| Records |
| Author |
During, G.; Picozzi, A.; Rica, S. |
| Title |
Breakdown of weak-turbulence and nonlinear wave condensation |
Type |
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| Year |
2009 |
Publication |
Physica D-Nonlinear Phenomena |
Abbreviated Journal |
Physica D |
| Volume |
238 |
Issue |
16 |
Pages |
1524-1549 |
| Keywords |
Weak-turbulence theory; Nonlinear Schrodinger equation; Wave condensation |
| Abstract |
The formation of a large-scale coherent structure (a condensate) as a result of the long time evolution of the initial value problem of a classical partial differential nonlinear wave equation is considered. We consider the nonintegrable and unforced defocusing NonLinear Schrodinger (NLS) equation as a representative model. In spite of the formal reversibility of the NLS equation, the nonlinear wave exhibits an irreversible evolution towards a thermodynamic equilibrium state. The equilibrium state is characterized by a homogeneous solution (condensate), with small-scale fluctuations superposed (uncondensed particles), which store the information necessary for “time reversal”. We analyze the evolution Of the cumulants of the random wave as originally formulated by DJ. Benney and P.G. Saffman [D.J. Bentley, P.G. Saffman, Proc. Roy. Soc. London A 289 (1966) 301] and A.C. Newell [A.C. Newell, Rev. Geophys. 6 (1968) 1]. This allows us to provide a self-consistent weak-turbulence theory of the condensation process, in which the nonequilibrium formation of the condensate is a natural consequence of the spontaneous regeneration of a non-vanishing first-order cumulant in the hierarchy of the cumulants' equations. More precisely, we show that in the presence of a small condensate amplitude, all relevant statistical information is contained in the off-diagonal second order cumulant, as described by the usual weak-turbulence theory. Conversely, in the presence of a high-amplitude condensate, the diagonal second-order cumulants no longer vanish in the long time limit, which signals a breakdown of the weak-turbulence theory. However, we show that all asymptotic closure of the hierarchy of the cumulants' equations is still possible provided one considers the Bogoliubov's basis rather than the standard Fourier's (free particle) basis. The nonequilibrium dynamics turns out to be governed by the Bogoliubov's off-diagonal second order cumulant, while the corresponding diagonal cumulants, as well as the higher order cumulants, are shown to vanish asymptotically. The numerical discretization of the NLS equation implicitly introduces an ultraviolet frequency cut-off. The simulations are in quantitative agreement with the weak turbulence theory without adjustable parameters, despite the fact that the theory is expected to breakdown nearby the transition to condensation. The fraction of condensed particles vs energy is characterized by two distinct regimes: For small energies (H << H-c) the Bogoliubov's regime is established, whereas for H less than or similar to H-c the small-amplitude condensate regime is described by the weak-turbulence theory. In both regimes we derive coupled kinetic equations that describe the coupled evolution of the condensate amplitude and the incoherent field component. The influence of finite size effects and of the dimensionality of the system are also considered. It is shown that, beyond the thermodynamic limit, wave condensation is reestablished in two spatial dimensions, in complete analogy with uniform and ideal 2D Bose gases. (C) 2009 Elsevier B.V. All rights reserved. |
| Address |
[Duering, Gustavo; Rica, Sergio] Univ Paris 06, Ecole Normale Super, Phys Stat Lab, F-75005 Paris, France, Email: rica@lps.ens.fr |
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Thesis |
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| Publisher |
Elsevier Science Bv |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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| Series Volume |
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Series Issue |
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Edition |
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| ISSN |
0167-2789 |
ISBN |
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Medium |
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Area  |
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Expedition |
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Conference |
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| Notes |
WOS:000268621400003 |
Approved |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
61 |
| Permanent link to this record |
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| Author |
Hojman, S.A.; Asenjo, F.A. |
| Title |
Dual wavefunctions in two-dimensional quantum mechanics |
Type |
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| Year |
2020 |
Publication |
Physics Letters A |
Abbreviated Journal |
Phys. Lett. A |
| Volume |
384 |
Issue |
13 |
Pages |
5 pp |
| Keywords |
Schrodinger equation; Dual solution; Bohm potential; Two-dimensions; Optics |
| Abstract |
It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefunctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to each other. This is a property of solutions with vanishing Bohm potential. These solutions can be extended to three-dimensional systems. We explicitly calculate dual solutions for physical systems, such as the repulsive harmonic oscillator and the two-dimensional hydrogen atom. These dual wavefunctions are also solutions of an analogue optical system in the eikonal limit. In this case, the potential is related to the refractive index, allowing the study of this two-dimensional dual wavefunction solutions with an optical (analogue) system. (C) 2020 Elsevier B.V. All rights reserved. |
| Address |
[Hojman, Sergio A.] Univ Adolfo Ibanez, Dept Ciencias, Fac Artes Liberales, Santiago 7491169, Chile, Email: sergio.hojman@uai.cl; |
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Thesis |
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| Publisher |
Elsevier |
Place of Publication |
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Editor |
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| Language |
English |
Summary Language |
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Original Title |
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| Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
0375-9601 |
ISBN |
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Medium |
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Expedition |
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Conference |
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| Notes |
WOS:000525434900002 |
Approved |
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| Call Number |
UAI @ eduardo.moreno @ |
Serial |
1152 |
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| Author |
Hojman, S.A.; Asenjo, F.A. |
| Title |
A new approach to solve the one-dimensional Schrodinger equation using a wavefunction potential |
Type |
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| Year |
2020 |
Publication |
Physics Letters A |
Abbreviated Journal |
Phys. Lett. A |
| Volume |
384 |
Issue |
36 |
Pages |
7 pp |
| Keywords |
Schrodinger equation; New exact solutions; Accelerating wavepackets; Bohm potential |
| Abstract |
A new approach to find exact solutions to one-dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non-vanishing Bohm potentials. For most of the potentials, no solutions to the Schrodinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non-vanishing Bohm potentials. New examples of this kind are found and discussed. (C) 2020 Elsevier B.V. All rights reserved. |
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Thesis |
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Place of Publication |
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Abbreviated Series Title |
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Edition |
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| ISSN |
0375-9601 |
ISBN |
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Approved |
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| Call Number |
UAI @ alexi.delcanto @ |
Serial |
1271 |
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