Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus--Yevick values of the fourth virial coefficient

As is well known, approximate integral equations for liquids, such as the hypernetted chain (HNC) and Percus--Yevick (PY) theories, are in general thermodynamically inconsistent in the sense that the macroscopic properties obtained from the spatial correlation functions depend on the route followed. In particular, the values of the fourth virial coefficient $B_4$ predicted by the HNC and PY approximations via the virial route differ from those obtained via the compressibility route. Despite this, it is shown in this paper that the value of $B_4$ obtained from the virial route in the HNC theory is exactly three halves the value obtained from the compressibility route in the PY theory, irrespective of the interaction potential (whether isotropic or not), the number of components, and the dimensionality of the system. This simple relationship is confirmed in one-component systems by analytical results for the one-dimensional penetrable-square-well model and the three-dimensional penetrable-sphere model, as well as by numerical results for the one-dimensional Lennard--Jones model, the one-dimensional Gaussian core model, and the three-dimensional square-well model.Comment: 8 pages; 4 figures; v2: slight change of title; proof extended to multicomponent fluid

Non-Equilibrium Time Evolution in Quantum Field Theory

The time development of equal-time correlation functions in quantum mechanics and quantum field theory is described by an exact evolution equation for generating functionals. This permits a comparison between classical and quantum evolution in non-equilibrium systems.Comment: 7 pages, LaTe

Are the energy and virial routes to thermodynamics equivalent for hard spheres?

The internal energy of hard spheres (HS) is the same as that of an ideal gas, so that the energy route to thermodynamics becomes useless. This problem can be avoided by taking an interaction potential that reduces to the HS one in certain limits. In this paper the square-shoulder (SS) potential characterized by a hard-core diameter $\sigma'$, a soft-core diameter $\sigma>\sigma'$ and a shoulder height $\epsilon$ is considered. The SS potential becomes the HS one if (i) $\epsilon\to 0$, or (ii) $\epsilon\to\infty$, or (iii) $\sigma'\to\sigma$ or (iv) $\sigma'\to 0$ and $\epsilon\to\infty$. The energy-route equation of state for the HS fluid is obtained in terms of the radial distribution function for the SS fluid by taking the limits (i) and (ii). This equation of state is shown to exhibit, in general, an artificial dependence on the diameter ratio $\sigma'/\sigma$. If furthermore the limit $\sigma'/\sigma\to 1$ is taken, the resulting equation of state for HS coincides with that obtained through the virial route. The necessary and sufficient condition to get thermodynamic consistency between both routes for arbitrary $\sigma'/\sigma$ is derived.Comment: 10 pages, 4 figures; v2: minor changes; to be published in the special issue of Molecular Physics dedicated to the Seventh Liblice Conference on the Statistical Mechanics of Liquids (Lednice, Czech Republic, June 11-16, 2006

Thermodynamic consistency of energy and virial routes: An exact proof within the linearized Debye-H\"uckel theory

The linearized Debye-H\"uckel theory for liquid state is shown to provide thermodynamically consistent virial and energy routes for any potential and for any dimensionality. The importance of this result for bounded potentials is discussed.Comment: 4 pages, 1 figure; v2: minor change

Emergence of coherence in the Mott--superfluid quench of the Bose-Hubbard model

We study the quench from the Mott to the superfluid phase in the Bose-Hubbard model and investigate the spatial-temporal growth of phase coherence, i.e., phase locking between initially uncorrelated sites. To this end, we establish a hierarchy of correlations via a controlled expansion into inverse powers of the coordination number $1/Z$. It turns out that the off-diagonal long-range order spreads with a constant propagation speed, forming local condensate patches, whereas the phase correlator follows a diffusion-like growth rate.Comment: 4 page

Quantum stochastic description of collisions in a canonical Bose gas

We derive a stochastic process that describes the kinetics of a one-dimensional Bose gas in a regime where three body collisions are important. In this situation the system becomes non integrable offering the possibility to investigate dissipative phenomena more simply compared to higher dimensional gases. Unlike the quantum Boltzmann equation describing the average momentum distribution, the stochastic approach allows a description of higher-order correlation functions in a canonical ensemble. As will be shown, this ensemble differs drastically from the grand canonical one. We illustrate the use of this method by determining the time evolution of the momentum mode particle number distribution and the static structure factor during the evaporative cooling process.Comment: 4 pages, 4 figure

Hamiltonian dynamics reveals the existence of quasi-stationary states for long-range systems in contact with a reservoir

We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the Hamiltonian Mean Field model and the equilibrium ensemble equivalence. We find that long-lasting quasi-stationary states persist in presence of the interaction with the environment. Our results indicate that quasi-stationary states are indeed reproducible in real physical experiments.Comment: Title changed, throughout revision of the tex

Instabilities and propagation of neutrino magnetohydrodynamic waves in arbitrary direction

In a previous work [16], a new model was introduced, taking into account the role of the Fermi weak force due to neutrinos coupled to magnetohydrodynamic plasmas. The resulting neutrino-magnetohydrodynamics was investigated in a particular geometry associated with the magnetosonic wave, where the ambient magnetic field and the wavevector are perpendicular. The corresponding fast, short wavelength neutrino beam instability was then obtained in the context of supernova parameters. The present communication generalizes these results, allowing for arbitrary direction of wave propagation, including fast and slow magnetohydrodynamic waves and the intermediate cases of oblique angles. The numerical estimates of the neutrino-plasma instabilities are derived in extreme astrophysical environments where dense neutrino beams exist