On the Adiabatic Expansion of the Visible Space in a Higher-Dimensional Cosmology

In the context of higher-dimensional cosmologies, with isotropic visible and internal space and multi-perfect fluid matter, we study the conditions under which adiabatic expansion of the visible external space is possible, when a time-dependent internal space is present. The analysis is based on a reinterpretation of the four-dimensional stress-energy tensor in the presence of the extra dimensions. This modifies the usual adiabatic energy conservation laws for the visible universe, leading to a new type of cosmological evolution which includes large-scale entropy production in four dimensions.     

Effects of a decaying cosmological fluctuation

We present the initial conditions for a decaying cosmological perturbation and study its signatures in the cosmic microwave background anisotropies and matter power spectra. An adiabatic decaying mode in the presence of components that are not described as perfect fluids (such as collisionless matter) decays slower than in a perfect-fluid dominated Universe and displays super-Hubble oscillations. Wilkinson Microwave Anisotropy Probe first year data constrain the decaying to growing ratio of scale invariant adiabatic fluctuations at the matter-radiation equality to less than 10%.     

Adiabatic index of hot dense stellar matter

We calculate the adiabatic index of hot dense stellar matter taking into account the full nuclear interaction in all possible channels.     

Dust-acoustic solitary waves in an adiabatic hot dusty plasma

An adiabatic hot dusty plasma (containing non-inertial adiabatic electron and ion fluids, and negatively charged inertial adiabatic dust fluid) is considered. The basic properties of arbitrary amplitude dust-acoustic (DA) solitary waves, which exist in such an adiabatic hot dusty plasma, are explicitly examined by the pseudo-potential approach. To compare the basic properties (critical Mach number, amplitude and width) of the DA solitary waves observed in a dusty plasma containing adiabatic electron, ion and dust fluids with those observed in a dusty plasma containing isothermal electron and ion fluids and adiabatic dust fluid, it has been found that the adiabatic effect of inertia-less electron and ion fluids has significantly modified the basic properties of the DA solitary waves, and that on the basic properties of the DA solitary waves, the adiabatic effect of electron and ion fluids is much more significant than that of the dust fluid.     

Constructing physically valid fluid spheres in general relativity

We extend a method by Goldman to include conditions which are both necessary and sufficient for construction of physically acceptable relativistic fluid spheres. We thus give the conditions for having finite and non-negative pressure and finite and positive density inside the fluid sphere. We also give conditions for the pressure gradient and the density gradient to be negative and for the speed of sound to be less than the speed of light in vacuum. We further give the condition for the trace of the energy-momentum tensor to be positive and for the relativistic adiabatic index to be larger than 4/3. A model given by Goldman is examined, and we find that all these conditions are fulfilled. We further show that this model is stable. However, we also give a class ofnew exact solutions, and show that these models are physically valied. These models are also stable with respect to small radial disturbances. We calculated the total mass, the density and the physical radius for these fluid spheres. Some of these spheres turn out to be extremely compact. They can have a radius of only several centimeters, but typically contain the mass of a planet. We put these models forward as tentative exact solutions for spheres which could contain the hidden dark matter in the universe.     

Conformal anisotropic relativistic charged fluid spheres with a linear equation of state

We obtain two new families of compact solutions for a spherically symmetric distribution of matter consisting of an electrically charged anisotropic fluid sphere joined to the Reissner–Nordstrom static solution through a zero pressure surface. The static inner region also admits a one parameter group of conformal motions. First, to study the effect of the anisotropy in the sense of the pressures of the charged fluid, besides assuming a linear equation of state to hold for the fluid, we consider the tangential pressure p _⊥ to be proportional to the radial pressure p _r , the proportionality factor C measuring the grade of anisotropy. We analyze the resulting charge distribution and the features of the obtained family of solutions. These families of solutions reproduce for the value C=1, the conformal isotropic solution for quark stars, previously obtained by Mak and Harko. The second family of solutions is obtained assuming the electrical charge inside the sphere to be a known function of the radial coordinate. The allowed values of the parameters pertained to these solutions are constrained by the physical conditions imposed. We study the effect of anisotropy in the allowed compactness ratios and in the values of the charge. The Glazer’s pulsation equation for isotropic charged spheres is extended to the case of anisotropic and charged fluid spheres in order to study the behavior of the solutions under linear adiabatic radial oscillations. These solutions could model some stage of the evolution of strange quark matter fluid stars.     

Adiabatic Index in Shock‐Compressed Beryllium

We present a method to measure the adiabatic index of a material under shock compression by X‐ray Thomson Scattering. A beryllium target is symmetrically compressed by two counterpropagating shock waves that collide in the target center, producing super dense states of matter of up to 6 fold compression. We measure the density before and after the shock collision and solve the Hugoniot relations for colliding shocks to infer the adiabatic index. Our results indicate that the adiabatic index stays rather high even in the high compression regime. This agrees with a linear scaling model taken from the SESAME equation of state and shows that the adiabatic index becomes significantly different from the ratio of heat capacities in this strongly coupled plasma (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of singularities in general relativity

The problem of singularities for a non-symmetric and isentropic motion of a perfect fluid under the assumption of adiabatic thermodynamic processes is investigated from the standpoint of a local observer. It is shown that, whatever the distribution of matter might be, there occurred a singularity in the past in the non-rotating parts of the universe and it must occur again in the future if the universe is closed. It is further shown that the occurrence of a singularity in a rotating fluid seems inevitable, when the relativistic equation of state is considered, because of extremely high concentration of rest mass, though the possibility of its avoidance may not be ignored.     

Dynamical instability of shear-free collapsing star in extended teleparallel gravity

We study the spherically symmetric collapsing star in terms of dynamical instability. We take the framework of extended teleparallel gravity with a non-diagonal tetrad, a power-law form of the model presenting torsion and a matter distribution as a non-dissipative anisotropic fluid. The vanishing shear scalar condition is adopted to gain insight in a collapsing star. We apply a first order linear perturbation scheme to the metric, the matter, and f(T) functions. The dynamical equations are formulated under this perturbation scheme to develop collapsing equation for finding dynamical instability limits in two regimes, such as the Newtonian and the post-Newtonian regime. We obtain a constraint-free solution of a perturbed time dependent part with the help of a vanishing shear scalar. The adiabatic index exhibits the instability ranges through the second dynamical equation which depend on physical quantities such as the density, the pressure components, the perturbed parts of the symmetry of the star, etc. We also develop some constraints on the positivity of these quantities and obtain instability ranges to satisfy the dynamical instability condition.     

Structure and adiabatic compression of dark matter halos: Simple analytic model

An analytical model is considered for describing the inner regions of dark matter halos. This model is based on the assumption that the density of dark matter varies according to the power law. The model concerns the distribution function in phase space that is expressed in terms of the adiabatic invariants (radial action and angular momentum). Two types, narrow and broad, are suggested for the angular part of the distribution function. The model makes it possible to explicitly describe the adiabatic compression of halos due to a change induced in the gravitational potential by the condensation of baryonic matter at the center. The change in the density of the dark matter halos is calculated and it is shown that the standard algorithm for calculating the adiabatic compression overestimates the halo density, particularly for the case of strong radial anisotropy.     

Exact conditions in finite-temperature density-functional theory

Density-functional theory (DFT) for electrons at finite temperature is increasingly important in condensed matter and chemistry. The exact conditions that have proven crucial in constraining and constructing accurate approximations for ground-state DFT are generalized to finite temperature, including the adiabatic connection formula. We discuss consequences for functional construction.     

Coherent matter-wave manipulation in the diabatic limit

Guided systems for coherent matter waves are expected to offer substantial improvements over unguided systems, but adiabatic coupler proposals have proven difficult to realize. We outline instead considerations for a coherence-preserving diabatic approach enabling filters, couplers, and interferometers that can accept multimode guide inputs of up to magneto-optical-trap temperatures.     

Equation of State of Newborn Neutron Star Matter with Untrapped Neutrinos

The equation of state of the newborn neutron star matter with untrapped neutrinos is calculated with the AV₁₈ potential along isentropic paths. The same calculations are done with the AV₁₄ potential for the sake of comparison. Temperature–density correlation, proton fraction, adiabatic index, and the velocity of sound are also obtained at different entropies. It is shown that the proton fraction (adiabatic index) increases (decreases) by increasing entropy. We have shown that our calculated equations of state obey the causality condition. The results are compared with those of others in the literature.     

Adiabatic density perturbations and matter generation from the minimal supersymmetric standard model

We propose that the inflaton is coupled to ordinary matter only gravitationally and that it decays into a completely hidden sector. In this scenario both baryonic and dark matter originate from the decay of a flat direction of the minimal supersymmetric standard model, which is shown to generate the desired adiabatic perturbation spectrum via the curvaton mechanism. The requirement that the energy density along the flat direction dominates over the inflaton decay products fixes the flat direction almost uniquely. The present residual energy density in the hidden sector is typically shown to be small.     

The stability of relativistic stars and the role of the adiabatic index

We study the stability of three analytical solutions of the Einstein’s field equations for spheres of fluid. These solutions are suitable to describe compact objects including white dwarfs, neutron stars and supermassive stars and they have been extensively employed in the literature. We re-examine the range of stability of the Tolman VII solution, we focus on the stability of the Buchdahl solution which is under contradiction in the literature and we examine the stability of the Nariai IV solution. We found that all the mentioned solutions are stable in an extensive range of the compactness parameter. We also concentrate on the effect of the adiabatic index on the instability condition. We found that the critical adiabatic index, depends linearly on the ratio of central pressure over central energy density \(P_c/{\mathcal{E}}_c\), up to high values of the compactness. Finally, we examine the possibility to impose constraints, via the adiabatic index, on realistic equations of state in order to ensure stable configurations of compact objects.     

Dynamic compression: what it is,making metallic H and magnetic fields of Uranus and Neptune

ABSTRACT

Static compression is a well-known method to achieve very high pressures in ‘cold’ (degenerate) condensed matter. Because dynamic compression is adiabatic, it achieves both high pressures and temperatures, which are tunable by choice of pressure-pulse shape. Dynamic compression uses supersonic hydrodynamic variables, which are straight forward to measure, to achieve a wide range of extreme thermodynamic states in degenerate condensed matter. Because dynamic compression developed primarily in national laboratories, it is relatively unknown to a significant portion of the high pressure community. This paper is a brief review of (i) dynamic compression itself, (ii) its application to making metallic fluid H (MFH) and (iii) implications of data generated at extreme conditions with dynamic compression for understanding the unusual magnetic fields of Uranus and Neptune, which are made primarily by convection of semiconducting and MFH. Metallic hydrogen made under dynamic and static compression is compared.     

Collectivity in the optical response. of small metal clusters

The question of whether the linear absorption spectra of metal clusters can be interpreted as density oscillations (collective “plasmons”) or can only be understood as transitions between distinct molecular states is still a matter of debate for clusters with only a few electrons. We calculate the photo-absorption spectra of Na₂ and Na₅ ⁺ comparing two different methods: quantum fluid dynamics and time-dependent density functional theory. The changes in the electronic structure associated with particular excitations are visualized in “snapshots” via transition densities. Our analysis shows that even for the smallest clusters, the observed excitations can be interpreted as intuitively understandable density oscillations. For Na₅ ⁺, the importance of self-interaction corrections to the adiabatic local density approximation is demonstrated. Received: 1 July 2001 / Published online: 10 October 2001     

Equation of State of Hot Neutrino Opaque Interior Matter of Neutron Star

The equation of state of hot neutrino opaque interior matter of the neutron star and some of its properties such as the free energy, effective mass, adiabatic index, and temperature are calculated along both isothermal and isentropic paths with the AV ₁₈ and AV ₁₄ potentials using the lowest order constrained variational method. We have shown that the calculated equation of state with the AV ₁₈ potential is harder than with the AV ₁₄ potential. It is found that there is no phase transition in the hot neutrino opaque interior matter of the neutron star. We have shown that for all values of density and entropy, the adiabatic index of neutron star matter is greater than . It is shown that our calculated equations of state obey the causality condition.     

Dynamical instability and the expansion-free condition

We study the dynamical instability of a spherically symmetric anisotropic fluid which collapses adiabatically under the condition of vanishing expansion scalar. The Newtonian and post Newtonian regimes are considered in detail. It is shown that within those two approximations the adiabatic index Γ₁, measuring the fluid stiffness, does not play any role. Instead, the range of instability is determined by the anisotropy of the fluid pressures and the radial profile of the energy density, independently of its stiffness, in a way which is fully consistent with results previously obtained from the study on the Tolman mass.     

Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories

The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the “shortcut to adiabaticity” (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.