Generalized Efimov effect in one dimension

Abstract

We study a one-dimensional quantum problem of two particles interacting with a third one via a scale-invariant subcritically attractive inverse square potential, which can be realized, for example, in a mixture of dipoles and charges confined to one dimension. We find that above a critical mass ratio, this version of the Calogero problem exhibits the generalized Efimov effect, the emergence of discrete scale invariance manifested by a geometric series of three-body bound states with an accumulation point at zero energy.

5+3 pages, 3 figures, published version

References in corpus (5)

• Many-Body Physics with Ultracold Gases
• Observation of the Efimov state of the helium trimer
• Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance
• Universal three-body parameter in heteronuclear atomic systems
• Electron Capture and Scaling Anomaly in Polar Molecules

Cited by in corpus (22)

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• Finite-range effects in ultradilute quantum drops
• A Pure Confinement Induced Trimer in One-Dimensional Atomic Waveguides
• Quantum vortices of strongly interacting photons
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• The three-body pseudo-potential for atoms confined in one dimension
• Investigating Effects of Relativistic Kinematics, Dimensionality, Interactions, and Short-Range Correlations on the Ratio of Quartic over Quadratic Nuclear Symmetry Energies
• Holding and transferring matter-wave solitons against gravity by spin-orbit-coupling tweezers
• D-dimensional three-body bound-state problem with zero range interactions
• Discrete Scale-Invariant Boson-Fermion Duality in One Dimension
• Universality of excited three-body bound states in one dimension
• Duality between the quantum inverted harmonic oscillator and inverse square potentials
• Bubble-bound state of triple-stranded DNA: Efimov Physics in DNA with repulsion
• SUSY shields the scaling symmetry of conformal quantum mechanics
• Three-body bound states of two bosons and one impurity in one dimension
• Efimov effect for two particles on a semi-infinite line
• Efimov Effect in Long-range Quantum Spin Chains
• Universality and tails of long range interactions in one dimension
• Fall-to-the-centre as a $\mathcal{P}\mathcal{T}$ symmetry breaking transition
• Discrete Scale Invariance and $U(2)$ Family of Two-Body Contact Interactions in One Dimension
• Reliability of the Born-Oppenheimer approximation in noninteger dimensions
• Welch's method transform of strange attractors of argon glow discharge plasmas: symmetric zero point energy fluctuations of particles, anti-particles and virtual particles