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Superfluidity and Chaos in low dimensional circuits.

Arwas G, Vardi A, Cohen D - Sci Rep (2015)

Bottom Line: Below we show that the standard Landau and Bogoliubov superfluidity criteria fail in low-dimensional circuits.Proper determination of the superfluidity regime-diagram must account for the crucial role of chaos, an ingredient missing from the conventional stability analysis.Accordingly, we find novel types of superfluidity, associated with irregular or chaotic or breathing vortex states.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel.

ABSTRACT
The hallmark of superfluidity is the appearance of "vortex states" carrying a quantized metastable circulating current. Considering a unidirectional flow of particles in a ring, at first it appears that any amount of scattering will randomize the velocity, as in the Drude model, and eventually the ergodic steady state will be characterized by a vanishingly small fluctuating current. However, Landau and followers have shown that this is not always the case. If elementary excitations (e.g. phonons) have higher velocity than that of the flow, simple kinematic considerations imply metastability of the vortex state: the energy of the motion cannot dissipate into phonons. On the other hand if this Landau criterion is violated the circulating current can decay. Below we show that the standard Landau and Bogoliubov superfluidity criteria fail in low-dimensional circuits. Proper determination of the superfluidity regime-diagram must account for the crucial role of chaos, an ingredient missing from the conventional stability analysis. Accordingly, we find novel types of superfluidity, associated with irregular or chaotic or breathing vortex states.

No MeSH data available.


Related in: MedlinePlus

Superfluidity regime diagram for M site circuits.(a) M = 3 ring with N = 37 particles; (b) M = 4 ring with N = 16 particles; (c) M = 5 ring with N = 11 particles. The model parameters are (Φ, u). The I of the state that carries maximal current is imaged at the background. We observe that the stability regions (large current) are not as expected from the linear stability analysis: the solid line indicates the energetic-stability border; the dashed lines indicate the dynamical stability borders. For clarity we also include a negative u region which is in fact a duplication of the upper sheet. In (a) the dotted line indicates the “swap” transition (see text); and the dots labeled (a–f) mark (Φ, u) coordinates that are used in Fig. 3 to demonstrate the different regimes.
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f1: Superfluidity regime diagram for M site circuits.(a) M = 3 ring with N = 37 particles; (b) M = 4 ring with N = 16 particles; (c) M = 5 ring with N = 11 particles. The model parameters are (Φ, u). The I of the state that carries maximal current is imaged at the background. We observe that the stability regions (large current) are not as expected from the linear stability analysis: the solid line indicates the energetic-stability border; the dashed lines indicate the dynamical stability borders. For clarity we also include a negative u region which is in fact a duplication of the upper sheet. In (a) the dotted line indicates the “swap” transition (see text); and the dots labeled (a–f) mark (Φ, u) coordinates that are used in Fig. 3 to demonstrate the different regimes.

Mentions: In Fig. 1 we plot the numerically determined (Φ, u) regime diagram for the superfluidity of rings with M = 3, 4, 5 sites. Image colors depict the current for the eigenstate that carries maximal current. The solid and dashed lines indicate the energetic and the dynamical stability borders, as determined from the BdG analysis (see below). The regime diagrams do not agree with the traditional analysis: For the M = 3 ring superfluidity persists beyond the border of dynamical stability, while for M > 3 the dynamical stability condition is not sufficient.


Superfluidity and Chaos in low dimensional circuits.

Arwas G, Vardi A, Cohen D - Sci Rep (2015)

Superfluidity regime diagram for M site circuits.(a) M = 3 ring with N = 37 particles; (b) M = 4 ring with N = 16 particles; (c) M = 5 ring with N = 11 particles. The model parameters are (Φ, u). The I of the state that carries maximal current is imaged at the background. We observe that the stability regions (large current) are not as expected from the linear stability analysis: the solid line indicates the energetic-stability border; the dashed lines indicate the dynamical stability borders. For clarity we also include a negative u region which is in fact a duplication of the upper sheet. In (a) the dotted line indicates the “swap” transition (see text); and the dots labeled (a–f) mark (Φ, u) coordinates that are used in Fig. 3 to demonstrate the different regimes.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4551964&req=5

f1: Superfluidity regime diagram for M site circuits.(a) M = 3 ring with N = 37 particles; (b) M = 4 ring with N = 16 particles; (c) M = 5 ring with N = 11 particles. The model parameters are (Φ, u). The I of the state that carries maximal current is imaged at the background. We observe that the stability regions (large current) are not as expected from the linear stability analysis: the solid line indicates the energetic-stability border; the dashed lines indicate the dynamical stability borders. For clarity we also include a negative u region which is in fact a duplication of the upper sheet. In (a) the dotted line indicates the “swap” transition (see text); and the dots labeled (a–f) mark (Φ, u) coordinates that are used in Fig. 3 to demonstrate the different regimes.
Mentions: In Fig. 1 we plot the numerically determined (Φ, u) regime diagram for the superfluidity of rings with M = 3, 4, 5 sites. Image colors depict the current for the eigenstate that carries maximal current. The solid and dashed lines indicate the energetic and the dynamical stability borders, as determined from the BdG analysis (see below). The regime diagrams do not agree with the traditional analysis: For the M = 3 ring superfluidity persists beyond the border of dynamical stability, while for M > 3 the dynamical stability condition is not sufficient.

Bottom Line: Below we show that the standard Landau and Bogoliubov superfluidity criteria fail in low-dimensional circuits.Proper determination of the superfluidity regime-diagram must account for the crucial role of chaos, an ingredient missing from the conventional stability analysis.Accordingly, we find novel types of superfluidity, associated with irregular or chaotic or breathing vortex states.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel.

ABSTRACT
The hallmark of superfluidity is the appearance of "vortex states" carrying a quantized metastable circulating current. Considering a unidirectional flow of particles in a ring, at first it appears that any amount of scattering will randomize the velocity, as in the Drude model, and eventually the ergodic steady state will be characterized by a vanishingly small fluctuating current. However, Landau and followers have shown that this is not always the case. If elementary excitations (e.g. phonons) have higher velocity than that of the flow, simple kinematic considerations imply metastability of the vortex state: the energy of the motion cannot dissipate into phonons. On the other hand if this Landau criterion is violated the circulating current can decay. Below we show that the standard Landau and Bogoliubov superfluidity criteria fail in low-dimensional circuits. Proper determination of the superfluidity regime-diagram must account for the crucial role of chaos, an ingredient missing from the conventional stability analysis. Accordingly, we find novel types of superfluidity, associated with irregular or chaotic or breathing vortex states.

No MeSH data available.


Related in: MedlinePlus