Universality of the weak pushed-to-pulled transition in systems with repulsive interactions

Cunden, Fabio Deelan; Facchi, Paolo; Ligabò, Marilena; Vivo, Pierpaolo

doi:10.1088/1751-8121/aad147

Cited by 32 publications

(30 citation statements)

References 48 publications

(70 reference statements)

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“…For k → −1, we recover the flat density of the 1dOCP. Also, in the limit k → ∞ we again get a flat density, consistent with the results for the 1d harmonically confined Yukawa gas 11,36 . We also performed Monte-Carlo (MC) simulations for several values of k, finding excellent agreement with our analytical predictions (see Fig.…”

Section: Pacs Numberssupporting

confidence: 88%

“…The support length k is non-universal and depends explicitly on k and the coupling strength J (for the exact expressions of k , see Eqs. (36) and (65) of Supp. Mat.…”

Section: Pacs Numbersmentioning

confidence: 97%

“…For k → ∞, the Riesz gas reduces to a truely short-ranged repulsive gas similar to the harmonically confined screened Coulomb or Yukawa-gas studied in Refs. 11,36. In addition, other values of k have either been realized in experimental setups or could potentially be realized 37 .…”

Section: Pacs Numbersmentioning

confidence: 99%

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Harmonically Confined Particles with Long-Range Repulsive Interactions

et al. 2019

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We study an interacting system of N classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repelling each other via pairwise interaction potential that behaves as a power law ∝ N i =j |xi − xj| −k (with k > −2) of their mutual distance. This is a generalization of the well known cases of the one component plasma (k = −1), Dyson's log-gas (k → 0 + ), and the Calogero-Moser model (k = 2). Due to the competition between harmonic confinement and pairwise repulsion, the particles spread over a finite region of space for all k > −2. We compute exactly the average density profile for large N for all k > −2 and show that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on k with distinct behavior for −2 < k < 1, k > 1 and k = 1. PACS numbers:Introduction: A gas of N classical particles, confined by a harmonic potential on a line and interacting with each other via pairwise repulsion, constitutes one of the simplest interacting particle systems that have been well studied in the past. It has seen a recent revival in the wake of the physics of cold atoms. When the pairwise repulsive interaction decays as a power-law of the distance between the particles, the energy of the so called Riesz gas 1 is given by

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Section: Pacs Numberssupporting

confidence: 88%

“…The support length k is non-universal and depends explicitly on k and the coupling strength J (for the exact expressions of k , see Eqs. (36) and (65) of Supp. Mat.…”

Section: Pacs Numbersmentioning

confidence: 97%

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Harmonically Confined Particles with Long-Range Repulsive Interactions

et al. 2019

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“…In these two-dimensional situations a natural extreme observable is the largest radius r max = max 1≤i≤N |z i | [224][225][226] (see also the discussion at the end of Section IV B 8 below). Further extensions have also been considered, either by studying various confining potentials (i.e., different from the quadratic well), which in some cases correspond to other interesting matrix models [227], or by studying Coulomb gases in higher dimensions d > 2 [228]. In the latter case many extreme value questions, like the distribution of the typical fluctuations of largest radius, remain open.…”

Section: Extreme Statistics In Random Matrix Theorymentioning

confidence: 99%

Extreme value statistics of correlated random variables: A pedagogical review

2020

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Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way to physics of disordered systems where one is interested in the statistics of the ground state energy. While the EVS of 'uncorrelated' variables are well understood, little is known for strongly correlated random variables. Only recently this subject has gained much importance both in statistical physics and in probability theory. In this review, we will first recall the classical EVS for uncorrelated variables and discuss the three universality classes of extreme value limiting distribution, known as the Gumbel, Fréchet and Weibull distribution. We then show that, for weakly correlated random variables with a finite correlation length/time, the limiting extreme value distribution can still be inferred from that of the uncorrelated variables using a renormalisation group-like argument. Finally, we consider the most interesting examples of strongly correlated variables for which there are very few exact results for the EVS. We discuss few examples of such strongly correlated systems (such as the Brownian motion and the eigenvalues of a random matrix) where some analytical progress can be made. We also discuss other observables related to extremes, such as the density of near-extreme events, time at which an extreme value occurs, order and record statistics, etc.

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“…These methods however often appear disconnected: in this Letter we unveil relations between some of them, valid at the edge. Strongly perturbed Coulomb gas are interesting correlated systems by themselves, extensively studied recently [52], but not much at their edge [53].…”

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confidence: 99%

Linear statistics and pushed Coulomb gas at the edge of β -random matrices: Four paths to large deviations

Krajenbrink¹,

Doussal²

2019

EPL

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The Airy β point process, ai ≡ N 2/3 (λi − 2), describes the eigenvalues λi at the edge of the Gaussian β ensembles of random matrices for large matrix size N → ∞. We study the probability distribution function (PDF) of linear statistics L = i tϕ(t −2/3 ai) for large parameter t. We show the large deviation forms E Airy,β [exp(−L)] ∼ exp(−t 2 Σ[ϕ]) and P (L) ∼ exp(−t 2 G(L/t 2 )) for the cumulant generating function and the PDF. We obtain the exact rate function Σ[ϕ] using four apparently different methods (i) the electrostatics of a Coulomb gas (ii) a random Schrödinger problem, i.e. the stochastic Airy operator (iii) a cumulant expansion (iv) a non-local non-linear differential Painlevé type equation. Each method was independently introduced previously to obtain the lower tail of the Kardar-Parisi-Zhang equation [1][2][3][4]. Here we show their equivalence in a more general framework. Our results are obtained for a class of functions ϕ, the monotonous soft walls, containing the monomials ϕ(x) = (u + x) γ + and the exponential ϕ(x) = e u+x and equivalently describe the response of a Coulomb gas pushed at its edge. The small u behavior of the excess energy Σ[ϕ] exhibits a change at γ = 3/2 between a non-perturbative hard wall like regime for γ < 3/2 (third order free-to-pushed transition) and a perturbative deformation of the edge for γ > 3/2 (higher order transition). Applications are given, among them: (i) truncated linear statistics such as N 1 i=1 ai, leading to a formula for the PDF of the ground state energy of N1 1 noninteracting fermions in a linear plus random potential (ii) ∼ (β − 2)/r 2 interacting spinless fermions in a trap at the edge of a Fermi gas (iii) traces of large powers of random matrices.√ β 2 v(x), H SAO = t −2/3 H SAO with energy levels b i = t −2/3 ε i = −t −2/3 a i and obtain

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Universality of the weak pushed-to-pulled transition in systems with repulsive interactions

Cited by 32 publications

References 48 publications

Harmonically Confined Particles with Long-Range Repulsive Interactions

Harmonically Confined Particles with Long-Range Repulsive Interactions

Extreme value statistics of correlated random variables: A pedagogical review

Linear statistics and pushed Coulomb gas at the edge of β -random matrices: Four paths to large deviations

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