Scattering Hypervolume of Fermions in Two Dimensions
- URL: http://arxiv.org/abs/2205.02658v2
- Date: Sun, 31 Jul 2022 12:50:37 GMT
- Title: Scattering Hypervolume of Fermions in Two Dimensions
- Authors: Zipeng Wang and Shina Tan
- Abstract summary: We define the three-body scattering hypervolume $D_F$ for identical spin-polarized fermions in two dimensions.
We derive the expansions of such a wave function when three fermions are far apart or one pair and the third fermion are far apart.
We also calculate the shifts of energy and of pressure of spin-polarized two-dimensional Fermi gases due to a nonzero $D_F$ and the three-body recombination rate of spin-polarized ultracold atomic Fermi gases in two dimensions.
- Score: 8.35070936044077
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We define the three-body scattering hypervolume $D_F$ for identical
spin-polarized fermions in two dimensions, by considering the wave function of
three such fermions colliding at zero energy and zero orbital angular momentum.
We derive the asymptotic expansions of such a wave function when three fermions
are far apart or one pair and the third fermion are far apart, and $D_F$
appears in the coefficients of such expansions. For weak interaction
potentials, we derive an approximate formula of $D_F$ by using the Born
expansion. We then study the shift of energy of three such fermions in a large
periodic area due to $D_F$. This shift is proportional to $D_F$ times the
square of the area of the triangle formed by the momenta of the fermions. We
also calculate the shifts of energy and of pressure of spin-polarized
two-dimensional Fermi gases due to a nonzero $D_F$ and the three-body
recombination rate of spin-polarized ultracold atomic Fermi gases in two
dimensions.
Related papers
- Measuring pair correlations in Bose and Fermi gases via atom-resolved microscopy [28.441455845282068]
We demonstrate atom-resolved detection of itinerant bosonic $23$Na and fermionic $6$Li quantum gases.
In contrast to prior work on lattice-trapped gases, here we realize microscopy of quantum gases in the continuum.
Our technique opens the door to the atom-resolved study of strongly correlated quantum gases of bosons, fermions, and their mixtures.
arXiv Detail & Related papers (2024-11-13T17:05:44Z) - Hamiltonian for a Bose gas with Contact Interactions [49.1574468325115]
We study the Hamiltonian for a Bose gas in three dimensions of $N geq 3$ spinless particles interacting via zero-range or contact interactions.
arXiv Detail & Related papers (2024-03-19T10:00:12Z) - Three-body scattering area for particles with infinite or zero scattering length in two dimensions [3.345575993695074]
We find that the ground state energy per particle of a zero-temperature dilute Bose gas with finite-range interactions is approximately $frachbar2 D 6mrho2$.
We derive a formula for the three-body recombination rate constant of the many-boson system in terms of the imaginary part of $D$.
arXiv Detail & Related papers (2024-02-03T16:24:40Z) - Energetics of the dissipative quantum oscillator [22.76327908349951]
We discuss some aspects of the energetics of a quantum Brownian particle placed in a harmonic trap.
Based on the fluctuation-dissipation theorem, we analyze two distinct notions of thermally-averaged energy.
We generalize our analysis to the case of the three-dimensional dissipative magneto-oscillator.
arXiv Detail & Related papers (2023-10-05T15:18:56Z) - The three-body scattering hypervolume of identical fermions in one
dimension [8.35070936044077]
We study the zero-energy collision of three identical spin-polarized fermions with short-range interactions in one dimension.
We derive the expansions of the three-body wave function when the three fermions are far apart or one pair and the third fermion are far apart.
We calculate the shifts of energy and of pressure of spin-polarized one-dimensional Fermi gases due to a nonzero $D_F$ and the three-body recombination rate in one dimension.
arXiv Detail & Related papers (2023-02-27T11:43:03Z) - Measurement phase transitions in the no-click limit as quantum phase
transitions of a non-hermitean vacuum [77.34726150561087]
We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians.
We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
arXiv Detail & Related papers (2023-01-18T09:26:02Z) - Coherent transfer of the transverse momentum of an optical vortex beam
to the motion of a single trapped ion [22.42090005507693]
We demonstrate the excitation, using a structured light beam carrying orbital angular momentum, of the center of mass motion of a single atom.
We characterize the coherent interaction by an effective transverse Lamb-Dicke factor $etamathrmexp_perp62(5)$ which is in agreement with our theoretical prediction $etamathrmtheo_perp57(1)$
arXiv Detail & Related papers (2022-06-10T06:15:08Z) - Two-body continuum states in non-integer geometry [0.0]
Wave functions, phase shifts and corresponding elastic cross sections are investigated for two short-range interacting particles in an external field.
We derive analytic expressions for scattering lengths and phase shifts using a square-well potential.
We show that the phase shifts are the same in both methods.
arXiv Detail & Related papers (2022-03-02T14:26:06Z) - Wave functions for high-symmetry, thin microstrip antennas and
two-dimensional quantum boxes [48.7576911714538]
For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions.
In two spatial dimensions, the symmetry of the box or microstrip antenna is an important feature that has often been overlooked in the literature.
arXiv Detail & Related papers (2021-08-18T00:57:42Z) - Three-Body Scattering Hypervolume of Particles with Unequal Masses [8.35070936044077]
We analyze the collision of three particles with arbitrary mass ratio at zero collision energy.
We generalize the three-body scattering hypervolume $D$ first defined for identical bosons in 2008.
We derive some properties of a two-component Bose gas with two-body scattering lengths.
arXiv Detail & Related papers (2021-03-25T14:29:44Z) - Field-theoretical aspects of one-dimensional Bose and Fermi gases with
contact interactions [0.0]
We investigate local quantum field theories for 1D Bose and Fermi gases with contact interactions.
Because of this three-body coupling, the three-body contact characterizing a local correlation appears in the energy relation for fermions.
The triads for the Tonks-Girardeau gas, which is a Bose gas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed.
arXiv Detail & Related papers (2020-11-24T09:04:03Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.