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

Fractionalization of angular momentum at finite temperature around a magnetic vortex

Sitenko, Yu A, Vlasii, N D

Published Aug 30, 2006• 1 citation
OpenAlex

Abstract

Ambiguities in the definition of angular momentum of a quantum-mechanical particle in the presence of a magnetic vortex are reviewed. We show that the long-standing problem of the adequate definition is resolved in the framework of the second-quantized theory at nonzero temperature. Planar relativistic Fermi gas in the background of a point-like magnetic vortex with arbitrary flux is considered, and we find thermal averages, quadratic fluctuations, and correlations of all observables, including angular momentum, in this system. The kinetic definition of angular momentum is picked out unambiguously by the requirement of plausible behaviour for the angular momentum fluctuation and its correlation with fermion number.

Related papers

Quantum oscillations in ultracold Fermi gases: Realizations with rotating gases or artificial gauge fields

Charles Grenier, Corinna Kollath, Antoine Georges

We consider the angular momentum of a harmonically trapped, noninteracting Fermi gas subject to either rotation or to an artificial gauge field. The angular momentum of the gas is shown to display oscillations as a function of the particle number or chemical potential. This phenomenon is analogous to the de Haas--van Alphen oscillations of the magnetization in the solid-state context. However, key differences exist between the solid-state and ultracold atomic gases that we point out and analyze. We explore the dependence of the visibility of these oscillations on the physical parameters and propose two experimental protocols for their observation. Due to the very strong dependence of the amplitude of the oscillations on temperature, we propose their use as a sensitive thermometer for Fermi gases in the low-temperature regime.

arXiv:1212.6189•Physical Review A•Mar 4, 2013•11 citations

Angular momentum in interacting many-body systems hides in phantom vortices

Storm Weiner, Marios C. Tsatsos, L. S. Cederbaum +1 more

Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the $\textit{phantom vortex}$ that, contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but $\textit{not}$ of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortex modes which so far seem to have evaded experimental detection.

arXiv:1409.7670•Sep 26, 2014•6 citations

Angular Momentum Quantization of a Charge-flux Composite: Quantum Electrodynamic Approach

Kicheon Kang

The fractional angular momentum of a two-dimensional charge-flux composite is a well-established phenomenon usually derived from a semiclassical Hamiltonian. However, when the composite is treated as an isolated system in free two-dimensional space, the fundamental rotational and reflection symmetries of the $O(2)$ group demand that its total angular momentum is strictly quantized. We address this conceptual discrepancy by applying a full quantum electrodynamic (QED) approach combined with Noether's theorem. We demonstrate that the interaction between the charge and flux, mediated by the vacuum electromagnetic field, generates an intrinsic interaction angular momentum composed of both field momentum and hidden relativistic momentum. This gauge-invariant interaction angular momentum exactly compensates for the fractional part of the kinetic angular momentum. Consequently, the net angular momentum of the composite strictly follows the integer or half-integer quantization rule. Our formalism clarifies that the conventional fractional spin corresponds to the expectation value of the kinetic angular momentum within the perturbed QED ground state. It also elucidates why the standard classical field angular momentum definition fails to capture this in two dimensions, due to non-vanishing boundary terms.

cond-mat.mes-hallCross-listedarXiv:2607.20283•Jul 23, 2026

Experimental Consequences of Proposed Angular Momentum Spectra for a Charged Spinless Particle in the Presence of Long-Range Magnetic Flux

Mark P. Silverman

A quantum interference experiment is proposed which can unambiguously test for odd half-integer eigenvalues in the angular momentum spectra predicted for a spinless charged particle orbiting, but not penetrating, a solenoid with confined magnetic field or a superconducting vortex with odd integer number of flux quanta.

Physical Review Letters•Nov 21, 1983•18 citations

Quantum fluctuations of a vortex in a dilute Bose–Einstein condensate

Jacek Dziarmaga, Jakub Meisner

A vortex in a quasi two-dimensional Bose–Einstein condensate is subject to the Magnus force and can be effectively described as a planar particle in a uniform magnetic field. Quantization of this effective particle leads to the lowest Landau level where the most localized wavefunction is a Gaussian. In this Gaussian state, vortex position seems to fluctuate with an average magnitude set by the magnetic width of the Gaussian. We readdress this problem using the number-conserving version of the Bogoliubov theory. We find that the Bogoliubov mode that might be interpreted as a fluctuation of vortex position actually does not contribute to quantum depletion in the centre of vortex core. Far in the Thomas–Fermi regime the only contribution comes from phonon modes, but it is an order of magnitude less than the simple estimate, based on the magnetic width of the effective Gaussian wave packet. At the same time density of non-condensed atoms inside vortex core is a factor of 0.23 less than far from the core. The non-condensed atoms are expelled from the core by centrifugal force.

arXiv:cond-mat/0410707•Journal of Physics B Atomic Molecular and Optical Physics•Nov 9, 2005•3 citations

Fractional Angular Momentum in Cold-Atom Systems

Yuhe Zhang, G. J. Sreejith, Nathan Gemelke +1 more

The quantum statistics of bosons or fermions are manifest through the even or odd relative angular momentum of a pair. We show theoretically that, under certain conditions, a pair of certain test particles immersed in a fractional quantum Hall state possesses, effectively, a fractional relative angular momentum, which can be interpreted in terms of fractional braid statistics. We propose that the fractionalization of the angular momentum can be detected directly through the measurement of the pair correlation function in rotating ultracold atomic systems in the fractional quantum Hall regime. Such a measurement will also provide direct evidence for the effective magnetic field resulting from Berry phases arising from attached vortices, and of excitations with a fractional particle number, analogous to the fractional charge of the electron fractional quantum Hall effect.

arXiv:1409.6251•Physical Review Letters•Oct 16, 2014•43 citations
Ambiguities in the definition of angular momentum of a quantum-mechanical particle in the presence of a magnetic vortex are reviewed. We show that the long-standing problem of the adequate definition is resolved in the framework of the second-quantized theory at nonzero temperature. Planar relativistic Fermi gas in the background of a point-like magnetic vortex with arbitrary flux is considered, and we find thermal averages, quadratic fluctuations, and correlations of all observables, including angular momentum, in this system. The kinetic definition of angular momentum is picked out unambiguously by the requirement of plausible behaviour for the angular momentum fluctuation and its correlation with fermion number.
We consider the angular momentum of a harmonically trapped, noninteracting Fermi gas subject to either rotation or to an artificial gauge field. The angular momentum of the gas is shown to display oscillations as a function of the particle number or chemical potential. This phenomenon is analogous to the de Haas--van Alphen oscillations of the magnetization in the solid-state context. However, key differences exist between the solid-state and ultracold atomic gases that we point out and analyze. We explore the dependence of the visibility of these oscillations on the physical parameters and propose two experimental protocols for their observation. Due to the very strong dependence of the amplitude of the oscillations on temperature, we propose their use as a sensitive thermometer for Fermi gases in the low-temperature regime.
Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex\textit{phantom vortex}phantom vortex that, contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but not\textit{not}not of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortex modes which so far seem to have evaded experimental detection.
The fractional angular momentum of a two-dimensional charge-flux composite is a well-established phenomenon usually derived from a semiclassical Hamiltonian. However, when the composite is treated as an isolated system in free two-dimensional space, the fundamental rotational and reflection symmetries of the O(2)O(2)O(2) group demand that its total angular momentum is strictly quantized. We address this conceptual discrepancy by applying a full quantum electrodynamic (QED) approach combined with Noether's theorem. We demonstrate that the interaction between the charge and flux, mediated by the vacuum electromagnetic field, generates an intrinsic interaction angular momentum composed of both field momentum and hidden relativistic momentum. This gauge-invariant interaction angular momentum exactly compensates for the fractional part of the kinetic angular momentum. Consequently, the net angular momentum of the composite strictly follows the integer or half-integer quantization rule. Our formalism clarifies that the conventional fractional spin corresponds to the expectation value of the kinetic angular momentum within the perturbed QED ground state. It also elucidates why the standard classical field angular momentum definition fails to capture this in two dimensions, due to non-vanishing boundary terms.
A vortex in a quasi two-dimensional Bose–Einstein condensate is subject to the Magnus force and can be effectively described as a planar particle in a uniform magnetic field. Quantization of this effective particle leads to the lowest Landau level where the most localized wavefunction is a Gaussian. In this Gaussian state, vortex position seems to fluctuate with an average magnitude set by the magnetic width of the Gaussian. We readdress this problem using the number-conserving version of the Bogoliubov theory. We find that the Bogoliubov mode that might be interpreted as a fluctuation of vortex position actually does not contribute to quantum depletion in the centre of vortex core. Far in the Thomas–Fermi regime the only contribution comes from phonon modes, but it is an order of magnitude less than the simple estimate, based on the magnetic width of the effective Gaussian wave packet. At the same time density of non-condensed atoms inside vortex core is a factor of 0.23 less than far from the core. The non-condensed atoms are expelled from the core by centrifugal force.
The quantum statistics of bosons or fermions are manifest through the even or odd relative angular momentum of a pair. We show theoretically that, under certain conditions, a pair of certain test particles immersed in a fractional quantum Hall state possesses, effectively, a fractional relative angular momentum, which can be interpreted in terms of fractional braid statistics. We propose that the fractionalization of the angular momentum can be detected directly through the measurement of the pair correlation function in rotating ultracold atomic systems in the fractional quantum Hall regime. Such a measurement will also provide direct evidence for the effective magnetic field resulting from Berry phases arising from attached vortices, and of excitations with a fractional particle number, analogous to the fractional charge of the electron fractional quantum Hall effect.