| 1. |
- Brack, M., et al.
(author)
-
Uniform semiclassical trace formula for U(3) → SO(3) symmetry breaking
- 2005
-
In: Journal of Physics A. - : Institute of Physics (IOP). - 0305-4470 .- 1361-6447. ; 38:46, s. 9941-9967
-
Journal article (peer-reviewed)abstract
- We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term . This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term for small ε in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbit families over the manifold which is covered by the parameters describing their four-fold degeneracy. Then, we obtain an analytical uniform trace formula for arbitrary ε which in the limit of strong perturbations (or high energy) asymptotically goes over into the correct trace formula of the full anharmonic system with SO(3) symmetry, and in the limit ε (or energy) →0 restores the HO trace formula with U(3) symmetry. We demonstrate that the gross-shell structure of this anharmonically perturbed system is dominated by the two-fold degenerate diameter and circular orbits, and not by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios ωr:ωφ ≤ N:M of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential V(r) ∝ r4.
|
|
| 2. |
|
|
| 3. |
- Cremon, Jonas, et al.
(author)
-
Rotational properties of a mixture of two Bose gases
- 2008
-
In: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 10
-
Journal article (peer-reviewed)abstract
- A rotating, two-component Bose-Einstein condensate is shown to exhibit vortices of multiple quantization, which are possible due to the interatomic interactions between the two species. Also, persistent currents are absent in this system. Finally, the order parameter has a very simple structure for a range of angular momenta.
|
|
| 4. |
- Kavoulakis, Georgios, et al.
(author)
-
Superfluidity in a gas of strongly interacting bosons
- 2006
-
In: Europhysics letters. - : Institute of Physics (IOP). - 0295-5075 .- 1286-4854. ; 76:2, s. 215-221
-
Journal article (peer-reviewed)abstract
- We consider small systems of bosonic atoms rotating in a toroidal trap. Using the method of exact numerical diagonalization of the many-body Hamiltonian, we examine the transition from the Bose-Einstein condensed state to the Tonks-Girardeau state. The system supports persistent currents in a wide range between the two limits, even in the absence of Bose-Einstein condensation.
|
|
| 5. |
- Manninen, Matti, et al.
(author)
-
Electron-Hole Duality and Vortex Rings in Quantum Dots
- 2005
-
In: Physical Review Letters. - 1079-7114. ; 94:10, s. 106405-106409
-
Journal article (peer-reviewed)abstract
- In a quantum-mechanical system, particle-hole duality implies that instead of studying particles, we can get equivalent information by studying the missing particles, the so-called holes. Using this duality picture for fermions in a rotating trap the vortices appear as holes in the Fermi sea. Here we predict that the formation of vortices in quantum dots at high magnetic fields causes oscillations in the energy spectrum which can be experimentally observed using accurate tunneling spectroscopy. We use the duality picture to show that these oscillations are caused by the localization of vortices in rings.
|
|
| 6. |
- Manninen, M., et al.
(author)
-
Vortex rings in two-dimensional harmonic traps
- 2006
-
In: Physica Scripta. - 0031-8949. ; T125, s. 31-36
-
Journal article (peer-reviewed)abstract
- We use the configuration interaction technique to study vortex formation in rotating systems of interacting spinless fermions and bosons trapped in a two-dimensional harmonic potential. In the fermionic case, the vortices appear as holes in the Fermi sea and localize in rings. The yrast spectrum is dominated by rigid rotation of the vortex ring, showing periodic oscillations. The Bose system shows a similar yrast spectrum and vortex formation. This can be explained by a one-to-one correspondence of the fermion and boson many-particle configurations. A simple mean-field model can reproduce the oscillations in the yrast spectrum, but fails to explain the localization of vortices.
|
|
| 7. |
- Reimann, Stephanie, et al.
(author)
-
Rotating quantum liquids crystallize
- 2006
-
In: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 8
-
Journal article (peer-reviewed)abstract
- Small crystallites form when finite quantal systems are set highly rotating. This crystallization is independent of the statistics of the particles, and occurs for both trapped bosons and fermions. The spin degree of freedom does not change the tendency for localization. In a highly rotating state, the strongly correlated bosonic and fermionic systems approach to that of classical particles.
|
|
| 8. |
- Reimann, Stephanie, et al.
(author)
-
Vortex localization in rotating clouds of bosons and fermions
- 2006
-
In: Physical Review A. ; 74:4
-
Journal article (peer-reviewed)abstract
- Finite quantal systems at high angular momenta may exhibit vortex formation and localization. These phenomena occur independent of the statistics of the repulsively interacting particles, which may be of bosonic or fermionic nature. We analyze the relation between vortex localization and formation of stable Wigner molecules at high angular momenta in the view of particle-hole duality. Trial wave functions for the vortex states and the corresponding fermion-boson relations are discussed.
|
|
| 9. |
- Rontani, Massimo, et al.
(author)
-
Cold Fermionic Atoms in Two-Dimensional Traps: Pairing versus Hund's Rule
- 2009
-
In: Physical Review Letters. - 1079-7114. ; 102:6, s. 1-060401
-
Journal article (peer-reviewed)abstract
- The microscopic properties of few interacting cold fermionic atoms confined in a two-dimensional (2D) harmonic trap are studied by numerical diagonalization. For repulsive interactions, a strong shell structure dominates, with Hund's rule acting at its extreme for the midshell configurations. In the attractive case, odd-even oscillations due to pairing occur simultaneously with deformations in the internal structure of the ground states, as seen from pair correlation functions.
|
|
| 10. |
- Räsänen, Esa, et al.
(author)
-
Giant vortices in rotating electron droplets
- 2006
-
In: Physical Review B. Condensed Matter and Materials Physics. ; 73:23, s. 235324-235330
-
Journal article (peer-reviewed)abstract
- We predict the formation of giant vortices in quasi-two-dimensional quantum dots at high magnetic fields, i.e., in rapidly rotating electron droplets. Our numerical results for quantum dots confined by a flat, anharmonic potential show ground states where vortices are accumulated in the center of the dot, thereby leading to large cores in the electron and current densities. The phenomenon is analogous to what was recently found in rotating Bose-Einstein condensates. The giant-vortex states leave measurable signatures in the ground-state energetics. The conditions for the giant-vortex formation as well as the internal structure of the vortex cores are discussed.
|
|
| 11. |
- Toreblad, Maria, et al.
(author)
-
Finite boson and fermion systems under extreme rotation: edge reconstruction and vortex formation
- 2006
-
In: Journal of Physics B: Atomic, Molecular and Optical Physics. - : IOP Publishing. - 0953-4075 .- 1361-6455. ; 39:12, s. 2721-2735
-
Journal article (peer-reviewed)abstract
- Vortices can form when finite quantal systems are set rotating. In the limit of small particle numbers, the vortex formation in a harmonically trapped fermion system, with repulsively interacting particles, shows similarities to the corresponding boson system, with vortices entering the rotating cloud for increasing rotation. For a larger number of fermions, N greater than or similar to 15, the fermion vortices compete and co-exist with (Chamon-Wen) edge-reconstructed ground states, forcing some ground states, as for example the central single vortex, into the spectrum of excited states. Experimentally, the fermion system could, for instance, be electrons in a semiconductor heterostructure, a quantum dot, and the corresponding boson system, a Bose-Einstein condensate in a magneto optical trap.
|
|
| 12. |
- Yu, Yongle, et al.
(author)
-
Supershell structure in trapped dilute Fermi gases
- 2005
-
In: Physical Review A. Atomic, Molecular, and Optical Physics. - : American Physical Society. - 1050-2947 .- 1094-1622. ; 72:5
-
Journal article (peer-reviewed)abstract
- We show that a dilute harmonically trapped two-component gas of fermionic atoms with a weak repulsive interaction has a pronounced super-shell structure: The shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the "magic numbers" occurring between the beat nodes by half a period. The length and amplitude of this beating mode depend on the strength of the interaction. We give a simple interpretation of the beat structure in terms of a semiclassical trace formula for the symmetry breaking U(3)→SO(3).
|
|
| 13. |
- Ögren, Magnus, 1977-, et al.
(author)
-
On the spin asymmetry of ground states in trapped two-component Fermi gases with repulsive interactions
- 2007
-
In: Journal of Physics B. - : Institute of Physics (IOP). - 0953-4075 .- 1361-6455. ; 40:13, s. 2653-2660
-
Journal article (peer-reviewed)abstract
- We examine the spin asymmetry of ground states for two-dimensional, harmonically trapped two-component gases of fermionic atoms at zero temperature with weakly repulsive short-range interactions. Our main result is that, in contrast to the three-dimensional case, in two dimensions a non-trivial spin-asymmetric phase can only be caused by the shell structure. A simple, qualitative description is given in terms of an approximate single-particle model, comparing well to the standard results of Hartree-Fock or direct diagonalization methods.
|
|
| 14. |
- Ögren, Magnus, 1977-, et al.
(author)
-
Super-shell structure in harmonically trapped fermionic gases and its semi-classical interpretation
- 2006
-
In: Physica Scripta. - : Royal Swedish Academy of Sciences. - 0031-8949 .- 1402-4896. ; :T125, s. 37-40
-
Journal article (peer-reviewed)abstract
- It was recently shown in self-consistent Hartree–Fock calculations that a harmonically trapped dilute gas of fermionic atoms with a repulsive two-body interaction exhibits a pronounced super-shell structure: the shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the 'magic numbers' occurring between the beat nodes by half a period. The length and amplitude of the beating mode depends on the strength of the interaction. We give a qualitative interpretation of the beat structure in terms of a semi-classical trace formula that uniformly describes the symmetry breaking U(3) → SO(3) in a three-dimensional harmonic oscillator potential perturbed by an anharmonic term ∝ r 4 with arbitrary strength. We show that at low Fermi energies (or particle numbers), the beating gross-shell structure of this system is dominated solely by the twofold degenerate circular and (diametrically) pendulating orbits.
|
|
