Momentum Distribution of a mass-imbalanced three-body system across the Efimov-Unatomic transition

summary

The gist

The gist The asymptotic momentum distribution at Dc is governed by a distinct logarithmic scaling structure, which differs fundamentally from both the log-periodic behavior of Efimov states and the

In short

The study investigates how changing spatial dimensions drives a transition between discrete and continuous scale invariance in mass-imbalanced three-body systems at a critical dimension Dc. The resulting momentum distribution at this transition exhibits a unique logarithmic scaling structure, requiring an additional quadratic-logarithmic term ($C_3''$) that depends sensitively on mass imbalance, revealing new universal scaling properties.

Key concepts

Critical Dimension ($D_c$): This is the specific spatial dimension where the physics of three-body systems undergoes a fundamental change, transitioning from one type of scale invariance (discrete) to another (continuous). Tuning the system's dimension across this point reveals emergent scaling behaviors not seen in standard regimes.
Intermediate Scaling Regime (SIR): This is a narrow region between the Efimov regime and the unatomic regime where neither description fully applies. The properties and size of this intermediate region are strongly influenced by the mass ratio of the particles, acting as a bridge between different physical behaviors.
Quadratic-Logarithmic Contribution ($C_3''$): This term is an extra component in the asymptotic momentum distribution scaling at $D_c$. Its coefficient depends heavily on how imbalanced the masses are and can change sign. It dictates how three-body contributions cancel at a specific momentum, leaving the two-body interaction dominant.
Scale Invariance Transition: This refers to the shift in how physical properties scale with changes in system parameters. The paper shows that tuning dimensionality acts as a control parameter that drives this transition, moving the system from discrete scaling (like Efimov states) to continuous scaling (like power laws).

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This episode discusses

Momentum Distribution of a mass-imbalanced three-body system across the Efimov-Unatomic transition · Paper Radio

The paper

Momentum Distribution of a mass-imbalanced three-body system across the Efimov-Unatomic transition · Read on arXiv

Instituto Tecnol´ogico de Aeron´autica · Universit´e Paris-Saclay · Instituto de F´ısica Teórica, Universidade Estadual Paulista

DOI: 10.1103/ngg6-1mk4

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Momentum Distribution of a mass-imbalanced three-body system across the Efimov-Unatomic transition".

Mira: Here's the gist of the paper. The gist The asymptotic momentum distribution at Dc is governed by a distinct logarithmic scaling structure, which differs fundamentally from both the log-periodic behavior of Efimov states and the power-law scaling of the unatomic regime.

Kai: Emergence of Scaling Regimes The study investigates how dimensionality acts as an effective control parameter driving the evolution from discrete to continuous scale invariance in a mass-imbalanced three-body system.

Mira: The analysis identifies a narrow interval separating these regimes, referred to as an intermediate scaling regime (SIR), whose extent is strongly controlled by the mass ratio.

Kai: Momentum Space Structure at Transition The momentum distribution at the critical dimension Dc is governed by a distinct scaling structure characterized by a logarithmic dependence that differs fundamentally from both the log-periodic oscillations of the Efimov regime and the power-law scaling of the unatomic regime.

Paper summary: Kai: So, to recap what we’ve seen, this paper investigates the single-particle momentum distribution and contact parameters for massimbalanced three-body systems at D c, where the transition between discrete and continuous scale invariance happens when tuning dimension between three and two.

Mira: They show that at this critical dimension D c, the asymptotic momentum distribution follows a distinct logarithmic scaling structure, which is fundamentally different from both the log-periodic behavior of Efimov states and the power-law scaling of the unatomic regime.

Lev: The main claim is that this specific structure requires introducing an additional three-body contact parameter associated with a quadratic logarithmic contribution.

Kai: This C three'' term leads to a finite and well-defined description of the momentum tail at the transition, which was incomplete in previous analyses where the three-body contribution became formally divergent <ref:2607.13769#pg1>.

Mira: They point out that this coefficient C three'' depends sensitively on the mass imbalance, changing sign depending on mass configurations and vanishing for identical particles <ref:2607.13769#pg1>.

Lev: For heavy-light-light systems, they found that the subleading three-body term vanishes at a characteristic momentum, leaving the leading two-body contribution at the order retained in the asymptotic expansion.

Kai: They also analyze a narrow intermediate region connecting those Efimov and unatomic regimes, identifying it as an intermediate scaling regime whose extent is strongly controlled by the mass ratio.

Mira: Essentially, this work establishes that D c is a regime with emergent scaling properties and provides quantitative momentum-space signatures for probing the transition between discrete and continuous scale invariance in few-body quantum systems.

Lev: It sets up a clear picture of how dimensionality acts as an effective control parameter driving the system across this boundary.

Conclusion: Kai: Looking at this whole thing, the title itself points to something central: how momentum distribution behaves when you cross that boundary between discrete and continuous scaling in a mass-imbalanced three-body system.

Mira: What’s important for the broader context is that they found a new way to characterize that transition using these specific contact parameters.

Lev: So, if you think about this for experimentalists, it means they can look at the high-momentum tail of a momentum distribution and see how the mass imbalance affects its shape right near D c.

Kai: It connects the abstract mathematical concept of scale invariance directly to measurable features in momentum space that aren't obvious from just looking at energy spectra.

Mira: The implication is that by controlling the mass ratio or tuning the effective spatial dimension, we can move systems across this phase transition and observe fundamentally different scaling behaviors.

Lev: It suggests that probing these regimes might reveal underlying conformal symmetries in few-body interactions in ways that are currently hard to access.

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