Energetics of a strongly correlated Fermi gas
arXiv:cond-mat/0505200 · doi:10.1016/j.aop.2008.03.004
Abstract
The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution: $$E_\text{internal}=\hbar^2ΩC/4πam+\sum_{\vect kσ}(\hbar^2 k^2/2m)(n_{\vect kσ}-C/k^4)$$ where the external potential energy is not included, is the scattering length, is the volume, $n_{\vect kσ}$ is the average number of fermions with wave vector $\vect k$ and spin , and $C\equiv\lim_{\vect k\to\infty} k^4 n_{\vect k\up} =\lim_{\vect k\to\infty} k^4 n_{\vect k\down}$. This result is a \textit{universal identity}. Its proof is facilitated by a novel mathematical idea, which might be of utility in dealing with ultraviolet divergences in quantum field theories. Other properties of this Fermi system, including the short-range structure of the one-body reduced density matrix and the pair correlation function, and the dimer-fermion scattering length, are also studied.
28 pages, 1 figure
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Cited by in corpus (515)
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- Spin incoherent liquid and interaction-driven criticality in 1D Hubbard model
- Probing Goldstino excitation through the tunneling transport in a Bose-Fermi mixture with explicitly broken supersymmetry
- Resonantly interacting -wave Fermi superfluid in two dimensions: Tan's contact and breathing mode
- Ground-state properties of a dilute two-dimensional Bose gas
- Observation of state-to-state hyperfine-changing collision in a Bose-Fermi mixture of Li and K atoms
- Optomechanical Response of a Strongly Interacting Fermi Gas
- Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
- Emergent -wave interactions in orbitally active quasi-two-dimensional Fermi gases
- Photo-excitation measurement of Tan's contact for a strongly interacting Fermi gas
- Fast logarithmic Fourier-Laplace transform of nonintegrable functions
- Numerical study of unitary fermions in one spatial dimension
- Many-body theories of density response for a strongly correlated Fermi gas
- Single-branch theory of ultracold Fermi gases with artificial Rashba spin-orbit coupling
- Contact parameters in two dimensions for general three-body systems
- Spin correlations and entanglement in partially magnetised ensembles of fermions
- Total Energy Dynamics and Asymptotics of the Momentum Distribution Following an Interaction Quench in a Two-component Fermi Gas
- Path-Integral Approach to Scale Anomaly at Finite Temperature
- Neutron matter within QCD sum rules
- Ultracold collisions between two light indistinguishable diatomic molecules: elastic and rotational energy transfer in HD+HD
- Nucleon Short-Range Correlations and High-Momentum Dynamics: Implications on the Equation of State of Dense Matter
- Dynamic virial theorem at nonequilibrium and applications
- Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
- Spectral flow of trimer states of two heavy impurities and one light condensed boson
- Resonance triplet dynamics in the quenched unitary Bose gas
- Three-body contact for fermions. I. General relations
- Boson-fermion pairing and condensation in two-dimensional Bose-Fermi mixtures
- Resonant scattering effect in spectroscopies of interacting atomic gases
- Toward precision Fermi liquid theory in two dimensions
- On nuclear short-range correlations and the zero-energy eigenstates of the Schrodinger equation
- Nuclear three-body short-range correlations in coordinate space
- Synergy between deep neural networks and the variational Monte Carlo method for small clusters
- Single particle momentum distributions for three-bosons in two and three dimensions and dimensional crossover
- Structural properties of bosonic He clusters with N=2-10 for different potential models at the physical point and at unitarity
- Observing Spatial Charge and Spin Correlations in a Strongly-Interacting Fermi Gas
- Temperature dependence of -wave contacts in a harmonically trapped Fermi gas
- Statistical properties of the momentum occupation numbers of the Tonks-Girardeau gas in a harmonic trap
- Examining the justification for the introduction of a fermion localization function
- Self-stabilized Bose polarons
- Tan's adiabatic sweep theorem from the variational theorem for the scattering length
- Tan's universal contact and collective oscillations of strongly interacting Fermi gases
- Exploring the Tan contact term in Yang-Mills theory
- A Composite Fermion Approach to the Ultracold Dilute Fermi Gas
- Dilational Symmetry-Breaking in Thermodynamics
- Scale Invariance in the Lowest Landau Level
- Exact Thermodynamics For Weakly Interacting Normal-Phase Quantum Gases: Equations of State For All Partial Waves
- Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas
- Reflections on dipolar quantum fluids
- BCS-BEC crossover of the strongly interacting Li-K mixture
- Quasiclassical molecular dynamics for the dilute Fermi gas at unitarity
- Universality and tails of long range interactions in one dimension
- Dynamical probing of high-order spin coherence in one-dimensional mixtures
- Two-Body Contact Dynamics in a Bose Gas near a Fano-Feshbach Resonance
- Energetics of three interacting mass-imbalanced bodies in a three-dimensional spherical harmonic trap
- Universal scattering phase shift in the presence of spin-orbit coupling
- Dilute Fermi and Bose Gases
- Repulsive Fermi and Bose Polarons in Quantum Gases
- Thermodynamic Properties of Universal Fermi Gases
- Measurement of -wave contacts in an ultracold Fermi gas of Li atoms
- Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
- Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions
- Radio-Frequency Spectroscopy and the Dimensional Crossover in Interacting Spin-Polarized Fermi Gases
- Systematic study of large-momentum distribution in nuclei with the operator product expansion
- Effective theory for strongly attractive one-dimensional fermions
- Adiabatic sweep theorem for three-dimensional dipolar Bose gases
- The variational theorem for the scattering length in low dimensions and its applications to universal systems
- Losses in interacting quantum gases: ultra-violet divergence and its regularization
- Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
- Toward an automated-algebra framework for high orders in the virial expansion of quantum matter
- Predicted Measurements of the Tensor-to-Scalar Transition in the CLAS12 Nuclear Targets Experiment
- The normal state of attractive Fermi gases from coupled-cluster theory
- An Effective Series Expansion to the Equation of State of Unitary Fermi Gases
- BEC-BCS Crossover with Feshbach Resonance for a Three-Hyperfine-Species Model
- Precision thermodynamics of the strongly interacting Fermi gas in two dimensions
- Two-body contact of a Bose gas near the superfluid--Mott-insulator transition
- Quantum N-Boson States and Quantized Motion of Solitonic Droplets: Universal Scaling Properties in Low Dimensions
- Dimer-projection contact and the clock shift of a unitary Fermi gas
- From few to many body degrees of freedom
- Single Particle Spectroscopies of -wave and -wave Interacting Bose Gases in Normal Phase
- Universal Relations in Long-range Quantum Spin Chains
- 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
- Two-band atomic superfluidity in the presence of an orbital Feshbach resonance
- Local energy density functional for superfluid Fermi gases from effective field theory
- Interaction quenches in Bose gases studied with a time-dependent hypernetted-chain Euler-Lagrange method
- Competition of light- and phonon-dressing in microwave-dressed Bose polarons
- Bounds on quantum Fisher information and uncertainty relations for thermodynamically conjugate variables
- Neutron Star Equation of State with Nucleon Short-Range Correlations: A Concise Review and Open Issues