Photonic crystals in biology

Poster Session, Tuesday, June 15
Theme A1 - B702
Density profiles and inertia moments of interacting bosons in anisotropic harmonic
confinement
A I. Mese 1 , P Capuzzi 2 , S. Aktas 1 , Z Akdeniz 3 and S E Okan 1
1 Department of Physics, Trakya University, 22030 Edirne, Turkey
2 Consejo Nacional de Investigaciones Cient´ıficas y T´ecnicas and Departamento de F´ısica,FCEyN,
Universidad de Buenos Aires, Buenos Aires, RA-1428, Argentina
3 Physics Department, Piri Reis University, 34940 Tuzla, Istanbul, Turkey
Abstract— We investigate the structural properties of a system, consisting of N strongly
coupled charged bosonic atoms (Rubidium), moving in two dimensions, and interacting through a
repulsive K 0 (r) potential [1] inside anisotropic two-dimensional harmonic traps, with N in the range
from 4 to 9. Increasing the anisotropy of the confinement potential can drive the system from a twodimensional
(2D) to a one-dimensional (1D) configuration. After that, we calculated inertia moment
depending on the anisotropy parameters and particle numbers.
Interest in a two-dimensional (2D) fluid of charged
bosons was greatly stimulated by the work of Nelson and
Seung [1], who showed that a fluid of flux lines in strongly
type-II superconducting materials can be mapped onto this
model system in statistical mechanics. The interaction
potential law is given by V ( r)
V0K
0(
r / r0
) , with V0
a coupling-strength parameter and K 0 x the modified
Bessel function behaving as lnx at short distances.
Following an early variational Monte Carlo study [2], the
transition between an Abrikosov lattice and a
homogeneous liquid of vortices was studied within this
mapping by means of the dislocation mechanism of
melting [3] and the density functional theory of freezing
[4]. A first-order transition from an Abrikosov lattice to a
bosonic superfluid of entangled vortices has also been
demonstrated by the path-integral Monte Carlo method
[5]. A triangular Abrikosov lattice is, of course, equivalent
to the Wigner lattice for a 2D Coulomb system.
In this work we use this very simple theoretical
method to evaluate the structure of small crystallites of
vortex lines within the Nelson–Seung mapping, by means
of self-consistent variational calculations on the
anisotropic harmonic trapped bosons with repulsive
interactions using a Gaussian wavefunction approximation
[6]. We investigate the density profiles of the ground state
configurations and compare with recent experiment [7]
and published numerical results [8]. In figure 1, we
calculate inertia moment as a function of coupling constant
for N=4, 5, 6 and 9 particles.
I x
/ I y
I x /I y
80
70
60
50
40
30
20
10
= 1.0
= 0.9
= 0.8
= 0.7
= 0.6
= 0.5
= 0.4
= 0.3
= 0.2
= 0.1
0
0 1 2 3 4 5 6
V0
/ w
100
80
60
40
20
0
= 1.0
= 0.9
= 0.8
= 0.7
= 0.6
= 0.5
= 0.4
= 0.3
= 0.2
= 0.1
0 1 2 3 4 5 6
V0
/ w
a) b)
I x /I y
90
80
70
60
50
40
30
20
10
0
= 1.0
= 0.9
= 0.8
= 0.7
= 0.6
= 0.5
= 0.4
= 0.3
= 0.2
= 0.1
0 1 2 3 4 5 6
V0
/ w
c) d)
I x / I y
50
40
30
20
10
0
= 1.0
= 0.9
= 0.8
= 0.7
= 0.6
= 0.5
= 0.4
= 0.3
= 0.2
= 0.1
0 1 2 3 4 5 6
Figure 1 We showed the ratio of inertia moments as a function of
coupling parameter for different anisotropy values.
Corresponding author: aihsanmese@yahoo.com
[1] Nelson D R and Seung H S, Phys. Rev. B, 39 9153, 1989
[2] Xing L and Tesanovic Z 1990 Phys. Rev. Lett. 65 794
[3] Ma H-R and Chui S T 1991 Phys. Rev. Lett. 67 505
[4] Sengupta S, Dasgupta C, Krishnamurthy H R, Menon G I and
Ramakrishnan T V 1991 Phys. Rev. Lett. 67 3444
[5] Nordborg H and Blatter G 1997 Phys. Rev. Lett. 79 1925
[6] A. I. Mese et al., J. Phys.: Condens. Matter 20 , 335222, 2008
[7] M Saint Jean and C Guthmann, J. Phys.: Condens. Matter 14
(2002) 13653–13660
[8] S. W. S. Apolinario, B. Partoens, and F. M. Peeters, Physical
Review E 72, 046122 2005
V0
/ w
6th Nanoscience and Nanotechnology Conference, zmir, 2010 262