Publications

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First-order transition in a model of prestige bias

Brian Skinner

SciPost Phys. 8, 030 (2020) · published 19 February 2020 | · pdf

One of the major benefits of belonging to a prestigious group is that it affects the way you are viewed by others. Here I use a simple mathematical model to explore the implications of this "prestige bias" when candidates undergo repeated rounds of evaluation. In the model, candidates who are evaluated most highly are admitted to a "prestige class", and their membership biases future rounds of evaluation in their favor. I use the language of Bayesian inference to describe this bias, and show that it can lead to a runaway effect in which the weight given to the prior expectation associated with a candidate's class becomes stronger with each round. Most dramatically, the strength of the prestige bias after many rounds undergoes a first-order transition as a function of the precision of the examination on which the evaluation is based.

2 citations
Dynamics of hot Bose-Einstein condensates: stochastic Ehrenfest relations for number and energy damping

Rob G. McDonald, Peter S. Barnett, Fradom Atayee, Ashton S. Bradley

SciPost Phys. 8, 029 (2020) · published 18 February 2020 | · pdf

Describing partially-condensed Bose gases poses a long-standing theoretical challenge. We present exact stochastic Ehrenfest relations for the stochastic projected Gross-Pitaevskii equation, including both number and energy damping mechanisms, and all projector terms that arise from the energy cutoff separating system from reservoir. We test the theory by applying it to the centre of mass fluctuations of a harmonically trapped prolate system, finding close agreement between c-field simulations and analytical results. The formalism lays the foundation to analytically explore experimentally accessible hot Bose-Einstein condensates.

2 citations
Coarse-grained curvature tensor on polygonal surfaces

Charlie Duclut, Aboutaleb Amiri, Joris Paijmans, Frank Jülicher

SciPost Phys. Core 5, 011 (2022) · published 11 March 2022 | · pdf

Using concepts from integral geometry, we propose a definition for a local coarse-grained curvature tensor that is well-defined on polygonal surfaces. This coarse-grained curvature tensor shows fast convergence to the curvature tensor of smooth surfaces, capturing with accuracy not only the principal curvatures but also the principal directions of curvature. Thanks to the additivity of the integrated curvature tensor, coarse-graining procedures can be implemented to compute it over arbitrary patches of polygons. When computed for a closed surface, the integrated curvature tensor is identical to a rank-2 Minkowski tensor. We also provide an algorithm to extend an existing C++ package, that can be used to compute efficiently local curvature tensors on triangulated surfaces.

2 citations
Equilibration of quantum cat states

Tony Jin

SciPost Phys. 9, 004 (2020) · published 8 July 2020 | · pdf

We study the equilibration properties of isolated ergodic quantum systems initially prepared in a cat state, i.e a macroscopic quantum superposition of states. Our main result consists in showing that, even though decoherence is at work in the mean, there exists a remnant of the initial quantum coherences visible in the strength of the fluctuations of the steady state. We back-up our analysis with numerical results obtained on the XXX spin chain with a random field along the z-axis in the ergodic regime and find good qualitative and quantitative agreement with the theory. We also present and discuss a framework where equilibrium quantities can be computed from general statistical ensembles without relying on microscopic details about the initial state, akin to the eigenstate thermalization hypothesis.

2 citations
Enstrophy without boost symmetry

Natalia Pinzani-Fokeeva, Amos Yarom

SciPost Phys. 12, 136 (2022) · published 21 April 2022 | · pdf

We construct an approximately conserved current for $2+1$ dimensional, Aristotelian (non boost invariant), fluid flow. When Aristotelian symmetry is enhanced to Galilean symmetry, this current matches the enstrophy current responsible for the inverse cascade in incompressible fluids. Other enhancements of Aristotelian symmetry discussed in this work include Lorentzian, Carrollian and Lifshitz scale symmetry.

2 citations
On the logarithmic bipartite fidelity of the open XXZ spin chain at $Δ=-1/2$

Christian Hagendorf, Gilles Parez

SciPost Phys. 12, 199 (2022) · published 24 June 2022 | · pdf

The open XXZ spin chain with the anisotropy $\Delta=-\frac12$ and a one-parameter family of diagonal boundary fields is studied at finite length. A determinant formula for an overlap involving the spin chain's ground-state vectors for different lengths is found. The overlap allows one to obtain an exact finite-size formula for the ground state's logarithmic bipartite fidelity. The leading terms of its asymptotic series for large chain lengths are evaluated. Their expressions confirm the predictions of conformal field theory for the fidelity.

2 citations
Quantum to classical mapping of the two-dimensional toric code in an external field

Sydney R. Timmerman, Zvonimir Z. Bandic, Roger G. Melko

SciPost Phys. Lect. Notes 57 (2022) · published 20 July 2022 | · pdf

Kitaev's toric code Hamiltonian in dimension D=2 has been extensively studied for its topological properties, including its quantum error correction capabilities. While the Hamiltonian is quantum, it lies within the class of models that admits a D+1 dimensional classical representation. In these notes, we provide details of a Suzuki-Trotter expansion of the partition function of the toric code Hamiltonian in the presence of an external magnetic field. By coupling additional degrees of freedom in the form of a matter field that can subsequently be gauged away, we explicitly derive a classical Hamiltonian on a cubic lattice which takes the form of a non-isotropic 3D Ising gauge theory.

2 citations
Generalised Gibbs Ensemble for spherically constrained harmonic models

Damien Barbier, Leticia F. Cugliandolo, Gustavo S. Lozano, Nicolás Nessi

SciPost Phys. 13, 048 (2022) · published 2 September 2022 | · pdf

We build and analytically calculate the Generalised Gibbs Ensemble partition function of the integrable Soft Neumann Model. This is the model of a classical particle which is constrained to move, on average over the initial conditions, on an $N$ dimensional sphere, and feels the effect of anisotropic harmonic potentials. We derive all relevant averaged static observables in the (thermodynamic) $N\rightarrow\infty$ limit. We compare them to their long-term dynamic averages finding excellent agreement in all phases of a non-trivial phase diagram determined by the characteristics of the initial conditions and the amount of energy injected or extracted in an instantaneous quench. We discuss the implications of our results for the proper Neumann model in which the spherical constraint is imposed strictly.

2 citations
Topological order in matrix Ising models

Sean A. Hartnoll, Edward A. Mazenc, Zhengyan D. Shi

SciPost Phys. 7, 081 (2019) · published 19 December 2019 | · pdf

We study a family of models for an $N_1 \times N_2$ matrix worth of Ising spins $S_{aB}$. In the large $N_i$ limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single `spherical' constraint. In this way we generalize the results of [1] to a wide class of Ising Hamiltonians with $O(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z})$ symmetry. The models can undergo topological large $N$ phase transitions in which the thermal expectation value of the distribution of singular values of the matrix $S_{aB}$ becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.

2 citations
A splash in a one-dimensional cold gas

Subhadip Chakraborti, Abhishek Dhar, P. L. Krapivsky

SciPost Phys. 13, 074 (2022) · published 29 September 2022 | · pdf

We consider a set of hard point particles distributed uniformly with a specified density on the positive half-line and all initially at rest. The particle masses alternate between two values, $m$ and $M$. The particles interact via collisions that conserve energy and momentum. We study the cascade of activity that results when the left-most particle is given a positive velocity. At long times we find that this leads to two fascinating features in the observed dynamics. First, in the bulk of the gas, a shock front develops separating the cold gas from a thermalized region. The shock-front travels sub-ballistically, with the bulk described by self-similar solutions of Euler hydrodynamics. Second, there is a splash region formed by the recoiled particles which move ballistically with negative velocities. The splash region is completely non-hydrodynamic and we propose two conjectures for the long time particle dynamics in this region. We provide a detailed analytic understanding of these coexisting regimes. These are supported by the results of molecular dynamics simulations.

2 citations

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