Simulating infinite vortex lattices in superfluids (original) (raw)
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Vortex Phases of Rotating Superfluids
Journal of Physics: Conference Series, 2013
We report on the first mathematically rigorous proofs of a transition to a giant vortex state of a superfluid in rotating anharmonic traps. The analysis is carried out within two-dimensional Gross-Pitaevskii theory at large coupling constant and large rotational velocity and is based on precise asymptotic estimates on the ground state energy. An interesting aspect is a significant difference between 'soft' anharmonic traps (like a quartic plus quadratic trapping potential) and traps with a fixed boundary. In the former case vortices persist in the bulk until the width of the annulus becomes comparable to the size of the vortex cores. In the second case the transition already takes place in a parameter regime where the size of vortices is very small relative to the width of the annulus. Moreover, the density profiles in the annulus are different in the two cases. In both cases rotational symmetry of the density in a true ground state is broken, even though a symmetric variational ansatz gives an excellent approximation to the energy.
Vortices and vortex lattices in quantum ferrofluids
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Massive Quantum Vortices in Superfluids
Journal of physics, 2023
We consider the dynamical properties of quantum vortices with filled massive cores, hence the term "massive vortices". While the motion of massless vortices is described by firstorder motion equations, the inclusion of core mass introduces a second-order time derivative in the motion equations and thus doubles the number of independent dynamical variables needed to describe the vortex. The simplest possible system where this physics is present, i.e. a single massive vortex in a circular domain, is thoroughly discussed. We point out that a massive vortex can exhibit various dynamical regimes, as opposed to its massless counterpart, which can only precess at a constant rate. The predictions of our analytical model are validated by means of numerical simulations of coupled Gross-Pitaevskii equations, which indeed display the signature of the core inertial mass. Eventually, we discuss a nice formal analogy between the motion of massive vortices and that of massive charges in two-dimensional domains pierced by magnetic fields.
Rotating superfluids in anharmonic traps: From vortex lattices to giant vortices
Physical Review A, 2011
We study a superfluid in a rotating anharmonic trap and explicate a rigorous proof of a transition from a vortex lattice to a giant vortex state as the rotation is increased beyond a limiting speed determined by the interaction strength. The transition is characterized by the disappearance of the vortices from the annulus where the bulk of the superfluid is concentrated due to centrifugal forces while a macroscopic phase circulation remains. The analysis is carried out within two-dimensional Gross-Pitaevskii theory at large coupling constant and reveals significant differences between 'soft' anharmonic traps (like a quartic plus quadratic trapping potential) and traps with a fixed boundary: In the latter case the transition takes place in a parameter regime where the size of vortices is very small relative to the width of the annulus whereas in 'soft' traps the vortex lattice persists until the width of the annulus becomes comparable to the vortex cores. Moreover, the density profile in the annulus where the bulk is concentrated is, in the 'soft' case, approximately gaussian with long tails and not of the Thomas-Fermi type like in a trap with a fixed boundary.
Hydrodynamic Boundary Conditions in Superfluids
Japanese Journal of Applied Physics, 1987
We derive boundary conditions that allow a three-dimensional periodic array of superfluid vortices to be modeled in a Cartesian domain. The method is applicable to vortices in the Gross-Pitaevskii description of a superfluid and to fluxtubes in the Ginzburg-Landau description of a superconductor. Unlike standard methods for modeling infinite arrays of vortices, the boundary conditions can be used to study the three-dimensional tangling and reconnection of vortex lines expected in superfluid turbulence. In the two-dimensional case, the boundary conditions include two parameters that determine the lattice offset, which for a single superfluid is essentially arbitrary. In the three-dimensional case the boundary conditions include three parameters that must satisfy a particular linear relationship. We present an algorithm for finding all vortex lattice states within a given domain. We demonstrate the utility of the boundary conditions in two specific problems with imperfect or tangled lattices.
Particles and fields in superfluids: Insights from the two-dimensional Gross-Pitaevskii equation
Physical Review A
We carry out extensive direct numerical simulations (DNSs) to investigate the interaction of active particles and fields in the two-dimensional (2D) Gross-Pitaevskii (GP) superfluid, in both simple and turbulent flows. The particles are active in the sense that they affect the superfluid even as they are affected by it. We tune the mass of the particles, which is an important control parameter. At the one-particle level, we show how light, neutral, and heavy particles move in the superfluid, when a constant external force acts on them; in particular, beyond a critical velocity, at which a vortex-antivortex pair is emitted, particle motion can be periodic or chaotic. We demonstrate that the interaction of a particle with vortices leads to dynamics that depends sensitively on the particle characteristics. We also demonstrate that assemblies of particles and vortices can have rich, and often turbulent spatiotemporal evolution. In particular, we consider the dynamics of the following illustrative initial configurations: (a) one particle placed in front of a translating vortex-antivortex pair; (b) two particles placed in front of a translating vortex-antivortex pair; (c) a single particle moving in the presence of counter-rotating vortex clusters; and (d) four particles in the presence of counter-rotating vortex clusters. We compare our work with earlier studies and examine its implications for recent experimental studies in superfluid Helium and Bose-Einstein condensates.
A vortex filament tracking method for the Gross–Pitaevskii model of a superfluid
Journal of Physics A: Mathematical and Theoretical, 2016
We present an accurate and robust numerical method to track quantized vortex lines in a superfluid described by the Gross-Pitaevskii equation. By utilizing the pseudovorticity field of the associated complex scalar order parameter of the superfluid, we are able to track the topological defects of the superfluid and reconstruct the vortex lines which correspond to zeros of the field. Throughout, we assume our field is periodic to allow us to make extensive use of the Fourier representation of the field and its derivatives in order to retain spectral accuracy. We present several case studies to test the precision of the method which include the evaluation of the curvature and torsion of a torus vortex knot, and the measurement of the Kelvin wave spectrum of a vortex line and a vortex ring. The method we present makes no a-priori assumptions on the geometry of the vortices and is therefore applicable to a wide range of systems such as a superfluid in a turbulent state that is characterised by many vortex rings coexisting with sound waves. This allows us to track the positions of the vortex filaments in a dense turbulent vortex tangle and extract statistical information about the distribution of the size of the vortex rings and the inter-vortex separations. In principle, the method can be extended to track similar topological defects arising in other physical systems.
Annals of Physics, 2014
We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popov's hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov's action, which, in particular, allows for weak solutions of the Gross-Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying within the phonon part of the spectrum, contrary to traditional view.
Vortex lattices in binary mixtures of repulsive superfluids
Physical Review A
We present an extension of the framework introduced in [1] to treat multicomponent systems, showing that new degrees of freedom are necessary in order to obtain the desired boundary conditions. We then apply this extended framework to the coupled Gross-Pitaevskii equations to investigate the ground states of two-component systems with equal masses thereby extending previous work in the lowest Landau limit [2] to arbitrary interactions within Gross-Pitaevskii theory. We show that away from the lowest-Landau level limit, the predominant vortex lattice consists of two interlaced triangular lattices. Finally, we derive a linear relation which accurately describes the phase boundaries in the strong interacting regimes.