Nambu-Goldstone modes propagating along topological defects: Kelvin and ripple modes from small to large systems

Takahashi, Daisuke; Kobayashi, Michikazu; Nitta, Muneto

doi:10.1103/physrevb.91.184501

Cited by 22 publications

(11 citation statements)

References 39 publications

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“…28) Extended semi-classical analysis: To demonstrate the anomalous behavior beyond the perturbation analysis, we introduce the semi-classical theory for the BdG equations, which can be used to describe low-energy modes far from a topological defect or an interface. 29,30) Here, we extend the theory to our case with complex excitation frequencies.…”

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confidence: 87%

Is a Doubly Quantized Vortex Dynamically Unstable in Uniform Superfluids?

2018

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We revisit the fundamental problem of the splitting instability of a doubly quantized vortex in uniform singlecomponent superfluids at zero temperature. We analyze the system-size dependence of the excitation frequency of a doubly quantized vortex through large-scale simulations of the Bogoliubov-de Gennes equation, and find that the system remains dynamically unstable even in the infinite-system-size limit. Perturbation and semi-classical theories reveal that the splitting instability radiates a damped oscillatory phonon as an opposite counterpart of a quasi-normal mode.Introduction: Vortices appear in many branches of physics. In particular, the structure, stability, and dynamics of vortices in nonlinear fields share common features in many physical systems. 1) Quantized vortices are prototypes among those vortices, playing a key role in the fluid dynamics of superfluid helium and Bose-Einstein condensates (BECs). [2][3][4][5] In general, quantized vortices are characterized by the winding number of the phase of the superfluid order parameter around the vortex core. A vortex whose winding number l is more than unity is called an l-quantized or multiply quantized vortex (MQV). Since the energy of an l-quantized vortex is generally larger than the sum of energies of l singly quantized vortices (SQVs), an MQV is energetically unstable and splits into SQVs in uniform systems. 6) In fact, MQVs have never been observed in equilibrium. However, this argument does not eliminate the possibility that MQVs survive as a metastable state at very low temperatures when energy dissipation is negligible.To investigate the splitting instability precisely, we need to analyze the microscopic structure of the vortex core. It is difficult to demonstrate such an analysis in the strongly correlated superfluid 4 He. Experimentally, there is no established technique to prepare an MQV in helium superfluids as an initial state of the instability problem. The realization of MQV in the BECs of ultra-cold gases sheds light on this problem, and vortex splitting has been observed. [7][8][9] The MQV in trapped systems can be dynamically unstable, and split into vortices with smaller winding numbers according to the Bogoliubovde Gennes (BdG) analysis at zero temperature. [10][11][12][13][14][15][16][17] Dynamic instability may occur when the excitation modes have complex frequencies as a result of coupling or "mixing" between two modes with positive and negative excitation energies. The negative energy mode, called the core mode, is localized at the vortex core and decreases the angular momentum of the system by −l in the direction along the core. The positive energy mode is a collective mode of the condensate. The instability depends on the atomic interaction strength in a complicated

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confidence: 87%

Is a Doubly Quantized Vortex Dynamically Unstable in Uniform Superfluids?

2018

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“…We have solved the BdGE for the case of the domain wall (see Eqs. (4.16-4.19) in 22 ). The limit of k → ∞, which in the bulk BEC results in the energy spectrum ε = 2 k 2 /2m+µ where m is the mass of the boson and µ = gn 0 is the chemical potential while g and n 0 are the coupling constant and the BEC particle density, respectively, then leads to ε = 2 k 2 /2m + µ − ∆.…”

Section: Introductionmentioning

confidence: 94%

“…We first derive the large and small wavelength solutions of the BdGE, noting that solely the large wavelength case has been considered before. 18,22 A. Large wavelengths First consider the case of κ → 0.…”

Section: Asymptotic Solutionsmentioning

confidence: 99%

“…16,18,20,21 While recently, Ref. 22 obtained such an analytical solution in the presence of a domain wall, it is restricted to large wavelengths, and furthermore faces the difficulty of extrapolation to the case of an infinitesize surface. We stress that even the classical ripplon (fractional power law) spectrum at small wavenumbers is not trivially obtained from the BdGE, where no classical (phenomenological) surface tension is assumed a priori.…”

Section: Introductionmentioning

confidence: 99%

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Exact surface-wave spectrum of a dilute quantum liquid

Pikhitsa

Fischer

2019

Phys. Rev. B

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We consider a dilute gas of bosons with repulsive contact interactions, described on the mean-field level by the Gross-Pitaevskiǐ equation, and bounded by an impenetrable "hard" wall (either rigid or flexible). We solve the Bogoliubov-de Gennes equations for excitations on top of the Bose-Einstein condensate analytically, by using matrix-valued hypergeometric functions. This leads to the exact spectrum of gapless Bogoliubov excitations localized near the boundary. The dispersion relation for the surface excitations represents for small wavenumbers k a ripplon mode with fractional power law dispersion for a flexible wall, and a phonon mode (linear dispersion) for a rigid wall. For both types of excitation we provide, for the first time, the exact dispersion relations of the dilute quantum liquid for all k along the surface, extending to k → ∞. The small wavelength excitations are shown to be bound to the surface with a maximal binding energy ∆ = 1 8 ( √ 17 − 3) 2 mc 2 0.158 mc 2 , which both types of excitation asymptotically approach, where m is mass of bosons and c bulk speed of sound. We demonstrate that this binding energy is close to the experimental value obtained for surface excitations of helium II confined in nanopores, reported in Phys. Rev. B 88, 014521 (2013). arXiv:1812.08002v2 [cond-mat.quant-gas]

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“…The formulas of dispersion relations interpolating small and large system sizes were recently obtained in Ref. [14]. A relationship between the number of NG modes and the homotopy group for topological solitons was also studied [15].…”

Section: Introductionmentioning

confidence: 99%

Interpolating relativistic and nonrelativistic Nambu-Goldstone and Higgs modes

Kobayashi

Nitta

2015

Phys. Rev. D

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When a continuous symmetry is spontaneously broken in nonrelativistic theories, there appear Nambu-Goldstone (NG) modes, the dispersion relations of which are either linear (type I) or quadratic (type II). We give a general framework to interpolate between relativistic and nonrelativistic NG modes, revealing a nature of type-I and -II NG modes in nonrelativistic theories. The interpolating Lagrangians have the nonlinear Lorentz invariance which reduces to the Galilei or Schrödinger invariance in the nonrelativistic limit. We find that type-I and type-II NG modes in the interpolating region are accompanied with a Higgs mode and a chiral NG partner, respectively, both of which are gapful. In the ultrarelativistic limit, a set of a type-I NG mode and its Higgs partner remains, while a set of a type-II NG mode and its gapful NG partner turns to a set of two type-I NG modes. In the nonrelativistic limit, the both types of accompanied gapful modes become infinitely massive, disappearing from the spectrum. The examples contain a phonon in Bose-Einstein condensates or helium superfluids, a phonon and magnon in spinor Bose-Einstein condensates, a magnon in ferromagnets, and a kelvon and dilaton-magnon localized around a Skyrmion line in ferromagnets.

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Nambu-Goldstone modes propagating along topological defects: Kelvin and ripple modes from small to large systems

Cited by 22 publications

References 39 publications

Is a Doubly Quantized Vortex Dynamically Unstable in Uniform Superfluids?

Is a Doubly Quantized Vortex Dynamically Unstable in Uniform Superfluids?

Exact surface-wave spectrum of a dilute quantum liquid

Interpolating relativistic and nonrelativistic Nambu-Goldstone and Higgs modes

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