arXiv subjects

Natasa Pavlovic

Publications and source records attributed to Natasa Pavlovic.

10 recordsLinked to original sources

arXiv2024

Ad-hoc hybrid-heterogeneous metropolitan-range quantum key distribution network

This paper presents the development and implementation of a versatile ad-hoc metropolitan-range Quantum Key Distribution (QKD) network. The approach presented integrates various types of physical channels and QKD protocols, and a mix of trusted and untrusted nodes. Unlike conventional QKD networks that predominantly depend on either fiber-based or free-space optical (FSO) links, the testbed presented amalgamates FSO and fiber-based links, thereby overcoming some inherent limitations. Various network deployment strategies have been considered, including permanent infrastructure and provisional ad-hoc links to eradicate coverage gaps. Furthermore, the ability to rapidly establish a network using portable FSO terminals and to investigate diverse link topologies is demonstrated. The study also showcases the successful establishment of a quantum-secured link to a cloud server.

quant-ph↗

arXiv2021

Rigorous derivation of a ternary Boltzmann equation for a classical system of particles

In this paper, we present a rigorous derivation of a new kinetic equation describing the limiting behavior of a classical system of particles with three particle elastic instantaneous interactions, which are modeled using a non-symmetric version of a ternary distance. The ternary collisional operator we derive can be seen as the first step towards obtaining a toy model for a non-ideal gas where higher order interactions are taken into account.

math.AP↗

arXiv2021

Global well-posedness of a binary-ternary Boltzmann equation

In this paper we show global well-posedness near vacuum for the binary-ternary Boltzmann equation. The binary-ternary Boltzmann equation provides a correction term to the classical Boltzmann equation, taking into account both binary and ternary interactions of particles, and may serve as a more accurate description model for denser gases in non-equilibrium. Well-posedness of the classical Boltzmann equation and, independently, the purely ternary Boltzmann equation follow as special cases. To prove global well-posedness, we use a Kaniel-Shinbrot iteration and related work to approximate the solution of the nonlinear equation by monotone sequences of supersolutions and subsolutions. This analysis required establishing new convolution type estimates to control the contribution of the ternary collisional operator to the model. We show that the ternary operator allows consideration of softer potentials than the one binary operator, consequently our solution to the ternary correction of the Boltzmann equation preserves all the properties of the binary interactions solution. These results are novel for collisional operators of monoatomic gases with either hard or soft potentials that model both binary and ternary interactions.

math.AP↗

arXiv2020

Rigorous derivation of a binary-ternary Boltzmann equation for a dense gas of hard spheres

This paper provides the first rigorous derivation of a binary-ternary Boltzmann equation describing the kinetic properties of a dense hard-spheres gas, where particles undergo either binary or ternary instantaneous interactions, while preserving momentum and energy. An important challenge we overcome in deriving this equation is related to providing a mathematical framework that allows us to detect both binary and ternary interactions. Furthermore, this paper introduces new algebraic and geometric techniques in order to eventually decouple binary and ternary interactions and understand the way they could succeed one another in time.

math.AP↗

arXiv2018

Moments and Regularity for a Boltzmann Equation via Wigner Transform

In this paper, we continue our study of the Boltzmann equation by use of tools originating from the analysis of dispersive equations in quantum dynamics. Specifically, we focus on properties of solutions to the Boltzmann equation with collision kernel equal to a constant in the spatial domain $\mathbb{R}^d$, $d\geq 2$, which we use as a model in this paper. Local well-posedness for this equation has been proven using the Wigner transform when $\left< v \right>^βf_0 \in L^2_v H^α_x$ for $\min (α,β) > \frac{d-1}{2}$. We prove that if $α,β$ are large enough, then it is possible to propagate moments in $x$ and derivatives in $v$ (for instance, $\left< x \right>^k \left< \nabla_v \right>^\ell f \in L^\infty_T L^2_{x,v}$ if $f_0$ is nice enough). The mechanism is an exchange of regularity in return for moments of the (inverse) Wigner transform of $f$. We also prove a persistence of regularity result for the scale of Sobolev spaces $H^{α,β}$; and, continuity of the solution map in $H^{α,β}$. Altogether, these results allow us to conclude non-negativity of solutions, conservation of energy, and the $H$-theorem for sufficiently regular solutions constructed via the Wigner transform. Non-negativity in particular is proven to hold in $H^{α,β}$ for any $α,β> \frac{d-1}{2}$, without any additional regularity or decay assumptions.

math.AP↗

arXiv2017

Global Flows with Invariant Measures for the Inviscid Modified SQG Equations

We consider the family known as modified or generalized surface quasi-geostrophic equations (mSQG) consisting of the classical inviscid surface quasi-geostrophic (SQG) equation together with a family of regularized active scalars given by introducing a smoothing operator of nonzero but possibly arbitrarily small degree. This family naturally interpolates between the 2D Euler equation and the SQG equation. For this family of equations we construct an invariant measure on a rough $L^2$-based Sobolev space and establish the existence of solutions of arbitrarily large lifespan for initial data in a set of full measure in the rough Sobolev space.

math.AP↗

arXiv2014

On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti

We prove the existence of scattering states for the defocusing cubic Gross-Pitaevskii (GP) hierarchy in ${\mathbb R}^3$. Moreover, we show that an energy growth condition commonly used in the well-posedness theory of the GP hierarchy is, in a specific sense, necessary. In fact, we prove that without the latter, there exist initial data for the focusing cubic GP hierarchy for which instantaneous blowup occurs.

math-ph↗

arXiv2014

Unconditional uniqueness for the cubic Gross-Pitaevskii hierarchy via quantum de Finetti

We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy in $\R^3$. One of the main tools in our analysis is the quantum de Finetti theorem. Our uniqueness result is equivalent to the one established in the celebrated works of Erdös, Schlein and Yau, \cite{esy1,esy2,esy3,esy4}.

math-ph↗

arXiv2007

A regularity criterion for the dissipative quasi-geostrophic equations

We establish a regularity criterion for weak solutions of the dissipative quasi-geostrophic equations in mixed time-space Besov spaces.

math.AP↗

arXiv2006

Global Well-Posedness for the $L^2$-critical nonlinear Schrödinger equation in higher dimensions

The initial value problem for the $L^{2}$ critical semilinear Schrödinger equation in $\R^n, n \geq 3$ is considered. We show that the problem is globally well posed in $H^{s}({\Bbb R^{n}})$ when $1>s>\frac{\sqrt{7}-1}{3}$ for $n=3$, and when $1>s> \frac{-(n-2)+\sqrt{(n-2)^2+8(n-2)}}{4}$ for $n \geq 4$. We use the ``$I$-method'' combined with a local in time Morawetz estimate.

math.AP↗