Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFourth- and fifth-order virial expansion of harmonically trapped fermions at unitarity
67
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-1/2 fermions in the unitary limit, confined in an isotropic harmonic potential. We present results for said coefficients as a function of trapping frequency (or, equivalently, temperature), which compare favorably with previous Monte Carlo calculations (available only at fourth order) as well as with our previous estimates in the untrapped limit (high temperature, low frequency). We use our estimates of the virial expansion, together with resummation techniques, to calculate the compressibility and spin susceptibility.
rate research
Read More
In the current era of precision quantum many-body physics, one of the most scrutinized systems is the unitary limit of the nonrelativistic spin-$1/2$ Fermi gas, due to its simplicity and relevance for atomic, condensed matter, and nuclear physics. The thermodynamics of this strongly correlated system is determined by universal functions which, at high temperature, are governed by universal virial coefficients $b_n$ that capture the effects of the $n$-body system on the many-body dynamics. Currently, $b_2$ and $b_3$ are well understood, but the situation is less clear for $b_4$, and no predictions have been made for $b_5$. To answer these open questions, we implement a nonperturbative analytic approach based on the Trotter-Suzuki factorization of the imaginary-time evolution operator, using progressively finer temporal lattice spacings. Implementing these factorizations and automated algebra codes, we obtain the interaction-induced change $Delta b_n$ from weak coupling to unitarity. At unitarity, we find: $Delta b_3 = -0.356(4)$, in agreement with previous results; $Delta b_4 = 0.062(2)$, in agreement with all previous theoretical estimates but at odds with experimental determinations; and $Delta b_5 = 0.078(6)$, which is a prediction. We show the impact of those answers on the density equation of state and Tan contact, and track their origin back to their polarized and unpolarized components.
Using a leading-order semiclassical approximation, we calculate the third- and fourth-order virial coefficients of nonrelativistic spin-1/2 fermions in a harmonic trapping potential in arbitrary spatial dimensions, and as functions of temperature, trapping frequency and coupling strength. Our simple, analytic results for the interaction-induced changes $Delta b_3$ and $Delta b_4$ agree qualitatively, and in some regimes quantitatively, with previous numerical calculations for the unitary limit of three-dimensional Fermi gases.
The virial expansion characterizes the high-temperature approach to the quantum-classical crossover in any quantum many-body system. Here, we calculate the virial coefficients up to the fifth-order of Fermi gases in 1D, 2D, and 3D, with attractive contact interactions, as relevant for a variety of applications in atomic and nuclear physics. To that end, we discretize the imaginary-time direction and calculate the relevant canonical partition functions. In coarse discretizations, we obtain analytic results featuring relationships between the interaction-induced changes $Delta b_3$, $Delta b_4$, and $Delta b_5$ as functions of $Delta b_2$, the latter being exactly known in many cases by virtue of the Beth-Uhlenbeck formula. Using automated-algebra methods, we push our calculations to progressively finer discretizations and extrapolate to the continuous-time limit. We find excellent agreement for $Delta b_3$ with previous calculations in all dimensions and we formulate predictions for $Delta b_4$ and $Delta b_5$ in 1D and 2D. We also provide, for a range of couplings,the subspace contributions $Delta b_{31}$, $Delta b_{22}$, $Delta b_{41}$, and $Delta b_{32}$, which determine the equation of state and static response of polarized systems at high temperature. As a performance check, we compare the density equation of state and Tan contact with quantum Monte Carlo calculations, diagrammatic approaches, and experimental data where available. Finally, we apply Pade and Pade-Borel resummation methods to extend the usefulness of the virial coefficients to approach and in some cases go beyond the unit-fugacity point.
Using a coarse temporal lattice approximation, we calculate the first few terms of the virial expansion of a three-species fermion system with a three-body contact interaction in $d$ spatial dimensions, both in homogeneous space as well as in a harmonic trapping potential of frequency $omega$. Using the three-body problem to renormalize, we report analytic results for the change in the fourth- and fifth-order virial coefficients $Delta b_4$ and $Delta b_5$ as functions of $Delta b_3$. Additionally, we argue that in the $omega to 0$ limit the relationship $b_n^text{T} = n^{-d/2} b_n$ holds between the trapped (T) and homogeneous coefficients for arbitrary temperature and coupling strength (not merely in scale-invariant regimes). Finally, we point out an exact, universal (coupling- and frequency-independent) relationship between $Delta b_3^text{T}$ in 1D with three-body forces and $Delta b_2^text{T}$ in 2D with two-body forces.
We investigate the Zeldovich effect in the context of ultra-cold, harmonically trapped quantum gases. We suggest that currently available experimental techniques in cold-atoms research offer an exciting opportunity for a direct observation of the Zeldovich effect without the difficulties imposed by conventional condensed matter and nuclear physics studies. We also demonstrate an interesting scaling symmetry in the level rearragements which has heretofore gone unnoticed.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
