Random matrix theory of singular values of rectangular complex matrices. I: Exact formula of one-body distribution function in fixed-trace ensemble

DOI10.1016/j.aop.2009.04.007zbMath1194.81104OpenAlexW2015603192MaRDI QIDQ1038505

Hiroto Kubotani, Satoshi Adachi, Mikito Toda

Publication date: 18 November 2009

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aop.2009.04.007

zbMATH Keywords

random matrix theoryquantum entanglementquantum chaosSchmidt decompositionSelberg integralfixed-trace ensembleSelberg-Kaneko integral

Mathematics Subject Classification ID

Quantum chaos (81Q50) Random matrices (algebraic aspects) (15B52) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Classical hypergeometric functions, ({}_2F_1) (33C05) Quantum coherence, entanglement, quantum correlations (81P40)

Related Items (8)

Bures–Hall ensemble: spectral densities and average entropies ⋮ Exact distribution of largest Schmidt eigenvalue for quantum entanglement ⋮ The difference between two random mixed quantum states: exact and asymptotic spectral analysis ⋮ Smallest eigenvalue density for regular or fixed-trace complex Wishart–Laguerre ensemble and entanglement in coupled kicked tops ⋮ Largest Schmidt eigenvalue of random pure states and conductance distribution in chaotic cavities ⋮ Compact smallest eigenvalue expressions in Wishart–Laguerre ensembles with or without a fixed trace ⋮ Exact eigenvalue order statistics for the reduced density matrix of a bipartite system ⋮ Fluctuations of the spectrum in rotationally invariant random matrix ensembles

Uses Software

• gmp

Cites Work

• Entanglement generation by the mixing property in a quantum non-linear system
• Some combinatorial properties of Jack symmetric functions
• Induced measures in the space of mixed quantum states
• Exact Formula of the Distribution of Schmidt Eigenvalues for Dynamical Formation of Entanglement in Quantum Chaos
• Selberg Integrals and Hypergeometric Functions Associated with Jack Polynomials
• Entropy of an n-system from its correlation with a k-reservoir
• Average entropy of a subsystem
• Proof of Page’s conjecture on the average entropy of a subsystem
• Geometry of Quantum States
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