Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1209.6206 · Physical Review Letters

Self-Consistent Multiple Complex-Kink Solutions in Bogoliubov–de Gennes and Chiral Gross-Neveu Systems

Daisuke A. Takahashi, Muneto Nitta

Published Mar 28, 2013• 45 citations
arXivHTMLPDF

Abstract

We exhaust all exact self-consistent solutions of complex-valued fermionic condensates in the (1+1)-dimensional Bogoliubov-de Gennes and chiral Gross-Neveu systems under uniform boundary conditions. We obtain n complex (twisted) kinks, or gray solitons, with 2n parameters corresponding to their positions and phase shifts. Each soliton can be placed at an arbitrary position while the self-consistency requires its phase shift to be quantized by π/N for N flavors.

DOI
10.1103/physrevlett.110.131601

Related papers

Bogoliubov–de Gennes soliton dynamics in unconventional Fermi superfluids

Daisuke A. Takahashi

Exact self-consistent soliton dynamics based on the Bogoliubov--de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an $\text{SU}(d)$-symmetric two-body interaction is presented. The derivation is based on the ansatz having the similar form as the Gelfand-Levitan-Marchenko equation in the inverse scattering theory. Our solutions can be regarded as a multicomponent generalization of the solutions recently derived by Dunne and Thies [Phys. Rev. Lett. 111, 121602 (2013)]. We also propose superpositions of occupation states, which make it possible to realize various filling rates even in one-flavor systems, and include Dirac and Majorana fermions. The soliton solutions in the $d=2$ systems, which describe the mixture of singlet $s$-wave and triplet $p$-wave superfluids, exhibit a variety of phenomena such as rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, $s\ensuremath{-}p$ mixed dynamics, and so on. These solutions are illustrated by animations, where order parameters are visualized by spherical harmonic functions. The full formulation of the BdG theory is also supported, and the double-counting problem of BdG eigenstates and $N$-flavor generalization are discussed.

arXiv:1509.04242•Physical review. B./Physical review. B•Jan 19, 2016•13 citations

On Reflectionless Nature of Self-Consistent Multi-Soliton Solutions in Bogoliubov–de Gennes and Chiral Gross–Neveu Models

Daisuke A. Takahashi, Muneto Nitta

arXiv:1307.3897•Journal of Low Temperature Physics•Oct 1, 2013•15 citations

Fractional excitation in one-dimensional two species fermionic superfluids

Fei Ye

We study one-dimensional two-species fermionic superfluids with order parameter twisted by an angle $\varphi$ at the two ends. By solving the corresponding Bogoliubov-de-Gennes equation, we obtain the U(1) soliton state which turns out to carry $\varphi S/(2\pi)$ spin, where $S$ is the spin of single fermion. For $Z_2$ soliton with $\varphi=\pi$, the localized state carries only $1/2$ of a single fermion spin. To conserve the total spin of the system as an integal multiple of $S$, we demonstrate, the localized fractional spin $\varphi S/(2\pi)$ can be compensated by an opposite total spin $-\varphi S/(2\pi)$, which distributes uniformly in space and is thus undetectable locally in the thermodynamic limit.

•Dec 20, 2015•0 citations

Dark–bright solitons in a superfluid Bose–Fermi mixture

Marek Tylutki, Alessio Recati, F. Dalfovo +1 more

The recent experimental realisation of Bose–Fermi superfluid mixtures of dilute ultracold atomic gases has opened new perspectives in the study of quantum many-body systems. Depending on the values of the scattering lengths and the amount of bosons and fermions, a uniform Bose–Fermi mixture is predicted to exhibit a fully mixed phase, a fully separated phase or, in addition, a purely fermionic phase coexisting with a mixed phase. The occurrence of this intermediate configuration has interesting consequences when the system is nonuniform. In this work we theoretically investigate the case of solitonic solutions of coupled Bogoliubov–de Gennes and Gross–Pitaevskii equations for the fermionic and bosonic components, respectively. We show that, in the partially separated phase, a dark soliton in Fermi superfluid is accompanied by a broad bosonic component in the soliton, forming a dark–bright soliton which keeps full spatial coherence.

arXiv:1601.01471•New Journal of Physics•May 9, 2016•35 citations

Moving solitons in a one-dimensional fermionic superfluid

Dmitry K. Efimkin, Victor M. Galitski

A fully analytical theory of a traveling soliton in a one-dimensional fermionic superfluid is developed within the framework of time-dependent self-consistent Bogoliubov--de Gennes equations, which are solved exactly in the Andreev approximation. The soliton manifests itself in a kinklike profile of the superconducting order parameter and hosts a pair of Andreev bound states in its core. They adjust to the soliton's motion and play an important role in its stabilization. A phase jump across the soliton and its energy decrease with the soliton's velocity and vanish at the critical velocity, corresponding to the Landau criterion, where the soliton starts emitting quasiparticles and becomes unstable. The ``inertial'' and ``gravitational'' masses of the soliton are calculated and the former is shown to be orders of magnitude larger than the latter. This results in a slow motion of the soliton in a harmonic trap, reminiscent of the observed behavior of a solitonlike texture in related experiments in cold fermion gases [T. Yefsah et al., Nature (London) 499, 426 (2013)]. Furthermore, we calculate the full nonlinear dispersion relation of the soliton and solve the classical equations of motion in a trap. The strong nonlinearity at high velocities gives rise to anharmonic oscillatory motion of the soliton. A careful analysis of this anharmonicity may provide a means to experimentally measure the nonlinear soliton spectrum in superfluids.

arXiv:1408.6511•Physical Review A•Feb 17, 2015•27 citations

Normal and anomalous solitons in the theory of dynamical Cooper pairing

Emil A. Yuzbashyan

We obtain multisoliton solutions of the time-dependent Bogoliubov--de Gennes equations or, equivalently, Gorkov equations that describe the dynamics of a fermionic condensate in the dissipationless regime. There are two kinds of solitons---normal and anomalous. At large times, normal multisolitons asymptote to unstable stationary states of the BCS Hamiltonian with zero order parameter (normal states), while the anomalous ones tend to eigenstates characterized by a nonzero anomalous average. Under certain circumstances, multisoliton solutions break up into sums of single solitons. In the linear analysis near the stationary states, solitons correspond to unstable modes. Generally, they are nonlinear extensions of these modes, so that a stationary state with $k$ unstable modes gives rise to a $k$-soliton solution. We relate parameters of the multisolitons to those of the asymptotic stationary state, which determines the conditions necessary for exciting solitons. We further argue that the dynamics in many physical situations is multisoliton.

arXiv:0807.3181•Physical Review B•Nov 7, 2008•41 citations
We exhaust all exact self-consistent solutions of complex-valued fermionic condensates in the (1+1)-dimensional Bogoliubov-de Gennes and chiral Gross-Neveu systems under uniform boundary conditions. We obtain n complex (twisted) kinks, or gray solitons, with 2n parameters corresponding to their positions and phase shifts. Each soliton can be placed at an arbitrary position while the self-consistency requires its phase shift to be quantized by π/N for N flavors.
Exact self-consistent soliton dynamics based on the Bogoliubov--de Gennes (BdG) formalism in unconventional Fermi superfluids/superconductors possessing an SU(d)\text{SU}(d)SU(d)-symmetric two-body interaction is presented. The derivation is based on the ansatz having the similar form as the Gelfand-Levitan-Marchenko equation in the inverse scattering theory. Our solutions can be regarded as a multicomponent generalization of the solutions recently derived by Dunne and Thies [Phys. Rev. Lett. 111, 121602 (2013)]. We also propose superpositions of occupation states, which make it possible to realize various filling rates even in one-flavor systems, and include Dirac and Majorana fermions. The soliton solutions in the d=2d=2d=2 systems, which describe the mixture of singlet sss-wave and triplet ppp-wave superfluids, exhibit a variety of phenomena such as rotating polar phases by soliton spins, SU(2)-DHN breathers, Majorana triplet states, $s\ensuremath{-}p$ mixed dynamics, and so on. These solutions are illustrated by animations, where order parameters are visualized by spherical harmonic functions. The full formulation of the BdG theory is also supported, and the double-counting problem of BdG eigenstates and NNN-flavor generalization are discussed.
We study one-dimensional two-species fermionic superfluids with order parameter twisted by an angle φ\varphiφ at the two ends. By solving the corresponding Bogoliubov-de-Gennes equation, we obtain the U(1) soliton state which turns out to carry φS/(2π)\varphi S/(2\pi)φS/(2π) spin, where SSS is the spin of single fermion. For Z2Z_2Z2​ soliton with φ=π\varphi=\piφ=π, the localized state carries only 1/21/21/2 of a single fermion spin. To conserve the total spin of the system as an integal multiple of SSS, we demonstrate, the localized fractional spin φS/(2π)\varphi S/(2\pi)φS/(2π) can be compensated by an opposite total spin −φS/(2π)-\varphi S/(2\pi)−φS/(2π), which distributes uniformly in space and is thus undetectable locally in the thermodynamic limit.
The recent experimental realisation of Bose–Fermi superfluid mixtures of dilute ultracold atomic gases has opened new perspectives in the study of quantum many-body systems. Depending on the values of the scattering lengths and the amount of bosons and fermions, a uniform Bose–Fermi mixture is predicted to exhibit a fully mixed phase, a fully separated phase or, in addition, a purely fermionic phase coexisting with a mixed phase. The occurrence of this intermediate configuration has interesting consequences when the system is nonuniform. In this work we theoretically investigate the case of solitonic solutions of coupled Bogoliubov–de Gennes and Gross–Pitaevskii equations for the fermionic and bosonic components, respectively. We show that, in the partially separated phase, a dark soliton in Fermi superfluid is accompanied by a broad bosonic component in the soliton, forming a dark–bright soliton which keeps full spatial coherence.
A fully analytical theory of a traveling soliton in a one-dimensional fermionic superfluid is developed within the framework of time-dependent self-consistent Bogoliubov--de Gennes equations, which are solved exactly in the Andreev approximation. The soliton manifests itself in a kinklike profile of the superconducting order parameter and hosts a pair of Andreev bound states in its core. They adjust to the soliton's motion and play an important role in its stabilization. A phase jump across the soliton and its energy decrease with the soliton's velocity and vanish at the critical velocity, corresponding to the Landau criterion, where the soliton starts emitting quasiparticles and becomes unstable. The ``inertial'' and ``gravitational'' masses of the soliton are calculated and the former is shown to be orders of magnitude larger than the latter. This results in a slow motion of the soliton in a harmonic trap, reminiscent of the observed behavior of a solitonlike texture in related experiments in cold fermion gases [T. Yefsah et al., Nature (London) 499, 426 (2013)]. Furthermore, we calculate the full nonlinear dispersion relation of the soliton and solve the classical equations of motion in a trap. The strong nonlinearity at high velocities gives rise to anharmonic oscillatory motion of the soliton. A careful analysis of this anharmonicity may provide a means to experimentally measure the nonlinear soliton spectrum in superfluids.
We obtain multisoliton solutions of the time-dependent Bogoliubov--de Gennes equations or, equivalently, Gorkov equations that describe the dynamics of a fermionic condensate in the dissipationless regime. There are two kinds of solitons---normal and anomalous. At large times, normal multisolitons asymptote to unstable stationary states of the BCS Hamiltonian with zero order parameter (normal states), while the anomalous ones tend to eigenstates characterized by a nonzero anomalous average. Under certain circumstances, multisoliton solutions break up into sums of single solitons. In the linear analysis near the stationary states, solitons correspond to unstable modes. Generally, they are nonlinear extensions of these modes, so that a stationary state with kkk unstable modes gives rise to a kkk-soliton solution. We relate parameters of the multisolitons to those of the asymptotic stationary state, which determines the conditions necessary for exciting solitons. We further argue that the dynamics in many physical situations is multisoliton.