Jonatan Lenells
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View article: Numerical scheme for the solution of the “bad” Boussinesq equation
Numerical scheme for the solution of the “bad” Boussinesq equation Open
We present a numerical scheme for the solution of the initial-value problem for the “bad” Boussinesq equation. The accuracy of the scheme is tested by comparison with exact soliton solutions as well as with recently obtained asymptotic for…
View article: Semiclassical limit of a non-polynomial q-Askey scheme
Semiclassical limit of a non-polynomial q-Askey scheme Open
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View article: On the mean-field antiferromagnetic gap for the half-filled 2D Hubbard model at zero temperature
On the mean-field antiferromagnetic gap for the half-filled 2D Hubbard model at zero temperature Open
We consider the antiferromagnetic gap for the half-filled two-dimensional (2D) Hubbard model (on a square lattice) at zero temperature in Hartree-Fock theory. It was conjectured by Hirsch in 1985 that this gap, $Δ$, vanishes like $\exp(-2π…
View article: Universality of Mean-Field Antiferromagnetic Order in an Anisotropic 3D Hubbard Model at Half-Filling
Universality of Mean-Field Antiferromagnetic Order in an Anisotropic 3D Hubbard Model at Half-Filling Open
We study Hartree–Fock theory at half-filling for the 3D anisotropic Hubbard model on a cubic lattice with hopping parameter t in the x - and y -directions and a possibly different hopping parameter $$t_z$$ in the z -direction; this mod…
View article: Boussinesq’s equation for water waves: the soliton resolution conjecture for Sector IV
Boussinesq’s equation for water waves: the soliton resolution conjecture for Sector IV Open
We consider the Boussinesq equation on the line for a broad class of Schwartz initial data relevant for water waves. In a recent work, we identified ten main sectors describing the asymptotic behavior of the solution, and for each of these…
View article: Balayage of measures: behavior near a cusp
Balayage of measures: behavior near a cusp Open
Let $μ$ be a positive measure supported on a domain $Ω$. We consider the behavior of the balayage measure $ν:=\mathrm{Bal}(μ,\partial Ω)$ near a point $z_{0}\in \partial Ω$ at which $Ω$ has an outward-pointing cusp. Assuming that the order…
View article: Semiclassical limit of a non-polynomial $q$-Askey scheme
Semiclassical limit of a non-polynomial $q$-Askey scheme Open
We prove a semiclassical asymptotic formula for the two elements $\mathcal M$ and $\mathcal Q$ lying at the bottom of the recently constructed non-polynomial hyperbolic $q$-Askey scheme. We also prove that the corresponding exponent is a g…
View article: Boussinesq’s Equation for Water Waves: Asymptotics in Sector V
Boussinesq’s Equation for Water Waves: Asymptotics in Sector V Open
We consider the Boussinesq equation on the line for a broad class of Schwartz initial data for which (i) no solitons are present, (ii) the spectral functions have generic behavior near \pm1, and (iii) the solution exists globally. In a rec…
View article: Numerical scheme for the solution of the "bad" Boussinesq equation
Numerical scheme for the solution of the "bad" Boussinesq equation Open
We present a numerical scheme for the solution of the initial-value problem for the ``bad'' Boussinesq equation. The accuracy of the scheme is tested by comparison with exact soliton solutions as well as with recently obtained asymptotic f…
View article: Universality of mean-field antiferromagnetic order in an anisotropic 3D Hubbard model at half-filling
Universality of mean-field antiferromagnetic order in an anisotropic 3D Hubbard model at half-filling Open
We study the 3D anisotropic Hubbard model on a cubic lattice with hopping parameter $t$ in the $x$- and $y$-directions and a possibly different hopping parameter $t_z$ in the $z$-direction; this model interpolates between the 2D and 3D Hub…
View article: Non-polynomial q-Askey Scheme: Integral Representations, Eigenfunction Properties, and Polynomial Limits
Non-polynomial q-Askey Scheme: Integral Representations, Eigenfunction Properties, and Polynomial Limits Open
We construct a non-polynomial generalization of the q -Askey scheme. Whereas the elements of the q -Askey scheme are given by q -hypergeometric series, the elements of the non-polynomial scheme are given by contour integrals, whose integra…
View article: Balayage of measures: behavior near a corner
Balayage of measures: behavior near a corner Open
We consider the balayage of a measure $μ$ defined on a domain $Ω$ onto its boundary $\partial Ω$. Assuming that $Ω$ has a corner of opening $πα$ at a point $z_0 \in \partial Ω$ for some $0 < α\leq 2$ and that $dμ(z) \asymp |z-z_{0}|^{2b-2}…
View article: Disk counting statistics near hard edges of random normal matrices: The multi-component regime
Disk counting statistics near hard edges of random normal matrices: The multi-component regime Open
We consider a two-dimensional point process whose points are separated into two disjoint components by a hard wall, and study the multivariate moment generating function of the corresponding disk counting statistics. We investigate the “ha…
View article: Boussinesq's equation for water waves: Asymptotics in Sector I
Boussinesq's equation for water waves: Asymptotics in Sector I Open
In a recent study, we showed that the large ( x , t ) \left(x,t) behavior of a class of physically relevant solutions of Boussinesq’s equation for water waves is described by ten main asymptotic sectors. In the sector adjacent to the…
View article: Exponential moments for disk counting statistics at the hard edge of random normal matrices
Exponential moments for disk counting statistics at the hard edge of random normal matrices Open
We consider the multivariate moment generating function of the disk counting statistics of a model Mittag-Leffler ensemble in the presence of a hard wall. Let n be the number of points. We focus on two regimes: (a) the “hard edge regime” w…
View article: The “good” Boussinesq equation : long-timeasymptotics
The “good” Boussinesq equation : long-timeasymptotics Open
We consider the initial-value problem for the "good" Boussinesq equation on the line.Using inverse scattering techniques, the solution can be expressed in terms of the solution of a 3 × 3-matrix Riemann-Hilbert problem.We establish formula…
View article: Miura transformation for the “good” Boussinesq equation
Miura transformation for the “good” Boussinesq equation Open
It is well known that each solution of the modified Korteveg–de Vries (mKdV) equation gives rise, via the Miura transformation, to a solution of the Korteveg–de Vries (KdV) equation. In this work, we show that a similar Miura‐type transfor…
View article: Toeplitz determinants with a one-cut regular potential and Fisher–Hartwig singularities I. Equilibrium measure supported on the unit circle
Toeplitz determinants with a one-cut regular potential and Fisher–Hartwig singularities I. Equilibrium measure supported on the unit circle Open
We consider Toeplitz determinants whose symbol has: (i) a one-cut regular potential $V$ , (ii) Fisher–Hartwig singularities and (iii) a smooth function in the background. The potential $V$ is associated with an equilibrium measure that is …
View article: The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem
The Bessel kernel determinant on large intervals and Birkhoff's ergodic theorem Open
The Bessel process models the local eigenvalue statistics near 0 of certain large positive definite matrices. In this work, we consider the probability where and is any non‐negative integer. We obtain asymptotics for this probability as th…
View article: Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation
Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation Open
We construct elliptic multi-soliton solutions of the spin non-chiral intermediate long-wave (sncILW) equation with periodic boundary conditions. These solutions are obtained by a spin-pole ansatz including a dynamical background term; we s…
View article: Wilson loops in the abelian lattice Higgs model
Wilson loops in the abelian lattice Higgs model Open
We consider the lattice Higgs model on Z 4 in the fixed length limit, with structure group given by Zn for n ě 2. We compute the expected value of the Wilson loop observable to leading order when the inverse temperature and hopping paramet…
View article: The soliton resolution conjecture for the Boussinesq equation
The soliton resolution conjecture for the Boussinesq equation Open
We analyze the Boussinesq equation on the line with Schwartz initial data belonging to the physically relevant class of global solutions. In a recent paper, we determined ten main asymptotic sectors describing the large $(x,t)$-behavior of…
View article: Boussinesq's equation for water waves: asymptotics in Sector I
Boussinesq's equation for water waves: asymptotics in Sector I Open
In a recent paper, we showed that the large $(x,t)$ behavior of a class of physically relevant solutions of Boussinesq's equation for water waves is described by ten main asymptotic sectors. In the sector adjacent to the positive $x$-axis,…
View article: Boussinesq's equation for water waves: the soliton resolution conjecture for Sector IV
Boussinesq's equation for water waves: the soliton resolution conjecture for Sector IV Open
We consider the Boussinesq equation on the line for a broad class of Schwartz initial data relevant for water waves. In a recent work, we identified ten main sectors describing the asymptotic behavior of the solution, and for each of these…
View article: Direct and inverse scattering for the Boussinesq equation with solitons
Direct and inverse scattering for the Boussinesq equation with solitons Open
In a recent paper, we developed an inverse scattering approach to the Boussinesq equation in the case when no solitons are present. In this paper, we extend this approach to include solutions with solitons.
View article: Conformal field theory, solitons, and elliptic Calogero--Sutherland models
Conformal field theory, solitons, and elliptic Calogero--Sutherland models Open
We construct a non-chiral conformal field theory (CFT) on the torus that accommodates a second quantization of the elliptic Calogero-Sutherland (eCS) model. We show that the CFT operator that provides this second quantization defines, at t…
View article: Exponential moments for disk counting statistics of random normal matrices in the critical regime
Exponential moments for disk counting statistics of random normal matrices in the critical regime Open
We obtain large n asymptotics for the m -point moment generating function of the disk counting statistics of the Mittag–Leffler ensemble, where n is the number of points of the process and m is arbitrary but fixed. We focus on the critical…