Multicritical edge statistics for the momenta of fermions in non-harmonic traps

Abstract

We compute the joint statistics of the momenta $p_i$ of $N$ non-interacting fermions in a trap, near the Fermi edge, with a particular focus on the largest one $p_{\max }$. For a $1d$ harmonic trap, momenta and positions play a symmetric role and hence, the joint statistics of momenta is identical to that of the positions. In particular, $p_{\max }$, as $x_{\max }$, is distributed according to the Tracy-Widom distribution. Here we show that novel "momentum edge statistics" emerge when the curvature of the potential vanishes, i.e. for "flat traps" near their minimum, with $V(x)\sim x^{2n}$ and $n>1$. These are based on generalisations of the Airy kernel that we obtain explicitly. The fluctuations of $p_{\max }$ are governed by new universal distributions determined from the $n$-th member of the second Painlevé hierarchy of non-linear differential equations, with connections to multicritical random matrix models. Finite temperature extensions and possible experimental signatures in cold atoms are discussed.

6 pages + 11 pages (Supplementary material), 2 figures

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• A Quantum Gas Microscope for Fermionic Atoms
• Growing interfaces uncover universal fluctuations behind scale invariance
• Homogeneous Atomic Fermi Gases
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• The entanglement entropy of one-dimensional gases
• The Pearcey Process
• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• Phase transitions and edge scaling of number variance in Gaussian random matrices
• Random matrices and entanglement entropy of trapped Fermi gases
• Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
• Wigner function of noninteracting trapped fermions
• Universal distribution of random matrix eigenvalues near the "birth of a cut" transition
• The Hamiltonian Structure of the Second Painleve Hierarchy
• Spectral order statistics of Gaussian random matrices: large deviations for trapped fermions and associated phase transitions
• Statistics of fermions in a $d$-dimensional box near a hard wall
• Higher Order Analogues of Tracy-Widom Distributions via the Lax Method
• Mixed correlation function and spectral curve for the 2-matrix model

Cited by in corpus (33)

• Extreme value statistics of correlated random variables: a pedagogical review
• Noninteracting fermions in a trap and random matrix theory
• Quantum information scrambling after a quantum quench
• Entanglement revivals as a probe of scrambling in finite quantum systems
• Linear statistics and pushed Coulomb gas at the edge of beta random matrices: four paths to large deviations
• Free fermions at the edge of interacting systems
• Statistics of first-passage Brownian functionals
• Large fluctuations of the KPZ equation in a half-space
• From Painlevé to Zakharov-Shabat and beyond: Fredholm determinants and integro-differential hierarchies
• Fredholm determinant solutions of the Painlevé II hierarchy and gap probabilities of determinantal point processes
• Counting statistics for non-interacting fermions in a rotating trap
• Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap
• Extreme boundary conditions and random tilings
• Wigner function for noninteracting fermions in hard wall potentials
• Universal edge scaling in random partitions
• Free fermions and $\alpha$-determinantal processes
• Noninteracting trapped Fermions in double-well potentials: inverted parabola kernel
• Unitary matrix models and random partitions: Universality and multi-criticality
• Generalized-Hydrodynamic approach to Inhomogeneous Quenches: Correlations, Entanglement and Quantum Effects
• Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature
• Gap probability for the hard edge Pearcey process
• Non-probabilistic fermionic limit shapes
• Recursion Relation for Toeplitz Determinants and the Discrete Painlevé II Hierarchy
• Nonequilibrium dynamics of noninteracting fermions in a trap
• Multicritical random partitions
• Multicritical Schur measures and higher-order analogues of the Tracy-Widom distribution
• Interface fluctuations associated with split Fermi seas
• A fully noncommutative Painlevé II hierarchy: Lax pair and solutions related to Fredholm determinants
• Classical group matrix models and universal criticality
• Universal Cusp Scaling in Random Partitions
• Asymptotics of the deformed higher order Airy-kernel determinants and applications
• Exact solvability and asymptotic aspects of generalized XX0 spin chains
• PhD thesis "Extreme value statistics of strongly correlated systems: fermions, random matrices and random walks"