Three-body scattering area for particles with infinite or zero scattering length in two dimensions

• URL: http://arxiv.org/abs/2402.02202v2
• Date: Sun, 28 Apr 2024 06:51:45 GMT
• Title: Three-body scattering area for particles with infinite or zero scattering length in two dimensions
• Authors: Junjie Liang, Shina Tan,
• Abstract summary: 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 $D$.
• Score: 3.345575993695074
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive the asymptotic expansions of the wave function of three particles having equal mass with finite-range interactions and infinite or zero two-dimensional scattering length colliding at zero energy and zero orbital angular momentum, from which a three-body parameter $D$ is defined. The dimension of $D$ is length squared, and we call $D$ three-body scattering area. We find that the ground state energy per particle of a zero-temperature dilute Bose gas with these interactions is approximately $\frac{\hbar^2 D }{6m}\rho^2$, where $\rho$ is the number density of the bosons, $m$ is the mass of each boson, and $\hbar$ is Planck's constant over $2\pi$. Such a Bose gas is stable at $D\geq 0$ in the thermodynamic limit, and metastable at $D<0$ in the harmonic trap if the number of bosons is less than $N_{cr}\approx 3.6413 \sqrt{\frac{\hbar}{m\omega |D|}}$, where $\omega$ is the angular frequency of the harmonic trap. If the two-body interaction supports bound states, $D$ typically acquires a negative imaginary part, and we find the relation between this imaginary part and the amplitudes of the pair-boson production processes. We derive a formula for the three-body recombination rate constant of the many-boson system in terms of the imaginary part of $D$.

Related papers

• Klein-Gordon oscillators and Bergman spaces [55.2480439325792]
  We consider classical and quantum dynamics of relativistic oscillator in Minkowski space $mathbbR3,1$. The general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic functions on the K"ahler-Einstein manifold $Z_6$.
  arXiv  Detail & Related papers  (2024-05-23T09:20:56Z)
• Quantum connection, charges and virtual particles [65.268245109828]
  A quantum bundle $L_hbar$ is endowed with a connection $A_hbar$ and its sections are standard wave functions $psi$ obeying the Schr"odinger equation. We will lift the bundles $L_Cpm$ and connection $A_hbar$ on them to the relativistic phase space $T*R3,1$ and couple them to the Dirac spinor bundle describing both particles and antiparticles.
  arXiv  Detail & Related papers  (2023-10-10T10:27:09Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• 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)
• On parametric resonance in the laser action [91.3755431537592]
  We consider the selfconsistent semiclassical Maxwell--Schr"odinger system for the solid state laser. We introduce the corresponding Poincar'e map $P$ and consider the differential $DP(Y0)$ at suitable stationary state $Y0$.
  arXiv  Detail & Related papers  (2022-08-22T09:43:57Z)
• Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity [77.34726150561087]
  We study the Hamiltonian for a system of N identical bosons interacting with an impurity. We introduce a three-body force acting at short distances. The effect of this force is to reduce to zero the strength of the zero-range interaction between two particles.
  arXiv  Detail & Related papers  (2022-02-25T15:34:06Z)
• Three-body recombination in a single-component Fermi gas with $p$-wave interaction [2.6641834518599308]
  We study the three-body recombination of identical fermionic atoms. We show that the rate constant of three-body recombination into weakly bound $p$-wave dimers can be written as $alpha_rm rec propto v5/2R1/2 k_T4.
  arXiv  Detail & Related papers  (2022-01-04T03:55:23Z)
• Ultracold spin-balanced fermionic quantum liquids with renormalized $P$-wave interactions [0.0]
  We consider a spin-balanced degenerate gas of spin-1/2 fermions governed by low-energy $P$-wave interactions. The energy per particle $barcalE$ in the many-body system is calculated by resumming the ladder diagrams.
  arXiv  Detail & Related papers  (2021-07-16T18:00:01Z)
• 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)
• On connection between perturbation theory and semiclassical expansion in quantum mechanics [0.0]
  Perturbation Theory in powers of the coupling constant $g$ and the semiclassical expansion in powers of $hbar1/2$ for the energies coincide. The equations which govern dynamics in two spaces, the Riccati-Bloch equation and the Generalized Bloch equation, respectively, are presented.
  arXiv  Detail & Related papers  (2021-02-09T03:13:56Z)
• Anharmonic oscillator: a solution [77.34726150561087]
  The dynamics in $x$-space and in $(gx)-space corresponds to the same energy spectrum with effective coupling constant $hbar g2$. A 2-classical generalization leads to a uniform approximation of the wavefunction in $x$-space with unprecedented accuracy.
  arXiv  Detail & Related papers  (2020-11-29T22:13:08Z)

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.