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Vortex Mass

Григорий Ефимович Воловик

Published Feb 26, 2009• 0 citations
Publisher

Abstract

Abstract The mass (inertia) of an object is determined as the response of the momentum of the object to its velocity. This chapter discusses the inertia of an object moving in the quantum vacuum of the Galilean quantum liquid. If it is a foreign object like a 3He atom moving in the quantum vacuum of superfluid 4He, then in addition to its bare mass the object acquires an extra mass, since it involves some part of the superfluid vacuum into motion. If the object is an excitation of the vacuum, like a vortex, all its mass is provided by the liquid. In addition to the associated hydrodynamic mass, which is similar to associated mass of external body moving in the liquid, there are two more contributions to a vortex mass. The ‘relativistic’ mass is the consequence of effective metric in superfluids. It is obtained as vortex energy divided by square of speed of sound, which plays the role of speed of light. In fermionic superfluids the Kopnin mass is added, which results from the fermion zero modes in the vortex core. This mass is related to peculiar phenomenon in quantum field theory. In the limit of smooth core these bound states behave as chiral massless fermions in the presence of magnetic field, and the additional vortex mass results from the non-zero density of states in magnetic field.

DOI
10.1093/acprof:oso/9780199564842.003.0024

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•Feb 26, 2009•0 citations
Abstract The mass (inertia) of an object is determined as the response of the momentum of the object to its velocity. This chapter discusses the inertia of an object moving in the quantum vacuum of the Galilean quantum liquid. If it is a foreign object like a 3He atom moving in the quantum vacuum of superfluid 4He, then in addition to its bare mass the object acquires an extra mass, since it involves some part of the superfluid vacuum into motion. If the object is an excitation of the vacuum, like a vortex, all its mass is provided by the liquid. In addition to the associated hydrodynamic mass, which is similar to associated mass of external body moving in the liquid, there are two more contributions to a vortex mass. The ‘relativistic’ mass is the consequence of effective metric in superfluids. It is obtained as vortex energy divided by square of speed of sound, which plays the role of speed of light. In fermionic superfluids the Kopnin mass is added, which results from the fermion zero modes in the vortex core. This mass is related to peculiar phenomenon in quantum field theory. In the limit of smooth core these bound states behave as chiral massless fermions in the presence of magnetic field, and the additional vortex mass results from the non-zero density of states in magnetic field.
Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov quasiparticles localized in the core. These bound states form the normal component, which is nonzero even in the low-temperature limit. In the collisionless regime ω 0 τ≫1 the normal component trapped by the vortex is unbound from the normal component in a bulk superfluid/superconductor and adds to the inertial mass of the moving vortex. In a d-wave superconductor the vortex mass has an additional factor of (B c2/B)1/2 due to the gap nodes.
Quantum vortices are commonly described as funnel-like objects around which the superfluid swirls, and their motion is typically modeled in terms of massless particles. Here we show that in Fermi superfluids the normal component confined in the vortex core provides the vortex with a finite inertial mass. This inertia imparts an unambiguous signature to the dynamic behavior of vortices, specifically manifesting as small-amplitude transverse oscillations which remarkably follow the prediction of a simple point-like model supplemented by an effective mass. We demonstrate this phenomenon through large-scale time-dependent simulations of Fermi superfluids across a wide range of interaction parameters, at both zero and finite temperatures, and for various initial conditions. Our findings pave the way for the exploration of inertial effects in superfluid vortex dynamics.
Vortex mass, which is the inertia of a quantum vortex, has never been observed in superfluids and is a long-standing problem in low-temperature physics. The impact of the mass is considered negligible in typical experiments with superfluid 4He^{4}\mathrm{He}4He. Recent developments of experimental techniques for manipulating quantum vortices in superfluid atomic gases have enabled us to test this problem more accurately. By introducing the vortex mass time and length as universal scales to many-body problems of massive quantum vortices, the theoretical description is formulated in the simplest manner and is universally applicable to different quantum fluids, including fermionic and multicomponent superfluids. There are two branches, the cyclotron and massless branches, for the circular motion of a pair of like-sign vortices. Finding a stable cyclotron branch for the motion of vortices is a clear evidence of vortex mass and superfluid $^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{B}$ is the specific example of a system where this phenomena could be observed. The impact of the mass on the massless branch is small but can be enhanced by taking the difference in the two-body dynamics of point vortices with different initial conditions. Our results imply that the vortex mass is a direct cause of the splitting instability of a doubly quantized vortex at absolute zero and that the vortex mass length characterizes the final state after the instability. It is also demonstrated that a pair of massive vortices with opposite circulations has a critical distance characterized by the vortex mass length, below which they are spontaneously annihilated without thermal fluctuations.
The paper reassesses the old but still controversial problem of the transverse force on a vortex and the vortex mass. The transverse force from free bulk quasiparticles on the vortex, both in the Bose and the Fermi liquids, originates from the Aharonov-Bohm effect. However, in the Fermi liquid, one should take into account peculiarities of the Aharonov-Bohm effect for BCS quasiparticles described by two-component spinor wave functions. There is no connection between the transverse force (either from free bulk quasiparticles or from vortex-core bound quasiparticles) and the spectral flow in the vortex core in superfluid Fermi liquid, in contrast to widely known claims. In fact, there is no steady spectral flow in the core of the moving vortex, and the analogy with the Andreev bound states in the superconductor--normal-metal--superconductor junction, where the spectral flow is really possible, is not valid in this respect. The role of the backflow on the vortex mass is clarified. The backflow is an inevitable consequence of a mismatch between the currents inside and outside the vortex core and restores the conservation of the particle number (charge) violated by this mismatch. In the Fermi liquid, the backflow compensates the current through the core bound states, which is a source of the vortex mass (the Kopnin mass). This results in renormalization of the Kopnin vortex mass by a numerical factor.
Abstract This chapter presents a general discussion of the phenomenon of superfluidity, starting from the famous Landau criterion for the critical velocity. The Landau expression for the normal (non-superfluid) component of the gas, expressed in terms of the elementary excitations of the system, is derived. The relationship between Bose–Einstein condensation and the phenomenon of superfluidity is outlined, with special focus on the role played by the phase of the order parameter, whose gradient fixes the velocity of the superfluid. The chapter derives the hydrodynamic equations of superfluids at both zero and finite temperatures and discuss the solutions for first and second sound. The formalism of quantum hydrodynamics is presented, with an application to the Beliaev decay of phonons and to the calculation of the fluctuations of the phase. It also discusses the consequences for superfluidity on the rotational properties and the spatial structure of vortex lines.
Abstract This chapter deals with the Fermi systems, where the low-energy effective theory involves both bosonic and fermionic fields. Above the phase transition to the superconducting or superfluid state, the overwhelming majority of systems consisting of fermionic particles (electrons in metals, neutrons in neutron stars, 3He atoms in 3He liquid, etc.) form a so-called Fermi liquid. Below transition new types of fermionic vacua emerge. This chapter discusses the Bardeen–Cooper–Schrieffer (BCS) theory for spin-triplet superfluids, which provide examples of different universality classes of fermionic vacua: fully gapped vacua, vacua with stable and marginal point nodes — Fermi points, and vacua with nodal lines — Fermi lines. It also discusses emergent ‘relativistic’ quasiparticles, fundamental constants and hierarchy of Planck energy scales in fermionic systems, problem of vacuum energy and cosmological term in bi-metric gravity, and mass generation for Standard Model fermions.