The Compressibility of Minimal Lattice Knots

The (isothermic) compressibility of lattice knots can be examined as a model of the effects of topology and geometry on the compressibility of ring polymers. In this paper, the compressibility of minimal length lattice knots in the simple cubic, face centered cubic and body centered cubic lattices are determined. Our results show that the compressibility is generally not monotonic, but in some cases increases with pressure. Differences of the compressibility for different knot types show that topology is a factor determining the compressibility of a lattice knot, and differences between the three lattices show that compressibility is also a function of geometry.Comment: Submitted to J. Stat. Mec

Temperature-dependent compressibility in graphene and two-dimensional systems

We calculate the finite temperature compressibility for two-dimensional semiconductor systems, monolayer graphene, and bilayer graphene within the Hartree-Fock approximation. We find that the calculated temperature dependent compressibility including exchange energy is non-monotonic. In 2D systems at low temperatures the inverse compressibility decreases first with increasing temperature, but after reaching a minimum it increases as temperature is raised further. At high enough temperatures the negative compressibility of low density systems induced by the exchange energy becomes positive due to the dominance of the finite temperature kinetic energy. The inverse compressibility in monolayer graphene is always positive and its temperature dependence appears to be reverse of the 2D semiconductor systems, i.e., it increases first with temperature and then decreases at high temperatures. The inverse compressibility of bilayer graphene shows the same non-monotonic behavior as ordinary 2D systems, but at high temperatures it approaches a constant which is smaller than the value of the non-interacting bilayer graphene. We find the leading order temperature correction to the compressibility within Hartree-Fock approximation to be $T^2 \ln T$ at low temperatures for all three systems.Comment: 19 pages, 9 figure

Compressibility of a two-dimensional extended Hubbard model

The compressibility of an extended $d-p$ Hubbard model is investigated by the Roth's two-pole approximation. Using the factorization procedure proposed by Beenen and Edwards, superconductivity with singlet $d_{x^2-y^2}$-wave pairing is also considered. Within this framework, the effects of $d-p$ hybridization and Coulomb interaction $U$ on the compressibility are studied carefully. It has been found that the compressibility diverges and then it becomes negative near the half-filling. Within Roth's method, it has been verified that an important contribution for the negative compressibility comes from the spin-correlation term $$ present in Roth's band shift. This correlation function plays an important role due to its high doping dependence. Also, its effects in the band shift and consequently in the compressibility are pronounced near the half-filling. The numerical results show that the hybridization acts in the sense of suppressing the negative compressibility near half-filling. Finally, the possibility of a connection between the negative compressibility and the phase separation is also discussed.Comment: 3 pages, 1 figure, accepted for publication in Physica

In situ measurements of density fluctuations and compressibility in silica glass as a function of temperature and thermal history

In this paper, small-angle X-ray scattering measurements are used to determine the different compressibility contributions, as well as the isothermal compressibility, in thermal equilibrium in silica glasses having different thermal histories. Using two different methods of analysis, in the supercooled liquid and in the glassy state, we obtain respectively the temperature and fictive temperature dependences of the isotheraml compressibility. The values obtained in the glass and supercooled liquid states are very close to each other. They agree with previous determinations of the literature. The compressibility in the glass state slightly decreases with increasing fictive temperature. The relaxational part of the compressibility is also calculated and compared to previous determinations. We discussed the small differences between the different determinations

How Compressible are Innovation Processes?

The sparsity and compressibility of finite-dimensional signals are of great interest in fields such as compressed sensing. The notion of compressibility is also extended to infinite sequences of i.i.d. or ergodic random variables based on the observed error in their nonlinear k-term approximation. In this work, we use the entropy measure to study the compressibility of continuous-domain innovation processes (alternatively known as white noise). Specifically, we define such a measure as the entropy limit of the doubly quantized (time and amplitude) process. This provides a tool to compare the compressibility of various innovation processes. It also allows us to identify an analogue of the concept of "entropy dimension" which was originally defined by R\'enyi for random variables. Particular attention is given to stable and impulsive Poisson innovation processes. Here, our results recognize Poisson innovations as the more compressible ones with an entropy measure far below that of stable innovations. While this result departs from the previous knowledge regarding the compressibility of fat-tailed distributions, our entropy measure ranks stable innovations according to their tail decay.Comment: 58 page

Compressibility in turbulent MHD and passive scalar transport: mean-field theory

We develop a mean-field theory of compressibility effects in turbulent magnetohydrodynamics and passive scalar transport using the quasi-linear approximation and the spectral $\tau$-approach. We find that compressibility decreases the $\alpha$ effect and the turbulent magnetic diffusivity both at small and large magnetic Reynolds numbers, Rm. Similarly, compressibility decreases the turbulent diffusivity for passive scalars both at small and large P\'eclet numbers, Pe. On the other hand, compressibility does not affect the effective pumping velocity of the magnetic field for large Rm, but it decreases it for small Rm. Density stratification causes turbulent pumping of passive scalars, but it is found to become weaker with increasing compressibility. No such pumping effect exists for magnetic fields. However, compressibility results in a new passive scalar pumping effect from regions of low to high turbulent intensity both for small and large P\'eclet numbers. It can be interpreted as compressible turbophoresis of noninertial particles and gaseous admixtures, while the classical turbophoresis effect exists only for inertial particles and causes them to be pumped to regions with lower turbulent intensity.Comment: 26 pages, 1 figure, final paper accepted for publication to JPP, jpp.cl

Compressibility of a 2D electron gas under microwave radiation

Microwave irradiation of a two-dimensional electron gas (2DEG) produces a non-equilibrium distribution of electrons, and leads to oscillations in the dissipative part of the conductivity. We show that the same non-equilibrium electron distribution induces strong oscillations in the 2DEG compressibility measured by local probes. Local measurements of the compressibility are expected to provide information about the domain structure of the zero resistance state of a 2DEG under microwave radiation.Comment: v2: analysis of the wave-vector dependence of the compressibility added; discussion of the Hall conductivity removed (shifted to cond-mat/0409590 in a revised form