A self-contained discussion of nonrelativistic quantum mechanical potential scattering in two dimensions is presented. The includes, among other topics, partial wave decomposition coordinate and momentum space, Lippmann–Schwinger integral equations for the wavefunction transition operator, optical theorem, unitarity relation operator. present definition amplitude terms asymptotic differs from usual definition. has certain advantages, example, writing theorem studying analytical properties amplitude.

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution Gross-Pitaevskii (GP) equation with both spherical axial symmetries. consider initiated by suddenly changing interatomic scattering length or harmonic trapping potential in a condensate. These changes introduce oscillations condensate which are studied detail. use time iterative split-step method for time-dependent GP equation, where all nonlinear linear non-derivative...

We study the vortex-bright solitons in a quasi-two-dimensional spin-orbit-coupled (SO-coupled) hyperfine spin-1 three-component Bose-Einstein condensate (BEC) using variational method and numerical solution of mean-field model. The ground state these is radially symmetric for weak ferromagnetic polar interactions. For sufficiently strong interaction, we observe emergence an asymmetric soliton as state. also numerically investigate stable moving binary collision between them. present model...

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in trapless three-dimensional attractive Bose-Einstein condensate (BEC) by rapid periodic temporal modulation scattering length alone using Feshbach resonance. This scheme also stabilizes rotating vortex two dimensions. Apart from possible experimental application BEC, present study suggests spatiotemporal solitons nonlinear optics three dimensions layered...

We investigate the zero-temperature properties of a superfluid Bose-Fermi mixture by introducing set coupled Galilei-invariant nonlinear Schr\"odinger equations valid from weak coupling to unitarity. The Bose dynamics is described Gross-Pitaevskii-type equation including beyond-mean-field corrections possessing correct weak-coupling and unitarity limits. two-component Fermi density-functional terms with present equivalent generalized hydrodynamics, which take into account also surface...

It is demonstrated for the three-dimensional three-particle system that a divergence arising from essentially same singularity structure of kernel scattering integral equation responsible both Efimov and Thomas effects. The above implies results dynamical calculation will be sensitive to details two-particle interaction. In two-dimensional systems, absent consequently observables become independent interaction model.

A recently proposed separable expansion of the $t$ matrix (assuming potential to be given) is rederived from Schwinger variational principle. Also, analytic expressions are given for integrals in if a superposition Yukawa potentials, and suitable choices functions. Calculations with two commonly used $S$-wave nucleon-nucleon potentials show that can converge significantly faster than unitary pole freedom choice functions exploited.

We study the localization of a noninteracting and weakly interacting Bose-Einstein condensate (BEC) with spin-orbit coupling loaded in quasiperiodic bichromatic optical lattice potential using numerical solution variational approximation binary mean-field Gross-Pitaevskii equation two pseudospin components. confirm existence stationary localized states presence Rabi couplings for an equal distribution atoms find that interaction between favors or delocalization BEC depending on phase...

We demonstrate stable and metastable vortex-bright solitons in a three-dimensional spin-orbit-coupled three-component hyperfine spin-1 Bose-Einstein condensate (BEC) using numerical solution variational approximation of mean-field model. The spin-orbit coupling provides attraction to form both attractive repulsive spinor BECs. ground state these is axially symmetric for weak polar interaction. For sufficiently strong ferromagnetic interaction, we observe the emergence fully asymmetric...

We demonstrate a supersolid-like spatially periodic square- and honeycomb-lattice crystallization of droplets in addition to the commonly studied triangular-lattice cylindrically symmetric quasi-two-dimensional trapped dipolar condensate, using beyond-mean-field model including quantum-fluctuation Lee-Huang-Yang-type interaction. These three types may appear for same atomic interaction trap frequencies. The energies $E$ all crystallizations as function number $N$ atoms satisfy universal...

A strongly dipolar $^{164}$Dy condensate of length $a_{\mathrm{dd}}=130.8a_0$, with $a_0$ the Bohr radius, hosts a wide variety eigenstates, such as droplet, droplet-lattice, and ring-topology states, self-bound droplets. Motivated by observation very NaCs molecules [Bigagli N et al. 2024 Nature 631 289], we demonstrate numerical simulation, using an improved mean-field model, including Lee-Huang-Yang interaction, that in $a_{\mathrm{dd}} = 2000a_0$, most above-mentioned states continue to...

We demonstrate the formation of dynamically stable giant vortices in a harmonically-trapped strongly dipolar $^{164}$Dy Bose-Einstein condensate under rotation around polarization direction atoms, employing numerical solution an improved mean-field model including Lee-Huang-Yang-type interaction, meant to stop collapse at high atom density. These are stationary, obtainable by imaginary-time propagation using Gaussian initial state, while appropriate phase vortex is imprinted on wave...

As in quantum field theory, for some singular two-body potentials, the momentum-space perturbative treatment of three-dimensional $N$-body problem is shown to exhibit ultraviolet divergences. Renormalization these models leads a scale and finite observables. For Dirac delta potential we carry on this renormalization two- three-body systems. A new divergence, hence scale, emerges each added particle. $N\ensuremath{\ge}3$ there are no divergences one two dimensions. The physical implications...

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation and use it to study resonance dynamics of trapped Bose-Einstein condensate induced by periodic variation in atomic scattering length. When frequency oscillation length is an even multiple one trapping frequencies along $x$, $y$, or $z$ direction, corresponding size executes resonant oscillation. Using concept differentiation matrix, partial-differential GP reduced set coupled...

We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic bright solitons in trapped degenerate Fermi gas mixed with Bose-Einstein condensate quasi-one-dimensional cigar-shaped geometry. Due strong Pauli-blocking repulsion among spin-polarized fermions at short distances there cannot be case repulsive boson-fermion interactions. However, we demonstrate that stable can formed for sufficiently attractive interaction mixture. also consider presence...

We introduce a quasianalytic nonlinear Schr\"odinger equation with beyond mean-field corrections to describe the dynamics of zero-temperature dilute superfluid Fermi gas in crossover from weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime, where ${k}_{F}|a|⪡1$ $a$ $s$-wave scattering length and ${k}_{F}$ momentum, through unitarity limit ${k}_{F}a\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$ Bose-Einstein condensation (BEC) regime ${k}_{F}a>0$. The energy our...

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects localization a noninteracting ideal Bose-Einstein condensate (BEC) in one-dimensional bichromatic quasiperiodic optical-lattice potential. Such potential, used recent experiment on BEC [Roati et al., Nature (London) 453, 895 (2008)], can be formed by superposition two standing-wave polarized laser beams with wavelengths. We investigate effect variation optical amplitudes and wavelengths...