arXiv subjects

S. V. Talalov

Publications and source records attributed to S. V. Talalov.

16 recordsLinked to original sources

arXiv2026

Quantum vortex in a fluid flow: negative effective mass and a novel mechanism for turbulence formation

We explore the movement of a thin, circular quantum vortex filament within an infinite cylindrical pipe. The fluid surrounding the vortex ring moves through the pipe at a non-zero velocity denoted by $v$. Our study examines the energy spectrum $E = E(p)$, where $p$ represents the total momentum of a vortex ring. We have demonstrated that the function $E(p)$ significantly depends on the velocity $v$. The discovered spectrum $E(p)$ reveals the existence of states with both negative and extremely large effective masses. We also explored the hypothesis regarding the existence of coupled vortex pairs possessing finite summary effective masses. Every pair consists of vortices that possess both positive and negative masses, with the magnitude of these masses being unrestricted. In our model, the criterion for the appearance of these states is based on comparing two numbers. The first is seen as a quantum counterpart to the Reynolds number, while the second represents its critical value for a flow with a single vortex. We also explore how this studied effect might contribute to the emergence of quantum turbulence. This study discusses a method for determining the critical Reynolds number in quantum turbulence, using the proposed model as a framework. Here, we use a new quantization technique for classical closed vortex filaments developed by the author earlier.

physics.flu-dyn↗

arXiv2025

Quantum vortices in entanglement: a novel idea for large vortex filaments

In this study, we propose a new approach to describing certain macroscopic objects that can arise in a quantum fluid. These objects are formed by means of quantum entanglement from the circular-shaped mesoscale and microscale vortices, and can be interpreted as a vortex filaments with any shape and size. The method is based on a quantization scheme for classical closed vortex filaments that was proposed by the author early \cite{Tal18,Tal22_1,Tal_Chaos25J}. The model we consider examines the instantaneous picture of the locations in space $\mathbb R_3$ of such filaments with a small, but non-zero, core diameter. Both energy and circulation of the studied filaments are calculated using the proposed approach. We demonstrate that the adopted concept leads to the emergence of secondary vortices around these investigated filament-like objects. We also study the specific mechanisms by which large vortex loops can disconnect and create the filament fragments . From our point of view, the proposed approach to describing vortex filaments within a vortex tangle can be seen as an important step toward understanding the appearance of quantum turbulence.

math-ph↗

arXiv2025

The study of the energy spectrum of a system of quantum micro-vortices in a bounded spatial domain

This study focuses on microscopic-sized quantum vortex filaments that are shaped like a circle. The model we considered examines loops with different radii and a small but non-zero core diameter. These loops are located in a bounded domain $D$. The quantization scheme of the classical vortices is based on the new approach proposed by the author \cite{Tal22_1,Tal24_2}. For these loops, we calculate both the quantized circulation and the energy spectrum, which are perfectly non-trivial. To understand how the results we have obtained can be used to describe the initial stage of turbulence in a quantum fluid, we study a system of $K$ random, non-interacting vortices. We explain how specific energy and circulation spectra lead to the occurrence of turbulence in the context of the developed approach.

cond-mat.quant-gas↗

arXiv2024

On the group-theoretical approach to energy quantization of a perturbed vortex ring: spectrum calculating in the pipe-type domain

In this study, the problem of the energy spectrum of a quantum vortex loop moving in a thin long pipe is solved for the first time. We quantize this dynamic system using a new method, which leads to non-trivial results for circulation $Γ$ and energy values $E$. It is shown that the spectrum has a quasi-continuous fractal structure. In the final form, we present the spectrum of the vortex loop in the form of a ''Regge trajectory'' $E = E(Γ)$. The vortex quantization problem is considered outside of two-fluid hydrodynamics and other conventional approaches. We also discuss ways to improve the model, which could allow us to apply the results we've obtained to describe a quantum turbulent flow.

math-ph↗

arXiv2024

The quantum vortices dynamics: spatio-temporal scale hierarchy and origin of turbulence

This study investigates the evolution and interaction of quantum vortex loops with a small but non-zero radius of core ${\sf a}$. The quantization scheme of the classical vortex system is based on the approach proposed by the author \cite{Tal,Tal_PhRF}. We consider small perturbations in the ring-shaped loops, which include both helical-type shape variations and small excitations of the flow in the vortex core. The quantization of the circulation $Γ$ is deduced from the first principles of quantum theory. As a result of our approach, the set of quantized circulation values is wider than the standard one. The developed theory introduces a hierarchical spatio-temporal scale in the quantum evolution of vortices. We also explore the applicability of this model for describing the origins of turbulence in quantum fluid flows. To achieve this specific objective, we employ the method of random Hamiltonians to describe the interaction of quantum vortex loops.

math-ph↗

arXiv2024

The turbulence development at its initial stage: a scenario based on the idea of vortices decay

In this paper, a model of the development of a quantum turbulence in its initial stage is proposed. The origin of the turbulence in the suggested model is the decay of vortex loops with an internal structure. We consider the initial stage of this process, before an equilibrium state is established. As result of our study, the density matrix of developing turbulent flow is calculated. The quantization scheme of the classical vortex rings system is based on the approach proposed by the author earlier.

physics.flu-dyn↗

arXiv2022

Closed Vortex Filament in a Cylindrical Domain: Circulation Quantization

This article investigates quantum oscillations of a vortex ring with zero thickness that evolves in a cylindrical domain $V = D \times [0,L]$. The symbol $D$ denotes the planar domain which is bounded by some closed connected curve $S$. The quantization scheme of this dynamical system is based on the approach proposed by the author earlier. As result, we find the discrete values $Γ_n$ for circulation $Γ$. In contrast to the traditional approach, where such quantities are usually postulated, the values $Γ_n$ are deduced rigorously as the consequence of the conventional scheme of quantum theory. The model demonstrates the splitting of levels also. In particular, the levels correction values depend on the domain $V$: both the cylinder height $L$ and the form of the curve $S$ affect the final formula for the quantities $Γ_n$. Moreover, we prove that the basic circulation levels demonstrate a "fine structure". These anomalous terms, which are proportional to the value $\hbar^2$, are calculated in the article as well. The conclusions are compared with some results of numerical simulations by other authors.

quant-ph↗

arXiv2021

Small Oscillations of a Vortex Ring: Hamiltonian Formalism and Quantization

This article investigates small oscillations of a vortex ring with zero thickness that evolves under the Local Induction Equation (LIE). We deduce the differential equation that describes the dynamics of these oscillations. We suggest the new approach to the Hamiltonian description of this dynamic system. This approach is based on the extension of the set of dynamical variables by adding the circulation $Γ$ as a dynamical variable. The constructed theory is invariant under the transformations of the Galilei group. The appearance of this group allows for a new viewpoint on the energy of a vortex filament with zero thickness. We quantize this dynamical system and calculate the spectrum of the energy and acceptable circulation values. The physical states of the theory are constructed with help of coherent states for the Heisenberg -Weyl group.

math-ph↗

arXiv2018

About the non-standard viewpoint on the dynamics of closed vortex filament

In this article we construct the Hamiltonian description of the closed vortex filament dynamics in terms of non-standard variables, phase space and constraints. The suggested approach makes obvious interpretation of considered system as a quasiparticle that possess certain external and internal degrees of the freedom. The constructed theory is invariant under the transformation of Galilei group. The appearance of this group allows for a new viewpoint on the energy of a closed vortex filament with zero thickness. The explicit formula for the effective mass of the quasiparticle 'closed vortex filament' is suggested.

math-ph↗

arXiv2017

The cosmic string as a channel for the massive particle teleportation

Here we prove the existence of a new type of the world-sheet string singularities - the cusps that are stable during the finite time. These singularities make the emission of the captured massive quantum particle possible in the frames of the author's model suggested earlier. In aggregate, we have a new mechanism of quantum teleportation of such particles at large distances.

math-ph↗

arXiv2016

A short study of a string on a plane: the energy and the effective mass

We investigate the new special class of the finite string on a plane, after the reduction from the relativistic $4D$ case. The suggested special form of the phase space allows to define the extended Galilei group as a group of the space - time symmetry for the considered system. The definition of the energy for the studied non-relativistic string through the Cazimir function of this group is suggested. The concept of the effective mass for the investigated dynamical system is introduced. The appearance of strong correlations between the degrees of freedom even on the classical level is discussed.

math-ph↗

arXiv2012

About the mechanism of matter transfer along cosmic string

We consider the quantum capture of nonrelativistic massive particle by the moving infinite curve (cosmic string in wire approximation). It is shown that the cusp appearing on a string at a certain point due to the string dynamics can make the wave function collapse at this point irrespective of the caption place.

math-ph↗

arXiv2011

The anyon model: an example inspired by string theory

We investigate the enlarged class of open finite strings in $(2+1)D$ space-time. The new dynamical system related to this class is constructed and quantized here. As the result, the energy spectrum of the model is defined by a simple formula ${\sf S} = α_n{\sf E} + c_n$; the spin ${\sf S}$ is an arbitrary number here but the constants $α_n$ and $c_n$ are eigenvalues for certain spectral problems in fermionic Fock space ${\bf H}_ψ$ constructed for the free 2D fermionic field.

math-ph↗

arXiv2011

Infinite planar string: cusps, braids and soliton exitations

We investigate infinite strings in $(2+1)D$ space-time, which may be considered as excitations of straight lines on the spatial plane. We also propose the hamiltonian description of such objects that differs from the standard hamiltonian description of the string. The hamiltonian variables are separated into two independent groups: the "internal" and "external" variables. The first ones are invariant under space-time transformations and are connected with the second form of the world-sheet. The "external" variables define the embedding of the world-sheet into space-time. The constructed phase space is nontrivial because the finite number of constraints entangles the variables from these groups. First group of the variables constitute the coefficients for the pair of first-order spectral problems; the solution of these problems is necessary for the reconstruction of the string world-sheet. We consider the excitations, which correspond to "N- soliton" solution of the spectral problem, and demonstrate that the reconstructed string has cuspidal points. World lines of such points form braids of various topologies.

math-ph↗

arXiv2001

The glueball Regge trajectory from the string-inspired theory

The special case of 4D string-like theory proposed early is investigated. Regge trajectories in the developed model are non-linear for small masses and the values of spin and have the different asymptotical slopes $α_p$. The value $α_p$ just as the form of the trajectory depends from the quantum state of some ''internal'' {relativistic invariant} variables. It is also shown that some trajectories have the asymptotical slope $α_g$=0.21 $Gev^{-2}$.

hep-ph↗

arXiv1998

About the Poisson Structure for D4 Spinning String

The model of D4 open string with non-Grassmann spinning variables is considered. The non-linear gauge, which is invariant both Poincaré and scale transformations of the space-time, is used for subsequent studies. It is shown that the reduction of the canonical Poisson structure from the original phase space to the surface of constraints and gauge conditions gives the degenerated Poisson brackets. Moreover it is shown that such reduction is non-unique. The conseption of the adjunct phase space is introduced. The consequences for subsequent quantization are discussed. Deduced dependence of spin $J$ from the square of mass $μ^2$ of the string generalizes the ''Regge spectrum`` for conventional theory.

hep-th↗