#
45th Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics

## Volume 59, Number 8

##
Monday–Friday, June 2–6, 2014;
Madison, Wisconsin

### Session P2: Invited Session: Strongly Interacting Bose Gases

4:00 PM–6:00 PM,
Thursday, June 5, 2014

Room: Ballroom CD

Chair: Peter Engels, Washington State University

Abstract ID: BAPS.2014.DAMOP.P2.4

### Abstract: P2.00004 : Universality and scaling in the $N$-body sector of Efimov physics

5:30 PM–6:00 PM

Preview Abstract
Abstract

####
Author:

Mario Gattobigio

(Universit\'e de Nice - INLN)

In this talk I will illustrate the universal behavior that we have found
inside the window of Efimov physics for systems made of $N\le 6$
particles~[1]. We
have solved the Schr\"odinger equation of the few-body systems using different
potentials, and we have changed the potential parameters in such a way to
explore a range of two-body scattering length, $a$, around the unitary limit,
$|a| \rightarrow \infty$. The ground- ($E_N^0$) and excited-state ($E^1_N)$ energies have been
analyzed by means of a recent-developed method which allows to remove
finite-range effects~[2]. In this way we show that
the calculated ground- and excited-state energies collapse over the same
universal curve obtained in the zero-range three-body systems.
Universality and scaling are reminiscent of critical
phenomena; in that
framework, the critical point is mapped onto a fixed point of the
Renormalization Group (RG) where the system displays scale-invariant (SI)
symmetry.
A consequence of SI symmetry is the scaling of the
observables: for different materials, in the same class of universality, a
selected observable can be represented as a function of the control parameter
and, provided that both the observable and the control parameter are scaled by
some material-dependent factor, all representations collapse onto a single
universal curve.
Efimov physics is a
more recent example of universality, but in this case the physics is governed by
a limit cycle on the RG flow with the emergence of a discrete scale invariance
(DSI).
The scaling of the few-body energies can be interpreted
as follow:
few-body systems (at least up to $N=6$), inside the
Efimov window, belong to the same class of universality, which is governed
by the limit cycle.
These results can be summarized by the following formula
\begin{equation}
E_N^n/E_2 = \tan^2\xi \\
\qquad
\kappa^n_N a_B + \Gamma^n_N =
\frac{\mathrm{e}^{-\Delta(\xi)/2s_0}}{\cos\xi}\,.
\end{equation}
where the function $\Delta(\xi)$ is universal and it is determined by the
three-body physics, and $s_0=1.00624$. The
parameter $\kappa^n_N$ appears as a scale parameter and the shift $\Gamma_n^N$
is a finite-range scale parameter introduced to take into account finite-range
corrections~[2].\\[4pt]
[1] M. Gattobigio and A. Kievsk, arXiv:1309.1927 (2013).\\[0pt]
[2] A. Kievsky and M. Gattobigio, Phys. Rev. A {\bf 87}, 052719 (2013).

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2014.DAMOP.P2.4