In the context of an ultracold Fermi gas, we derive conservation laws for mass, energy and momentum based on a generalized nonlocal Boltzmann equation with gradient corrections in the collision integral. The corrections are expressed in terms of effective collision duration, particle displacement and changes of total momentum and energy. Their origin is in the in-medium T matrix. Using variations of the optical theorem, we show that in the collision integral the particle-hole symmetry can be recast into a form of collision symmetry amenable to semiclassical simulation. Pauli-blocked collisions are distinguished from Bose-stimulated nondissipative ones; the latter are not present in the absence of gradient corrections. Consolidating with the microscopic theory, we extract local conservation laws for a general time-dependent interaction potential, and demonstrate how both types of collisions affect densities and flows of conserving quantities. Comparison is made with the approach of Nozières and Schmitt-Rink in the limit of thermal equilibrium. Under approximations used for normal-state ultracold Fermi gases interacting via Feshbach resonances we demonstrate the effect of the collision delay on the shear viscosity.
In the context of an ultracold Fermi gas, we derive conservation laws for mass, energy and momentum based on a generalized nonlocal Boltzmann equation with gradient corrections in the collision integral. The corrections are expressed in terms of effective collision duration, particle displacement and changes of total momentum and energy. Their origin is in the in-medium T matrix. Using variations of the optical theorem, we show that in the collision integral the particle-hole symmetry can be recast into a form of collision symmetry amenable to semiclassical simulation. Pauli-blocked collisions are distinguished from Bose-stimulated nondissipative ones; the latter are not present in the absence of gradient corrections. Consolidating with the microscopic theory, we extract local conservation laws for a general time-dependent interaction potential, and demonstrate how both types of collisions affect densities and flows of conserving quantities. Comparison is made with the approach of Nozières and Schmitt-Rink in the limit of thermal equilibrium. Under approximations used for normal-state ultracold Fermi gases interacting via Feshbach resonances we demonstrate the effect of the collision delay on the shear viscosity.
We review the non-relativistic Green's-function approach to the kinetic equations for Fermi liquids far from equilibrium. The emphasis is on the consistent treatment of the off-shell motion between collisions and on the non-instant and non-local picture of binary collisions. The resulting kinetic equation is of the Boltzmann type, and it represents an interpolation between the theory of transport in metals and the theory of moderately dense gases. The free motion of particles is renormalised by various mean field and mass corrections in the spirit of Landau's quasiparticles in metals. The collisions are non-local in the spirit of Enskog's theory of non-ideal gases. The collisions are moreover non-instant, a feature which is absent in the theory of gases, but which is shown to be important for dense Fermi systems. In spite of its formal complexity, the presented theory has a simple implementation within the Monte-Carlo simulation schemes. Applications in nuclear physics are given for heavy-ion reactions and the results are compared with the former theory and recent experimental data. The effect of the off-shell motion and the non-local and non-instant collisions on the dynamics of the system can be characterised in terms of thermodynamic functions such as the energy density or the pressure tensor. Non-equilibrium counterparts of these functions and the corresponding balance equations are derived and discussed from two points of view. Firstly, they are used to prove the conservation laws. Secondly, the role of individual microscopic mechanisms in fluxes of particles and momenta and in transformations of the energy is clarified.
We derive and analyze an effective quantum Boltzmann equation in the kinetic regime for the interactions of four distinguishable types of fermionic spin- particles, starting from a general quantum field Hamiltonian. Each particle type is described by a time-dependent, 2 × 2 spin-density ('Wigner') matrix. We show that density and energy conservation laws as well as the H-theorem hold, and enumerate additional conservation laws depending on the interaction. The conserved quantities characterize the thermal (Fermi–Dirac) equilibrium state. We illustrate the approach to equilibrium by numerical simulations in the isotropic three-dimensional setting.
We study the formation and the dynamics of a shock wave originating from the collision between two ultracold clouds of strongly interacting fermions as observed at a lower temperature in an experiment by Joseph et al. [Phys. Rev. Lett. 106, 150401 (2011)]. We use the Boltzmann equation within the test-particle method to describe the evolution of the system in the normal phase. We also show a direct comparison with the hydrodynamic approach and insist on the necessity of including a shear-viscosity and a thermal-conductivity term in the equations to prevent unphysical behavior from taking place.
Differential conservation equations are derived for the mass-, momentum-, and energy-density operators for a 1-component simple fluid of Bose or Fermi particles with arbitrary pairwise interactions. These equations are used in a statistical mechanical derivation of exact equations of motion for the expectations of these operators. The equations of motion are coupled to equations relating these expectations to the local temperature, chemical potential, and fluid velocity. The coupled equations are closed in the sense that the expectations and their thermodynamic conjugates listed above are the only unknowns, although some of the dependence in the equations on the conjugates is expressed only implicitly. The equations of motion are memory-retaining nonlocal generalizations of the classical hydrodynamic equations and apply to a normal fluid arbitrarily far from equilibrium. The formalism is not carried as far as has the corresponding classical formalism because the local equilibrium expectation of the momentum density here does not equal the fluid velocity times the expectation of the mass density as is true in classical statistical mechanics.
A kinetic equation of nonlocal and noninstantaneous character unifies the achievements of transport in dense quantum gases with the Landau theory of quasiclassical transport in Fermi systems. Large cancellations in the off-shell motion appear, which are usually hidden in non-Markovian behaviors. The remaining corrections are expressed in terms of shifts in space and time that characterize the nonlocality of the scattering process. In this way, it is possible to recast quantum transport into a quasiclassical picture. In addition to the quasiparticle, the balance equations for density, momentum, energy, and entropy also include correlated two-particle contributions beyond the Landau theory. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. For Maxwellian particles with time-dependent s-wave scattering, the correlated parts of the observables are calculated and a sign change of the latent heat is reported at a universal ratio of scattering length to the thermal de Broglie wavelength. This is interpreted as a change from correlational heating to cooling.
In non-diffusive conduction regimes of strongly correlated quantum electron systems, electromagnetic perturbations simultaneously probe the electronic dynamics in time and space: the exchanged energy ℏω excites retarded, i.e., frequency-dependent, many-body interactions, while the probing spatial modulation renders the response spatially nonlocal, i.e., dependent on the external wave vector q. This work derives the nonlocal electrodynamic response of such dynamical quantum fluids assuming local but frequency-dependent self-energies and particle-hole irreducible two-particle vertex functions, and preserving charge/mass conservation. The latter is ensured by Bethe-Salpeter equations for renormalized interaction vertices, entering the Kubo formalism for two-particle correlation functions (e.g., for density, currents, momentum, stress). Within such a framework, exact symmetry criteria for the absence of vertex corrections are inferred. In particular, vertex corrections vanish at q=0 for single-particle dispersions that are even and bare interaction vertices that are odd with respect to specific momentum-space point group transformations, including inversion for vector vertices, and mirror reflections or two- or higher-fold rotations for tensor vertices. If the dispersion is isotropic, vertex corrections vanish from the transverse part (⊥q) of vectorial vertices (such as for electric/particle current) at any finite ℏω and q. These cancellations extend to the full current-current correlation function for quadratic isotropic dispersion. Further symmetry breaking, multiband effects, and the additional imposition of momentum conservation, are discussed, with application to the Hall viscosity of Landau levels. Explicit expressions for generic nonlocal correlation functions are derived for Fermi liquids and non-Fermi liquids.