Particle distribution tail and related energy formula

Abstract

We present a simple derivation of the energy formula found by Tan, relative to the single channel hamiltonian relevant for ultracold Fermi gases. This derivation is generalized to particles with different masses, to arbitrary mixtures, and to two-dimensional space. We show how, in a field theoretical approach, the $1/k^4$ tail in the momentum distribution and the energy formula arise in a natural way. As a specific example, we consider quantitative calculations of the energy, from different formulas within the ladder diagrams approximation in the normal state. The comparison of the results provides an indication on the quality of the approximation.

15 pages, 1 figure

References in corpus (7)

• Theory of ultracold Fermi gases
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Number of closed-channel molecules in the BEC-BCS crossover
• Universal Properties of the Ultra-Cold Fermi Gas
• Self-consistent theory for molecular instabilities in a normal degenerate Fermi gas in the BEC-BCS crossover

Cited by in corpus (79)

• Exploring the Thermodynamics of a Universal Fermi Gas
• Efimov Physics: a review
• BCS-BEC Crossover and the Unitary Fermi Gas
• The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
• Contact Measurements on Atomic BEC
• Universal few-body physics and cluster formation
• Time dependent impurity in ultracold fermions: orthogonality catastrophe and beyond
• General relations for quantum gases in two and three dimensions. Two-component fermions
• Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• General relations for quantum gases in two and three dimensions. II. Bosons and mixtures
• Universal Relations for Identical Bosons from 3-Body Physics
• Comparing and contrasting nuclei and cold atomic gases
• Radio frequency spectroscopy of polarons in ultracold Bose gases
• Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases
• Short-Time Operator Product Expansion for rf Spectroscopy of a Strongly-interacting Fermi Gas
• Evidence for universal relations describing a gas with $p$-wave interactions
• Temperature dependence of the contact in a unitary Fermi gas
• Universal equation of state and pseudogap in the two-dimensional Fermi gas
• BEC-BCS crossover and universal relations in unitary Fermi gases
• Universal Short-Distance Structure of the Single-Particle Spectral Function of Dilute Fermi Gases
• Universal relations for the two-dimensional spin-1/2 Fermi gas with contact interactions
• Momentum-resolved observation of thermal and quantum depletion in an interacting Bose gas
• Observation of quantum-limited spin transport in strongly interacting two-dimensional Fermi gases
• Short-distance and short-time structure of a unitary Fermi gas
• Universal properties of Fermi gases in arbitrary dimensions
• Universal high-momentum asymptote and thermodynamic relations in a spinless Fermi gas with a resonant $p$-wave interaction
• Universal contact of strongly interacting fermions at finite temperatures
• Temperature and coupling dependence of the universal contact intensity for an ultracold Fermi gas
• Universal thermodynamics of a strongly interacting Fermi gas: theory versus experiment
• Experimental evaluation of the nuclear neutron-proton contact
• A two-dimensional Fermi liquid with attractive interactions
• Quasiparticle energy in a strongly interacting homogeneous Bose-Einstein condensate
• Single-Particle Momentum Distribution of an Efimov trimer
• Contact and Momentum Distribution of the Unitary Fermi Gas
• Ground state of a resonantly interacting Bose gas
• Isotropic contact forces in arbitrary representation: heterogeneous few-body problems and low dimensions
• The contact in the unitary Fermi gas across the superfluid phase transition
• Universal Tan relations for quantum gases in one dimension
• Comparative study of one-dimensional Bose and Fermi gases with contact interactions from the viewpoint of universal relations for correlation functions
• Diagrammatic Monte Carlo algorithm for the resonant Fermi gas
• High-temperature expansion for interacting fermions
• Single-Particle Momentum Distributions of Efimov States in Mixed-Species Systems
• Exact equivalence between one-dimensional Bose gases interacting via hard-sphere and zero-range potentials
• Hartree shift in unitary Fermi gases
• Ballistic quench-induced correlation waves in ultracold gases
• P-Wave Contact Tensor -- Universal Properties of Axisymmetry-Broken P-Wave Fermi Gases
• Tan's two-body contact across the superfluid transition of a planar Bose gas
• A supercircle description of universal three-body states in two dimensions
• Tan's distributions and Fermi-Huang pseudopotential in momentum space
• Excitation picture of an interacting Bose gas
• Stationary and dynamical properties of two harmonically trapped bosons in the crossover from two dimensions to one
• A simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy
• Dimensional Effects on the Momentum distribution of Bosonic Trimer States
• Ground-state properties of dilute one-dimensional Bose gas with three-body repulsion
• Contact formalism for coupled channels
• Tan's contact as an indicator of completeness and self-consistency of a theory
• Universal Relations of Ultracold Fermi Gases with Arbitrary Spin-Orbit Coupling
• On the survival of the quantum depletion of a condensate after release from a magnetic trap
• Universal contact and collective excitations of a strongly interacting Fermi gas
• Critical behavior of Tan's contact for bosonic systems with a fixed chemical potential
• A Universal Energy Functional for Trapped Fermi Gases with Large Scattering Length
• Isothermal sweep theorems for ultra-cold quantum gases in a canonical ensemble
• Ground-state properties of a dilute two-dimensional Bose gas
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
• Photo-excitation measurement of Tan's contact for a strongly interacting Fermi gas
• Three-body contact for fermions. I. General relations
• Contact parameters in two dimensions for general three-body systems
• Tan's universal contact and collective oscillations of strongly interacting Fermi gases
• Universal Relations for Fermions with Large Scattering Length
• Dilute Fermi and Bose Gases
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
• The variational theorem for the scattering length in low dimensions and its applications to universal systems
• Universal Bound States in Long-range Spin Chains with an Impurity
• Two-body contact of a Bose gas near the superfluid--Mott-insulator transition
• An Effective Series Expansion to the Equation of State of Unitary Fermi Gases
• From few to many body degrees of freedom
• BEC-BCS Crossover with Feshbach Resonance for a Three-Hyperfine-Species Model
• Universal Relations in Long-range Quantum Spin Chains