arXiv subjects

Boris A. Khanikati

Publications and source records attributed to Boris A. Khanikati.

3 recordsLinked to original sources

arXiv2026

Emptiness formation in the Lieb-Liniger gas: hydrodynamic instantons and a conjectured rate function

We study the emptiness formation probability (EFP) in the ground state of the repulsive one-dimensional Lieb-Liniger Bose gas. For a macroscopic empty interval of length $2R$, its leading asymptotic behavior is described by a rate function $f(γ_0)$, defined by $-\log P(R)\sim(ρ_0R)^2f(γ_0)$, where $ρ_0$ is the mean density and $γ_0$ is the dimensionless interaction strength. We propose a parameter-free integral equation for $f(γ_0)$. Starting from the exact dual-field Fredholm-determinant representation of the EFP, we show how the conjectured kernel arises formally and identify the uniform asymptotic statement that remains to be proven for a rigorous derivation. The conjecture reproduces the Tonks-Girardeau and weak-coupling limits, as well as the first correction obtained independently in both limits. It also agrees at the few-percent level with numerical minimization of the Lieb-Liniger hydrodynamic action over more than four orders of magnitude in coupling. The numerical calculation yields the corresponding emptiness instantons and their astroid-like vacuum regions.

cond-mat.quant-gas↗

arXiv2026

On the collapse of three point vortices on surfaces

Point vortices represent an important reduced model describing two-dimensional ideal fluid dynamics. It is well known that there exist three-vortex configurations on the Euclidean plane $\mathbb{R}^2$ that exhibit finite-time singularities, i.e., collapse to a single point. Moreover, in $\mathbb{R}^2$, such collapses occur only self-similarly. Here, we investigate the extent to which this phenomenon persists on curved surfaces. We show that self-similar collapse is a universal feature of surfaces of nonnegative constant curvature, namely the plane and the sphere. In contrast, on the hyperbolic plane, it is shown that self-similar collapsing solutions do not exist with respect to any distance variable defined by an analytic function of the geodesic distance. Finally, we establish the existence of nearly self-similar collapse of three vortices on arbitrary smooth surfaces embedded in $\mathbb{R}^3$.

physics.flu-dyn↗

arXiv2025

Time-diffracting 2D wave vortices

Wave vortices constitute a large family of wave entities, closely related to phase singularities and orbital angular momentum (OAM). So far, two main classes of localized wave vortices have been explored: (i) transversely-localized monochromatic vortex beams that carry well-defined longitudinal OAM and propagate/diffract along the longitudinal $z$-axis in space, and (ii) 2D-localized spatiotemporal vortex pulses that carry the more elusive transverse (or tilted) OAM and propagate/diffract along both the $z$-axis and time. Here we introduce another class of wave vortices which are localized in a 2D $(x,y)$ plane, do not propagate in space (apart from uniform radial deformations), and instead propagate/diffract solely along time. These vortices possess well-defined transverse OAM and can naturally appear in 2D wave systems, such as surface polaritons or water waves. We provide a general integral expression for time-diffracting 2D wave vortices, their underlying ray model, and examples of approximate and exact wave solutions. We also analyze the temporal Gouy phase closely related to the rotational evolution in such vortices. Finally, we show that time-diffracting 2D vortices can provide strong spatiotemporal concentration of energy and OAM at sub-wavelength and oscillation-period scales.

physics.optics↗