Microscopic derivation of the hydrodynamic equations for the superfluid fermi-systems (original) (raw)

Relation connecting thermodynamics and transport of atomic unitary Fermi superfluids

Physical Review A

The shear viscosity has been shown to be equal to the product of pressure and relaxation time in normal scale-invariant fluids, but the presence of superfluidity at low temperatures can alter the relation. By using the mean-field BCS-Leggett theory with a gauge-invariant linear response theory for unitary Fermi superfluids, we present an explicit relation between thermodynamic quantities, including the pressure and chemical potential, and transport coefficients, including the shear viscosity, superfluid density, and anomalous shear viscosity from momentum transfer via Cooper pairs. The relation is modified when pairing fluctuations associated with noncondensed Cooper pairs are considered. Within a pairing fluctuation theory consistent with the BCS-Leggett ground state, we found an approximate relation for unitary Fermi superfluids. The exact mean-field relation and the approximate one with pairing flucutaions advance our understanding of relations between equilibrium and transport quantities in superfluids, and they help determine or constrain quantities which can be otherwise difficult to measure.

Dissipative superfluid hydrodynamics for the unitary Fermi gas

Physical Review A, 2021

Jiaxun Hou and Thomas Schäfer Department of Physics, North Carolina State University, Raleigh, NC 27695 Abstract In this work we establish constraints on the temperature dependence of the shear viscosity η in the superfluid phase of a dilute Fermi gas in the unitary limit. Our results are based on analyzing experiments that measure the aspect ratio of a deformed cloud after release from an optical trap. We discuss how to apply the two-fluid formalism to the unitary gas, and provide a suitable parametrization of the equation of state. We show that in expansion experiments the difference between the normal and superfluid velocities remains small, and can be treated as a perturbation. We find that expansion experiments favor a shear viscosity that decreases significantly in the superfluid regime. Using an exponential parametrization we find η(Tc/(2TF )) ∼< η(Tc/TF )/e, where Tc is the critical temperature, TF is the local Fermi temperature of the gas, and e is Euler’s number.

Probing two-fluid hydrodynamics in a trapped Fermi superfluid at unitarity

2007

We develop a variational approach to calculate the density response function at finite temperatures of the lowest-lying two-fluid modes in a trapped two-component Fermi superfluid close to a Feshbach resonance. The out-of-phase oscillations, which are the analogue in trapped gases of second sound in uniform superfluids, have so far not been observed in cold-atom experiments. At unitarity, we show that these modes are observable at finite temperatures via two-photon Bragg scattering, whose spectrum is related to the imaginary part of density response function. This provides direct evidence for superfluidity and a promising way to test microscopic results for thermodynamics at unitarity.

Local Equilibrium Approach for Fermi Systems and Quantum Hydrodynamics

The quantum distribution function is derived to reach an accordance with quantum hydrodynamics and to conserve quantum properties of the system. This distribution function, when calculating statistical averages, leads to correct local values of the fundamental physical quantities; and the local conservation laws of the microscopic quantum hydrodynamics can be obtained from such statistics by passing to mathematical expectatives. The equation for the one-particle distribution function generates the many-particle distribution functions. Then, the BBGKYhierarchy equations are obtained. The one-particle statistical operator of a system of fermions in the local equilibrium at arbitrary temperatures is calculated. The dynamics of local hydrodynamic functions (chemical potential, hydrodynamic velocity, and temperature) completely determine the dynamics of the one-particle statistical operator. The quantum hydrodynamic equations for the proton-neutron system at low temperatures are obtained from the equation for one-particle distribution function.

Superfluidity in two-component fermionic systems

Eprint Arxiv 0705 1201, 2007

Different types of superfluid ground states have been investigated in systems of two species of fermions with Fermi surfaces that do not match. This study is relevant for cold atomic systems, condensed matter physics and quark matter. In this paper we consider this problem in the case the fermionic quasi-particles can transmute into one another and only their total number is conserved. We use a BCS approximation to study superconductivity in two-band metallic systems with inter and intra-band interactions. Tuning the hybridization between the bands varies the mismatch of the Fermi surfaces and produces different instabilities. For inter-band attractive interactions we find a first order normal-superconductor and a homogeneous metastable phase with gapless excitations. In the case of intra-band interactions, the transition from the superconductor to the normal state as hybridization increases is continuous and associated with a quantum critical point. The case when both interactions are present is also considered.

Towards quantum turbulence in cold atomic fermionic superfluids

Journal of Physics B: Atomic, Molecular and Optical Physics

Fermionic superfluids provide a new realization of quantum turbulence, accessible to both experiment and theory, yet relevant to phenomena from both cold atoms to nuclear astrophysics. In particular, the strongly interacting Fermi gas realized in cold-atom experiments is closely related to dilute neutron matter in neutron star crusts. Unlike the liquid superfluids 4 He (bosons) and 3 He (fermions), where quantum turbulence has been studied in laboratory for decades, superfluid Fermi gases stand apart for a number of reasons. They admit a rather reliable theoretical description based on density functional theory (dft) called the time-dependent superfluid local density approximation (tdslda) that describes both static and dynamic phenomena. Cold atom experiments demonstrate exquisite control over particle number, spin polarization, density, temperature, and interaction strength. Topological defects such as domain walls and quantized vortices, which lie at the heart of quantum turbulence, can be created and manipulated with time-dependent external potentials, and agree with the time-dependent theoretical techniques. While similar experimental and theoretical control exists for weakly interacting Bose gases, the unitary Fermi gas is strongly interacting. The resulting vortex line density is extremely high, and quantum turbulence may thus be realized in small systems where classical turbulence is suppressed. Fermi gases also permit the study of exotic superfluid phenomena such as the Larkin-Ovchinnikov-Fulde-Ferrell (loff) pairing mechanism for polarized superfluids which may give rise to 3D supersolids, and a pseudo-gap at finite temperatures that might affect the regime of classical turbulence. The dynamics associated with these phenomena has only started to be explored. Finally, superfluid mixtures have recently been realized, providing experimental access to phenomena like Andreev-Bashkin entrainment predicted decades ago. Superfluid Fermi gases thus provide a rich forum for addressing phenomena related to quantum turbulence with applications ranging from terrestrial superfluidity to astrophysical dynamics in neutron stars.

Superfluidity and superconductivity in relativistic fermion systems

Physics Reports, 1984

I. Relativistic gap equations 327 3.1. Electromagnetic field fluctuation effects 1.1. Relativistic gap matrices 327 3.2. Electroweak effects in superconductors 1.2. Helicity amplitudes for spin 1/2 scattering 329 3.3. p-wave superconductivity 1.3. Gap equations 331 4. Pairing in quark matter 1.4. jP =~+ pairing 334 4.1. The order parameter for superfluid quark matter 1.5. The Ginzburg-Landau region 336 4.2. Superconductivity in quark matter 1.6. Gradient terms 338 4.3. Colour superconductivity in quark matter 1.7. Direct derivation of the Ginzburg-Landau free energy 341 Appendix A. Angular integrals 2. Superfluid neutron star matter 344 Appendix B. J = 2 projections 3. Superconducting electron systems 349 References

Two-component Fermi systems: II. Superfluid coupled cluster theory

Zeitschrift f�r Physik B Condensed Matter, 1988

In this second paper of a series the coupled cluster method (CCM) or exp(S) formalism is applied to two-component Fermi superfluids using a Bardeen-Cooper-Schrieffer (BCS) ground state as a zeroth-order approximation. We concentrate on developing the formalism necessary for carrying out eventual numerical calculations on realistic superconducting systems. We do this by generalising the one-component formalism in an appropriate manner and by using the results in the first paper of this series, where we studied twocomponent Fermi fluids. We stress the previous successes of the CCM, both from the point of view of analytic and numerical results, and we further indicate its potential for studying superconductivity. We restrict ourselves here to a so-called ring plus single particle energy (RING+SPE) approximation for general potentials and show how it can be formulated as a set of four coupled, bilinear integral equations for the clusterintegrated amplitudes. These latter amplitudes are themselves derived from the four-point functions of the system which provide a measure of the two-particle/two-hole component in the true ground-state wavefunction with respect to the BCS model state. We indicate how to obtain possible analytic solutions.

MODIFIED BOGOLYUBOV'S DERIVATION OF THE TWO-FLUID HYDRODYNAMICS

A consistent microscopic derivation of the two-fluid hydrodynam-ics for superfluid helium-4 in the ideal approximation is represented. The starting point in our formalism is a system of Heisen-berg's equation of motion for both normal and anomalous correlation functions. The use of a mixed Wigner representation allows us to perform the expansion of the equations of motion for correlation functions in gradients directly, very easily, and with a rigorous mathematics. To find the hydrodynamic flows, we have constructed a local equilibrium statistical operator for superfluid helium in the reference frame, where the condensate is at rest.