Large momentum part of fermions with large scattering length

Abstract

It is well known that the momentum distribution of the two-component Fermi gas with large scattering length has a tail proportional to $1/k^4$ at large $k$. We show that the magnitude of this tail is equal to the adiabatic derivative of the energy with respect to the reciprocal of the scattering length, multiplied by a simple constant. This result holds at any temperature (as long as the effective interaction radius is negligible) and any large scattering length; it also applies to few-body cases. We then show some more connections between the $1/k^4$ tail and various physical quantities, in particular the rate of change of energy in a DYNAMIC sweep of the inverse scattering length.

11 pages, 1 figure; a typo corrected

References in corpus (3)

• Weakly bound dimers of fermionic atoms
• Probing Pair-Correlated Fermionic Atoms through Correlations in Atom Shot Noise
• Three-boson problem near a narrow Feshbach resonance

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• Ultracold collisions between two light indistinguishable diatomic molecules: elastic and rotational energy transfer in HD+HD
• Spectral properties and observables in ultracold Fermi gases
• Nucleon Short-Range Correlations and High-Momentum Dynamics: Implications on the Equation of State of Dense Matter
• Three-body contact for fermions. I. General relations
• Numerical study of unitary fermions in one spatial dimension
• Crossovers in Unitary Fermi Systems
• Contact parameters in two dimensions for general three-body systems
• On nuclear short-range correlations and the zero-energy eigenstates of the Schrodinger equation
• Synergy between deep neural networks and the variational Monte Carlo method for small ${}^{4}H{e}_N$ clusters
• Statistical properties of the momentum occupation numbers of the Tonks-Girardeau gas in a harmonic trap
• Toward precision Fermi liquid theory in two dimensions
• Temperature dependence of $p$-wave contacts in a harmonically trapped Fermi gas
• Dilational Symmetry-Breaking in Thermodynamics
• Examining the justification for the introduction of a fermion localization function
• Pseudogap regime of a two-dimensional uniform Fermi gas
• Structural properties of bosonic He clusters with N=2-10 for different potential models at the physical point and at unitarity
• Maxwell relation between entropy and atom-atom pair correlation
• Nuclear three-body short-range correlations in coordinate space
• Scale Invariance in the Lowest Landau Level
• Tan's universal contact and collective oscillations of strongly interacting Fermi gases
• Tan's adiabatic sweep theorem from the variational theorem for the scattering length
• Kovtun-Son-Starinets Conjecture and Effects of Mass Imbalance in the Normal State of an Ultracold Fermi Gas in the BCS-BEC Crossover Region
• Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions
• BCS-BEC crossover of the strongly interacting ${}^6$Li-${}^{40}$K mixture
• How to measure the free energy and partition function from atom-atom correlations
• Radio-Frequency Spectroscopy and the Dimensional Crossover in Interacting Spin-Polarized Fermi Gases
• Universality and tails of long range interactions in one dimension
• Measurement of $p$-wave contacts in an ultracold Fermi gas of ${}^6$Li atoms
• Thermodynamic Properties of Universal Fermi Gases
• Hybrid-pair superfluidity in a strongly driven Fermi gas
• Dilute Fermi and Bose Gases
• Universal Relations for Fermions with Large Scattering Length
• Quasiclassical molecular dynamics for the dilute Fermi gas at unitarity
• Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas
• Repulsive Fermi and Bose Polarons in Quantum Gases
• Dynamical probing of high-order spin coherence in one-dimensional mixtures
• Two-Body Contact Dynamics in a Bose Gas near a Fano-Feshbach Resonance
• Efimov Effect in Long-range Quantum Spin Chains
• Energetics of three interacting mass-imbalanced bodies in a three-dimensional spherical harmonic trap
• Effects of dilute neutron matter on the neutron star crust equation of state
• Exact Thermodynamics For Weakly Interacting Normal-Phase Quantum Gases: Equations of State For All Partial Waves
• Universal scattering phase shift in the presence of spin-orbit coupling
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
• Achieving one-dimensionality with attractive fermions
• Two-body contact of a Bose gas near the superfluid--Mott-insulator transition
• The variational theorem for the scattering length in low dimensions and its applications to universal systems
• Toward an automated-algebra framework for high orders in the virial expansion of quantum matter
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Adiabatic sweep theorem for three-dimensional dipolar Bose gases
• An Effective Series Expansion to the Equation of State of Unitary Fermi Gases
• Predicted Measurements of the Tensor-to-Scalar Transition in the CLAS12 Nuclear Targets Experiment
• Quantum N-Boson States and Quantized Motion of Solitonic Droplets: Universal Scaling Properties in Low Dimensions
• Single Particle Spectroscopies of $p$-wave and $d$-wave Interacting Bose Gases in Normal Phase
• BEC-BCS Crossover with Feshbach Resonance for a Three-Hyperfine-Species Model
• The normal state of attractive Fermi gases from coupled-cluster theory
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Universal Bound States in Long-range Spin Chains with an Impurity
• Dimer-projection contact and the clock shift of a unitary Fermi gas
• Local energy density functional for superfluid Fermi gases from effective field theory
• Competition of light- and phonon-dressing in microwave-dressed Bose polarons
• Heuristic machinery for thermodynamic studies of SU(N) fermions with neural networks
• Probing non-Gaussian correlations through entanglement generation in a many-body quantum system
• Neutron Star Equation of State with Nucleon Short-Range Correlations: A Concise Review and Open Issues
• Two-band atomic superfluidity in the presence of an orbital Feshbach resonance
• Emergence of Fermi's Golden Rule in the Probing of a Quantum Many-Body System
• Arbitrary interaction quench phenomena in harmonically trapped two-body systems
• Universal Relations in Long-range Quantum Spin Chains
• Exploring beyond-mean-field logarithmic divergences in Fermi-polaron energy