A Fully Self-Consistent Treatment of Collective Fluctuations in Quantum Liquids

The new scheme employed (throughout the thermodynamic phase space), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions are formulated (in a manner analogous to the classical case) to provide a new quantum approach for describing structure at the microscopic level, as well as characterize the thermodynamic properties of material systems. A major point of this paper is that ...

This short essay discusses the application of Bogoliubov's theory of superfluidity in the context of quantum phase transitions.

Quantum effects in material systems are often pronounced at low energies and become insignificant at high temperatures. We find that, perhaps counterintuitively, certain quantum effects may follow the opposite route and become sharp when extrapolated to high temperature within a "classical" liquid phase. In the current work, we suggest basic quantum bounds on relaxation (and thermalization) times, examine kinetic theory by taking into account such possible fundamental quantum...

Advances in controlling and measuring systems of ultra-cold atoms provided strong motivation to theoretical investigations of quantum dynamics in closed many-body systems. Fundamental questions on quantum dynamics and statistical mechanics are now within experimental reach: How is thermalization achieved in a closed quantum system? How does quantum dynamics cross over to effective classical physics? Can such a thermal or classical fate be evaded? In these lectures, given at t...

A new method is proposed for the calculation of full density matrix and thermodynamic functions of a many-boson system. Explicit expressions are obtained in the pair correlations approximation for an arbitrary temperature. The theory is self-consistent in the sence that the calculated properties at low temperatures coincide with that of Bogoliubov theory and in the high-temperature limit lead to the results for classical non-ideal gas in the random phase approximation. The ph...

The past decade has seen atomic Bose-Einstein condensates emerge as a promising prototype system to explore the quantum mechanical form of turbulence, buoyed by a powerful experimental toolbox to control and manipulate the fluid, and the amenity to describe the system from first-principles. This article presents an overview of quantum turbulence in atomic condensates, from its history and fundamental motivations, its characteristics and key results to date, and finally to som...

The dynamical properties of liquid lithium at several thermodynamic states near the triple point have been studied within the framework of the mode-coupling theory. We present a self-consistent scheme which, starting from the knowledge of the static structural properties of the liquid system, allows the theoretical calculation of several single-particle and collective dynamical properties. The study is complemented by performing Molecular Dynamics simulations, and the obtaine...

The time-convolutionless mode-coupling (TMCT) equation for the intermediate scattering function $f_{\alpha}(q,t)$ derived recently by the present author is transformed into a simple nonlinear recursion formula for a generating function $\Omega_{\alpha}(\bm{q},t)(=-\ln[f_{\alpha}(q,t)]/q^2)$, where $\alpha=c$ stands for a collective case and $\alpha=s$ for a self case. By employing the same simplification on the nonlinear memory function as that proposed by the mode-coupling t...

These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario derived from the solution to some solvable models (p-spin and the like) that are intimately connected to the mode coupling approach (and similar ones) to super-cooled liquids. At the end we list a number of open problems of great relevance in this context. These Sec...

A novel method to determine the density and temperature of a system is proposed based on quantum fluctuations typical of Fermions in the limit where the reached temperature T is small compared to the Fermi energy $\epsilon_f$ at a given density $\rho$. Quadrupole and particle multiplicity fluctuations relations are derived in terms of $\frac{T}{\epsilon_f}$. This method is valid for infinite and finite fermionic systems, in particular we apply it to heavy ion collisions using...