mass in galaxies. We extend our previous studies, based on ray-tracing through the Millennium Simulation, by including the stellar components predicted by galaxy formation models. We find that the inclusion of these components greatly enhances the probability for strong lensing compared to a `dark matter only' universe. The identification of the `lenses' associated with strong-lensing events reveals that the stellar mass of galaxies (i) significantly enhances the strong-lensing cross-sections of group and cluster halos, and (ii) gives rise to strong lensing in smaller halos, which would not produce noticeable effects in the absence of the stars. Even if we consider only image splittings >10 arcsec, the luminous matter can enhance the strong-lensing optical depths by up to a factor of 2.

astro-ph↗

arXiv2008

Imaging the Cosmic Matter Distribution using Gravitational Lensing of Pregalactic HI

21-cm emission from neutral hydrogen during and before the epoch of cosmic reionisation is gravitationally lensed by material at all lower redshifts. Low-frequency radio observations of this emission can be used to reconstruct the projected mass distribution of foreground material, both light and dark. We compare the potential imaging capabilities of such 21-cm lensing with those of future galaxy lensing surveys. We use the Millennium Simulation to simulate large-area maps of the lensing convergence with the noise, resolution and redshift-weighting achievable with a variety of idealised observation programmes. We find that the signal-to-noise of 21-cm lens maps can far exceed that of any map made using galaxy lensing. If the irreducible noise limit can be reached with a sufficiently large radio telescope, the projected convergence map provides a high-fidelity image of the true matter distribution, allowing the dark matter halos of individual galaxies to be viewed directly, and giving a wealth of statistical and morphological information about the relative distributions of mass and light. For instrumental designs like that planned for the Square Kilometer Array (SKA), high-fidelity mass imaging may be possible near the resolution limit of the core array of the telescope.

astro-ph↗

arXiv2007

Strong lensing optical depths in a \LambdaCDM universe

We investigate strong gravitational lensing in the concordance $Λ$CDM cosmology by carrying out ray-tracing along past light cones through the Millennium Simulation, the largest simulation of cosmic structure formation ever carried out. We extend previous ray-tracing methods in order to take full advantage of the large volume and the excellent spatial and mass resolution of the simulation. As a function of source redshift we evaluate the probability that an image will be highly magnified, will be highly elongated or will be one of a set of multiple images. We show that such strong lensing events can almost always be traced to a single dominant lensing object and we study the mass and redshift distribution of these primary lenses. We fit analytic models to the simulated dark halos in order to study how our optical depth measurements are affected by the limited resolution of the simulation and of the lensing planes that we construct from it. We conclude that such effects lead us to underestimate total strong-lensing cross sections by about 15 percent. This is smaller than the effects expected from our neglect of the baryonic components of galaxies. Finally we investigate whether strong lensing is enhanced by material in front of or behind the primary lens. Although strong lensing lines-of-sight are indeed biased towards higher than average mean densities, this additional matter typically contributes only a few percent of the total surface density.

astro-ph↗

arXiv2006

Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation

We calculate exactly both the microcanonical and canonical thermodynamic functions (TDFs) for a one-dimensional model system with piecewise constant Lennard-Jones type pair interactions. In the case of an isolated $N$-particle system, the microcanonical TDFs exhibit (N-1) singular (non-analytic) microscopic phase transitions of the formal order N/2, separating N energetically different evaporation (dissociation) states. In a suitably designed evaporation experiment, these types of phase transitions should manifest themselves in the form of pressure and temperature oscillations, indicating cooling by evaporation. In the presence of a heat bath (thermostat), such oscillations are absent, but the canonical heat capacity shows a characteristic peak, indicating the temperature-induced dissociation of the one-dimensional chain. The distribution of complex zeros (DOZ) of the canonical partition may be used to identify different degrees of dissociation in the canonical ensemble.

cond-mat.stat-mech↗

arXiv2006

Phase Transitions in Small Systems: Microcanonical vs. Canonical Ensembles

We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and interacting via Lennard-Jones-type pair potentials. By means of these simple examples it can be shown already that the microcanonical thermodynamic functions of a small system may exhibit rich oscillatory behavior and, in particular, singularities (non-analyticities) separating different microscopic phases. These microscopic phases may be identified as different microphysical dissociation states of the small system. The microscopic oscillations of microcanonical thermodynamic quantities (e.g. temperature, heat capacity, or pressure) should in principle be observable in suitably designed evaporation/dissociation experiments (which must realize the physical preconditions of the microcanonical ensemble). By contrast, singular phase transitions cannot occur, if a small system is embedded into an infinite heat bath (thermostat), corresponding to the canonical ensemble. For the simple model systems under consideration, it is nevertheless possible to identify a smooth canonical phase transition by studying the distribution of complex zeros of the canonical partition function.

cond-mat.stat-mech↗