Tan's contact as an indicator of completeness and self-consistency of a theory

Abstract

It is well known that, Tan's contact could be calculated by using any of following three methods: by the asymptotic behavior of momentum distribution; by Tan's adiabatic sweep theorem; or by the operator product expansion as an expectation value of the interaction term. We argue that, if a theory describing Bose (or Fermi) system with the only contact interaction is self consistent, then it should lead to the same result in all three cases. As an example we considered MFT based approaches and established that among existing approximations of MFT, the Hartree - Fock - Bogoliubov (HFB) approach is the most self consistent. Actually, HFB is able to describe existing experimental data on Tan's contact for dilute Bose gas, but fails to predict its expected behavior at large gas parameter $(\gamma >0.015)$. So, for appropriate description of properties of a Bose gas even at zero temperature, this approximation needs to be expanded by taking into account fluctuations in higher order then the second one.

arXiv comment20 pages, 6 figures

References in corpus (25)

• Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Theory of the Weakly Interacting Bose Gas
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Finite Temperature Models of Bose-Einstein Condensation
• Verification of universal relations in a strongly interacting Fermi gas
• Contact Measurements on Atomic BEC
• Universal dynamics of a degenerate unitary Bose gas
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
• General relations for quantum gases in two and three dimensions. II. Bosons and mixtures
• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Universal Relations for Identical Bosons from 3-Body Physics
• Two and Three-body Contacts in the Unitary Bose Gas
• Particle distribution tail and related energy formula
• Short-Time Operator Product Expansion for rf Spectroscopy of a Strongly-interacting Fermi Gas
• Representative statistical ensembles for Bose systems with broken gauge symmetry
• Momentum-resolved observation of thermal and quantum depletion in an interacting Bose gas
• Transition Temperature for Weakly Interacting Homogeneous Bose Gases
• Path-Integral Ground-State and Superfluid Hydrodynamics of a Bosonic Gas of Hard Spheres
• Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions
• Stability of the homogeneous Bose-Einstein condensate at large gas parameter
• Phase Transitions in Three-Dimensional Bosonic Systems in Optical Lattices

Cited by in corpus (6)

• Breakdown of Tan's relation in lossy one-dimensional Bose gases
• Self-consistent theory of a homogeneous binary Bose mixture with strong repulsive interspecies interaction
• On the survival of the quantum depletion of a condensate after release from a magnetic trap
• Critical behavior of Tan's contact for bosonic systems with a fixed chemical potential
• On the anomalous density of a dilute homogeneous Bose gas
• Hugenholtz -- Pines relations and the critical temperature of a Rabi coupled binary Bose system