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

We discuss the hydrodynamic representation of a wide class of quantum media exhibiting similar elementary excitations and dispersion properties. The representation covers quantum systems characterized by any type of (long-range) self-interaction, associated with an arbitrary potential. It also accounts for possible nonlinearities, which may arise e.g., due to short-range interactions (collisions) in the case of bosons, or from the Pauli exclusion principle for fermions. The a...

We analyze dynamics of quantum supercooled liquids in terms of tagged particle dynamics. Unlike the classical case, uncertainty in the position of a particle in quantum liquid leads to qualitative changes. We demonstrate these effects in the dynamics of the first two moments of displacements, namely, the mean-squared displacement, $\langle \Delta r^2(t)\rangle$, and $\langle \Delta r^4(t)\rangle$. Results are presented for a hard sphere liquid using mode-coupling theory (MCT)...

We introduce a quasi-equilibrium formalism in the theory of liquids in order to obtain a set of coarse grained long time dynamical equations for the two point density correlation functions. Our scheme allows to use typical approximations devised for equilibrium to study long time glassy dynamics. We study the Hypernetted Chain (HNC) approximation and a recent closure scheme by Szamel. In both cases we get dynamical equations that have the structure of the Mode-Coupling (MCT) ...

This book introduces the theoretical description and properties of quantum fluids. The focus is on gaseous atomic Bose-Einstein condensates and, to a minor extent, superfluid helium, but the underlying concepts are relevant to other forms of quantum fluids such as polariton and photonic condensates. The book is pitched at the level of advanced undergraduates and early postgraduate students, aiming to provide the reader with the knowledge and skills to develop their own resear...

We determine the effects of quantum fluctuations about the T=0 mean field solution of the BCS-BEC crossover in a dilute Fermi gas using the functional integral method. These fluctuations are described in terms of the zero point motion of collective modes and the virtual scattering of gapped quasiparticles. We calculate their effects on various measurable properties, including chemical potential, ground state energy, the gap, the speed of sound and the Landau critical velocity...

The formalism of density functional theory (DFT) can be easily extended to the time dependent case (TDDFT). However, while in the static case the theory is well established and is expected to be, at least in principle, an exact approach for the determination of energy and density profiles of inhomogeneous systems, the applicability of TDDFT to the investigation of dynamic phenomena (for example propagation of collective phenomena) is less obvious especially in the microscopic...

A quantum Langevin equation for the amplitudes of the collective modes in Bose-Einstein condensate is derived. The collective modes are coupled to a thermal reservoir of quasi-particles, whose elimination leads to the quantum Langevin equation. The dissipation rates are determined via the correlation function of the fluctuating force and are evaluated in the local-density approximation for the spectrum of quasi-particles and the Thomas-Fermi approximation for the condensate. ...

Ultracold atomic quantum gases belong to the most exciting challenges of modern physics. Their theoretical description has drawn much from classical field equations. These mean-field approximations are in general reliable for dilute gases in which the atoms collide only rarely with each other, and for situations where the gas is not too far from thermal equilibrium. With present-day technology it is, however, possible to drive and observe a system far away from equilibrium. F...

The equations of motion for the density modes of a fluid, derived from Newton's equations, are written as a linear generalized Langevin equation. The constraint imposed by the fluctuation-dissipation theorem is used to derive an exact form for the memory function. The resulting equations, solved under the assumption that the noise, and consequently density fluctuations, of the liquid are gaussian distributed, are equivalent to the random-phase-approximation for the static str...

The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates which are characterized by quantized vorticity, uperfluidity and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence which have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary...