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2022 ◽  
Vol 105 (1) ◽  
Kyoshiro Sakaguchi ◽  
Keisuke Jimbo ◽  
Hiroki Saito

2022 ◽  
Vol 4 (1) ◽  
Akhilesh Kumar Verma ◽  
Rahul Pandit ◽  
Marc E. Brachet

2022 ◽  
Vol 12 (1) ◽  
V. A. Stephanovich ◽  
W. Olchawa

AbstractWe study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under “fractional” we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy index $$\alpha$$ α . We speculate that the latter substitution corresponds to phenomenological account for disorder in a system. Using analytical (variational and perturbative) and numerical arguments, we have shown that while in the case of Schrödinger equation with the ordinary Laplacian (corresponding to Lévy index $$\alpha =2$$ α = 2 ), the soliton is unstable, even infinitesimal difference $$\alpha$$ α from 2 immediately stabilizes the soliton texture. Our analytical and numerical investigations of $$\omega (N)$$ ω ( N ) dependence ($$\omega$$ ω is soliton frequency and N its mass) show (within the famous Vakhitov–Kolokolov criterion) the stability of our soliton texture in the fractional $$\alpha <2$$ α < 2 case. Direct numerical analysis of the linear stability problem of soliton texture also confirms this point. We show analytically and numerically that fractional Schrödinger equation with quintic nonlinearity admits the existence of (stable) soliton textures at $$2/3<\alpha <2$$ 2 / 3 < α < 2 , which is in accord with existing literature data. These results may be relevant to both Bose–Einstein condensates in cold atomic gases and optical solitons in the disordered media.

2022 ◽  
Vol 128 (2) ◽  
S. Musolino ◽  
H. Kurkjian ◽  
M. Van Regemortel ◽  
M. Wouters ◽  
S. J. J. M. F. Kokkelmans ◽  

2022 ◽  
Afifa Yedjour ◽  
Hanane Benmahdjoub ◽  
Abdelaali Boudjemaa

Abstract We study the diffusion of an expanding Bose-Einstein condensate released from a harmonic trap in a three-dimensional speckle disorder potential. To this end, we use the first Born approximation and examine the density profiles at short and long times. Analytical results are presented in different regimes. The spatiotemporal evolution of the density profiles is examined. We find that at long times and for a fixed disorder strength, the profile of the atomic average density decreases in power law. The time evolution of the typical size of the condensate is explored numerically.

2022 ◽  
Vol 47 (1) ◽  
Enric Pérez ◽  
Joana Ibáñez

AbstractIn this paper, we deal with the historical origins of Fermi–Dirac statistics, focusing on the contribution by Enrico Fermi of 1926. We argue that this statistics, as opposed to that of Bose–Einstein, has been somewhat overlooked in the usual accounts of the old quantum theory. Our main objective is to offer a critical analysis of Fermi’s seminal paper and its immediate impact. Secondly, we are also interested in assessing the status of the particle concept in the years 1926–1927, especially regarding the germ of quantum indistinguishability. We will see, for example, that the first applications of the Fermi–Dirac statistics to the study of metals or stellar matter had a technical nature, and that their main instigators barely touched upon interpretative matters. Finally, we will discuss the reflections and remarks made in these respects in two famous events in physics of 1927, the Como conference and the fifth Solvay congress.

Satadal Datta ◽  
Uwe R Fischer

Abstract The dynamics of sound in a fluid is intrinsically nonlinear. We derive the consequences of this fact for the analogue gravitational field experienced by sound waves, by first describing generally how the nonlinearity of the equation for phase fluctuations back-reacts on the definition of the background providing the effective space-time metric. Subsequently, we use the analytical tool of Riemann invariants in one-dimensional motion to derive source terms of the effective gravitational field stemming from nonlinearity. Finally, we show that the consequences of nonlinearity we derive can be observed with Bose-Einstein condensates in the ultracold gas laboratory.

2022 ◽  
Vol 105 (1) ◽  
Ling-Zheng Meng ◽  
Shu-Wen Guan ◽  
Li-Chen Zhao

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