On the creation of quantized vortex lines in rotating He II

Loffredo, Maria I.; Morato, Laura M.

doi:10.1007/bf02874411

Cited by 65 publications

(39 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The starting point of the following estimates is 6, differentiated with respect to t: Finally, in view of (49), (18), (20), and integration by parts, it holds h» <{ST + S0) f {iplxt + V& + V>t + + iplxx)dx Step 3: combination of the estimates for ip, ipt, and iptt-We combine the estimates (44) and (54) and obtain for some constant f3\ > 0, using (21), …”

Section: Jomentioning

confidence: 99%

See 1 more Smart Citation

Quantum Euler-Poisson systems: global existence and exponential decay

Jüngel¹,

Li²

2004

Quart. Appl. Math.

View full text Add to dashboard Cite

Abstract.A one-dimensional transient quantum Euler-Poisson system for the electron density, the current density, and the electrostatic potential in bounded intervals is considered. The equations include the Bohm potential accounting for quantum mechanical effects and are of dispersive type. They are used, for instance, for the modelling of quantum semiconductor devices. The existence of local-in-time solutions with small initial velocity is proven for general pressure-density functions. If a stability condition related to the subsonic condition for the classical Euler equations is imposed, the local solutions are proven to exist globally in time and tend to the corresponding steady-state solution exponentially fast as the time tends to infinity.

show abstract

Section: Jomentioning

confidence: 99%

“…I n k=1 dxk V p Equations (l)- (2) can be interpreted as the pressureless Euler equations including the quantum Bohm potential <3) 2 \fp They have been used for the modeling of superfluids like Helium II [16,20].…”

Section: Introductionmentioning

confidence: 99%

Quantum Euler-Poisson systems: global existence and exponential decay

Jüngel¹,

Li²

2004

Quart. Appl. Math.

View full text Add to dashboard Cite

show abstract

“…quantum diodes [17,18], quantum dots and nanowires [27], nano-photonics [28,29], ultra-small electronic devices [30]) and micro-plasmas [31]. Quantum transport models similar to the QHD plasma model has also been used in superfluidity [32] and superconductivity [33], as well as the study of metal clusters and nanoparticles, where they are referred to as nonstationary ThomasFermi models [34]. The density functional theory [35,36,37] incorporates electron-electron correlations, which are neglected in the present paper.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Quantum Plasma Physics

Shukła

Eliasson

Shaikh

2009

Astrophysics and Space Science Proceedings

View full text Add to dashboard Cite

Summary.We present simulation studies of the formation and dynamics of dark solitons and vortices, and of nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) dense in quantum electron plasmas. The electron dynamics in the latter is governed by a pair of equations comprising the nonlinear Schrödinger and Poisson system of equations, which conserves electrons and their momentum and energy. Nonlinear fluid simulations are carried out to investigate the properties of fully developed two-dimensional (2D) electron fluid turbulence in a dense Fermi (quantum) plasma. We report several distinguished features that have resulted from our 2D computer simulations of the nonlinear equations which govern the dynamics of nonlinearly interacting electron plasma oscillations (EPOs) in the Fermi plasma. We find that a 2D quantum electron plasma exhibits dual cascades, in which the electron number density cascades towards smaller turbulent scales, while the electrostatic potential forms larger scale eddies. The characteristic turbulent spectrum associated with the nonlinear electron plasma oscillations determined critically by quantum tunneling effect. The turbulent transport corresponding to the large-scale potential distribution is predominant in comparison with the small-scale electron number density variation, a result that is consistent with the classical diffusion theory. The dynamics of the CPEM waves is also governed by a nonlinear schrödinger equation, which is nonlinearly coupled with the nonlinear Schrödinger equation of the EPOs via the relativistic ponderomotive force, the relativistic electron mass increase in the CPEM field, and the electron density fluctuations. The present governing equations in one spatial dimension admit stationary solutions in the form a dark envelope soliton. The dynamics of the latter reveals its robustness. Furthermore, we numerically demonstrate the existence of cylindrically symmetric two-dimensional quantum electron vortices, which survive during collisions. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma.

show abstract

“…), intense laser-solid density plasma experiments [8], and ultrasmall electronic devices [9] [10], carbon nanotubes [11] and quantum diodes [12]. Quantum hydrodynamical models have also revealed important features occurring in superfluidity [13] and superconductivity [14]. We now consider a cylindrical nanowire of radius a and length L a, in such a way that the system can be regarded as quasi one-dimensional along the longitudinal direction.…”

mentioning

confidence: 99%

Nonlocal plasmon excitation in metallic nanostructures

Ali

Terças²,

Mendonça³

2011

Phys. Rev. B

View full text Add to dashboard Cite

We investigate the excitation of electrostatic wakefields in metallic nanostructures (nanowires) due to the propagation of a short electron pulse. For that purpose, a dispersive (nonlocal) dielectric response of the system is considered, accounting for both the finiteness of the system and the quantum (Bohm) difraction of the conduction electron band, generalizing the results obtained previously in the literature [Phys. Rev. Lett. 103, 097403 (2009)]. We discuss on the stability conditions of wakefields and show that the underling mechanism can be useful to investigate new sources of radiation in the extreme-ultra-violet (XUV) range.Experimental techniques [1] have been developed for the fabrication of metallic nanostructures (nanowires) of the order of 10 nm or less, recently receiving a considerable attention of the scientific community. Nanowires, compared to other low-dimensional systems, have two conned directions, still leaving one unconned direction for electrical conduction. Due to their unique density of states, such systems are expected to exhibit significantly different optical, electrical, and magnetic properties from their bulk 3D crystalline counterparts, specially in the limit of small diameters. Even if the number of electrons involved in the relevant features is high, and therefore a continuum description is expected to be adequate, the current models still lack of completeness. One of the most striking cases is related with the dielectric response. It was experimentally shown that anomalous absorption can occur in thin metal films [2] due to the excitation of plasmons [3]. Liu et al. [4] have recently approached this problem for arbitrarily shaped nanostructures, though neglecting the wavenumber dependence in their model. Recently, McMahon et al [5] have introduced the effects of the nonlocal response by adding dispersion terms (proportional to the wavevector k) in the Drude dielectric function of the bulk (conduction) electrons, as described bywhere ∞ (≈ 1) is the value for ω → ∞, ω p and v F stand for the plasma frequency and the electron Fermi velocity, respectively, and γ represents the electron collision frequency. However, it is well known that further quantum mechanical effects [6] are associated with electrons at nanoscales, playing a significant role in the dispersion of collective modes and instabilities, and therefore are expected to play an important role in nanowires, as well. In particular, such quantum effects become important when the thermal wavelength is comparable to the typical dimensions of the system. In this Letter, we extend the dispersive Drude model in order to cast these quantum corrections and derive a nonlocal dielectric constant for quasi one-dimensional nanostructures (nanowires). More specifically, we take into account the effects of i) the finiteness of the system along the transverse direction and ii) the quantum diffraction (Bohm potential) due to a gradient of the electronic density. We then apply our result to investigate the excitation of wakefields due to...

show abstract

On the creation of quantized vortex lines in rotating He II

Cited by 65 publications

References 17 publications

Quantum Euler-Poisson systems: global existence and exponential decay

Quantum Euler-Poisson systems: global existence and exponential decay

Nonlinear Quantum Plasma Physics

Nonlocal plasmon excitation in metallic nanostructures

Contact Info

Product

Resources

About