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Traveling waves in two-component Bose-Einstein condensates whose dynamics is described by the Manakov limit of the Gross-Pitaevskii equations are considered in general situation with relative motion of the components when their chemical…

Quantum Gases · Physics 2015-06-23 A. M. Kamchatnov , V. V. Sokolov

We consider several effects of the matter wave dynamics which can be observed in Bose-Einstein condensates embedded into optical lattices. For low-density condensates we derive approximate evolution equations, the form of which depends on…

Soft Condensed Matter · Physics 2009-11-10 V. A. Brazhnyi , V. V. Konotop

We study the approach to equilibrium, described by a Gibbs measure, for a system on a $d$-dimensional torus evolving according to a stochastic nonlinear Schr\"odinger equation (SNLS) with a high frequency truncation. We prove exponential…

Mathematical Physics · Physics 2015-06-04 J. L. Lebowitz , Ph. Mounaix , W. -M. Wang

We extend earlier work [Phys.Rev.Lett. 84, 3740 (2000)] on the statistical mechanics of the cubic one-dimensional discrete nonlinear Schrodinger (DNLS) equation to a more general class of models, including higher dimensionalities and…

Statistical Mechanics · Physics 2007-05-23 Magnus Johansson , Kim O. Rasmussen

The kinetics of nonequilibrium Bose-Einstein condensates are considered within the framework of the Gross-Pitaevskii equation. A systematic derivation is given for weak small-scale perturbations of a steady confined condensate state. This…

Mathematical Physics · Physics 2020-06-10 Yuri Lvov Sergey Nazarenko Robert West

In this paper, we present a microscopic derivation of the two-dimensional focusing cubic nonlinear Schr\"odinger equation starting from an interacting $N$-particle system of Bosons. The interaction potential we consider is given by…

Mathematical Physics · Physics 2018-08-01 M. Jeblick , P. Pickl

We study the time evolution of weakly interacting Bose gases on a three-dimensional torus of arbitrary volume. The coupling constant is supposed to be inversely proportional to the density, which is considered to be large and independent of…

Mathematical Physics · Physics 2025-12-12 Daniele Ferretti , Kalle Koskinen

We consider the cubic nonlinear Schr\"odinger (NLS) equation set on a two dimensional box of size $L$ with periodic boundary conditions. By taking the large box limit $L \to \infty$ in the weakly nonlinear regime (characterized by smallness…

Analysis of PDEs · Mathematics 2013-08-29 Erwan Faou , Pierre Germain , Zaher Hani

We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the…

Quantum Gases · Physics 2016-04-20 T. Congy , A. Kamchatnov , N. Pavloff

The fundamental question of how Bose-Einstein condensates tunnel into a barrier is addressed. The cubic nonlinear Schrodinger equation with a finite square well potential, which models a Bose-Einstein condensate in a quasi-one-dimensional…

Condensed Matter · Physics 2009-11-07 L. D. Carr , K. W. Mahmud , W. P. Reinhardt

We study the long-time behavior of solutions to the nonlinear Schr\"odinger / Gross-Pitaevskii equation (NLS/GP) with a symmetric double-well potential, continuing work of the 2nd and 3rd authors. NLS/GP governs nearly-monochromatic guided…

Analysis of PDEs · Mathematics 2014-08-22 Roy H. Goodman , Jeremy L. Marzuola , Michael I. Weinstein

The evolution of an interacting two-component Bose-Einstein condensate from an initial phase state leads to a spin squeezed state that may be used in atomic clocks to increase the signal-to-noise ratio, opening the way to quantum metrology.…

Quantum Physics · Physics 2013-06-11 Alice Sinatra , Yvan Castin , Emilia Witkowska

We consider the one-dimensional Lieb-Liniger model (bosons interacting via 2-body delta potentials) in the infinite coupling constant limit (the so-called Tonks-Girardeau model). This model might be relevant as a description of atomic Bose…

Statistical Mechanics · Physics 2020-03-06 Stephane Ouvry , Alexios P. Polychronakos

We derive an effective nonpolynomial Schrodinger equation (NPSE) for self-repulsive or attractive BEC in the nearly-1D cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. Besides the…

Other Condensed Matter · Physics 2009-11-13 L. Salasnich , A. Cetoli , B. A. Malomed , F. Toigo , L. Reatto

The dynamics of Bose-Einstein condensates trapped in a deep optical lattice is governed by a discrete nonlinear equation (DNL). Its degree of nonlinearity and the intersite hopping rates are retrieved from a nonlinear tight-binding…

Condensed Matter · Physics 2009-11-10 Augusto Smerzi , Andrea Trombettoni

At finite temperatures below the phase transition point, the Bose-Einstein condensation, the macroscopic occupation of a single quantum state by particles of integer spin, is not complete. In the language of superfluid helium, this means…

Mathematical Physics · Physics 2015-09-16 Dionisios Margetis

We study density isolines in quantum turbulence under the Schramm-Loewner framework using direct numerical simulations of the truncated Gross-Pitaevskii equation, in both spherical and cylindrical traps with three-dimensional dynamics.…

Quantum Gases · Physics 2024-07-31 J. Amette Estrada , M. Noseda , P. J. Cobelli , P. D. Mininni

Using the method of locally equilibrium statistical operator we consider the thermalized relativistic quantum fields in an oscillatory trap. We compare this thermal picture of the confined boson gas with non-relativistic model of…

Nuclear Theory · Physics 2007-05-23 Yu. M. Sinyukov , S. V. Akkelin , R. Lednicky

We present a mathematically rigorous analysis of the ground state of a dilute, interacting Bose gas in a three-dimensional trap that is strongly confining in one direction so that the system becomes effectively two-dimensional. The…

Mathematical Physics · Physics 2007-05-23 K. Schnee , J. Yngvason

We report results of a systematic analysis of matter-wave gap solitons (GSs) in three-dimensional self-repulsive Bose-Einstein condensates (BECs) loaded into a combination of a cigar-shaped trap and axial optical-lattice (OL) potential.…

Quantum Gases · Physics 2019-06-06 A. Muñoz Mateo , V. Delgado , Boris A. Malomed