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Academic literature on the topic 'Gross-Pitaevskii regime'

Author: Grafiati
Published: 11 March 2023

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Journal articles on the topic "Gross-Pitaevskii regime"

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Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. "Complete Bose–Einstein Condensation in the Gross–Pitaevskii Regime." Communications in Mathematical Physics 359, no. 3 (November 9, 2017): 975–1026. http://dx.doi.org/10.1007/s00220-017-3016-5.

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Basti, Giulia, Serena Cenatiempo, Alessandro Olgiati, Giulio Pasqualetti, and Benjamin Schlein. "Ground state energy of a Bose gas in the Gross–Pitaevskii regime." Journal of Mathematical Physics 63, no. 4 (April 1, 2022): 041101. http://dx.doi.org/10.1063/5.0087116.

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We review some rigorous estimates for the ground state energy of dilute Bose gases. We start with Dyson’s upper bound, which provides the correct leading order asymptotics for hard spheres. Afterward, we discuss a rigorous version of Bogoliubov theory, which recently led to an estimate for the ground state energy in the Gross–Pitaevskii regime, valid up to second order, for particles interacting through integrable potentials. Finally, we explain how these ideas can be combined to establish a new upper bound, valid to second order, for the energy of hard spheres in the Gross–Pitaevskii limit. Here, we only sketch the main ideas; details will appear elsewhere.
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Cenatiempo, Serena. "Bogoliubov theory for dilute Bose gases: The Gross-Pitaevskii regime." Journal of Mathematical Physics 60, no. 8 (August 2019): 081901. http://dx.doi.org/10.1063/1.5096288.

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4

Béthuel, Fabrice, Raphaël Danchin, and Didier Smets. "On the linear wave regime of the Gross-Pitaevskii equation." Journal d'Analyse Mathématique 110, no. 1 (January 2010): 297–338. http://dx.doi.org/10.1007/s11854-010-0008-1.

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Michelangeli, Alessandro, Phan Thành Nam, and Alessandro Olgiati. "Ground state energy of mixture of Bose gases." Reviews in Mathematical Physics 31, no. 02 (February 27, 2019): 1950005. http://dx.doi.org/10.1142/s0129055x19500053.

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We consider the asymptotic behavior of a system of multi-component trapped bosons, when the total particle number [Formula: see text] becomes large. In the dilute regime, when the interaction potentials have the length scale of order [Formula: see text], we show that the leading order of the ground state energy is captured correctly by the Gross–Pitaevskii energy functional and that the many-body ground state fully condensates on the Gross–Pitaevskii minimizers. In the mean-field regime, when the interaction length scale is [Formula: see text], we are able to verify Bogoliubov’s approximation and obtain the second order expansion of the ground state energy. While such asymptotic results have several precursors in the literature on one-component condensates, the adaptation to the multi-component setting is non-trivial in various respects and the analysis will be presented in detail.
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Zloshchastiev, Konstantin G. "Sound Propagation in Cigar-Shaped Bose Liquids in the Thomas-Fermi Approximation: A Comparative Study between Gross-Pitaevskii and Logarithmic Models." Fluids 7, no. 11 (November 19, 2022): 358. http://dx.doi.org/10.3390/fluids7110358.

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A comparative study is conducted of the propagation of sound pulses in elongated Bose liquids and Bose-Einstein condensates in Gross-Pitaevskii and logarithmic models, by means of the Thomas-Fermi approximation. It is demonstrated that in the linear regime the propagation of small density fluctuations is essentially one-dimensional in both models, in the direction perpendicular to the cross section of a liquid’s lump. Under these approximations, it is demonstrated that the speed of sound scales as a square root of particle density in the case of the Gross-Pitaevskii liquid/condensate, but it is constant in a case of the homogeneous logarithmic liquid.
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Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. "Optimal Rate for Bose–Einstein Condensation in the Gross–Pitaevskii Regime." Communications in Mathematical Physics 376, no. 2 (September 13, 2019): 1311–95. http://dx.doi.org/10.1007/s00220-019-03555-9.

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8

Ma, Li, and Jing Wang. "Sharp Threshold of the Gross-Pitaevskii Equation with Trapped Dipolar Quantum Gases." Canadian Mathematical Bulletin 56, no. 2 (June 1, 2013): 378–87. http://dx.doi.org/10.4153/cmb-2011-181-2.

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AbstractIn this paper, we consider the Gross-Pitaevskii equation for the trapped dipolar quantum gases. We obtain the sharp criterion for the global existence and finite time blow-up in the unstable regime by constructing a variational problem and the so-called invariant manifold of the evolution flow.
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9

Brennecke, Christian. "The low energy spectrum of trapped bosons in the Gross–Pitaevskii regime." Journal of Mathematical Physics 63, no. 5 (May 1, 2022): 051101. http://dx.doi.org/10.1063/5.0089630.

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Bogoliubov theory {N. N. Bogoliubov, Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947) [J. Phys. (USSR) 11, 23 (1947) (in English)]} provides important predictions for the low energy properties of the weakly interacting Bose gas. Recently, Bogoliubov’s predictions were justified rigorously by Boccato et al. [Acta Math. 222(2), 219–335 (2019)] for translation invariant systems in the Gross–Pitaveskii regime, where N bosons in [Formula: see text] interact through a potential whose scattering length is of size N−1. In this article, we review recent results from the work of Brennecke et al. [Ann. Henri Poincaré 23, 1583–1658 (2022)], a joint work with Schlein and Schraven, which extends the analysis for translation invariant systems to systems of bosons in [Formula: see text] that are trapped by an external potential.
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10

Nam, Phan Thành, Marcin Napiórkowski, Julien Ricaud, and Arnaud Triay. "Optimal rate of condensation for trapped bosons in the Gross–Pitaevskii regime." Analysis & PDE 15, no. 6 (November 10, 2022): 1585–616. http://dx.doi.org/10.2140/apde.2022.15.1585.

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Books on the topic "Gross-Pitaevskii regime"

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Kavokin, Alexey V., Jeremy J. Baumberg, Guillaume Malpuech, and Fabrice P. Laussy. Quantum Fluids of Light. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198782995.003.0010.

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In this chapter, we deal with polaritons as a “quantum fluid of light”, described by variants of the Gross–Pitaevskii equation. We discuss how interactions between flowing polaritons and a defect allow to study their superfluid regime and generate topological defects. Including spin gives rise to an effective magnetic field (polariton spin-orbit coupling) that acts on the topological defects—half-solitons and half-vortices—behaving as effective magnetic monopoles. We describe various techniques to create periodic potentials, that can lead to the formation of polaritonic bands and gaps with a unique flexibility. Special focus is given to topologically nontrivial bands, leading to a polariton topological insulator, based on a polariton graphene analog.
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Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.
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Book chapters on the topic "Gross-Pitaevskii regime"

1

Benedikter, Niels, Marcello Porta, and Benjamin Schlein. "The Gross-Pitaevskii Regime." In Effective Evolution Equations from Quantum Dynamics, 37–56. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24898-1_5.

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