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Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models

Arpan Bhattacharyya, S. Shajidul Haque, Ghadir Jafari, Jeff Murugan, Dimakatso Rapotu

TL;DR

Problem: how decoherence and non-Gaussianity influence spectral statistics and quantum information metrics in random-matrix models. Approach: compute spectral form factor and Krylov (spread) complexity for two modified RMT classes—non-Gaussian quartic/sextic and Gaussian-noise models—using ensemble averaging and Krylov basis methods, with Lindblad dynamics for the open system. Key findings: decoherence suppresses the SFF early-time dip in both models; non-Gaussianity and noise produce distinct long-time and complexity behaviors; Krylov complexity deviates from Gaussian RMT for both models, with g_c and γ_c controlling transitions. Significance: shows SFF and Krylov complexity provide complementary insights into quantum chaos in open systems and suggests extensions to non-Hermitian ensembles and analytical treatment.

Abstract

We study the spectral properties of two classes of random matrix models: non-Gaussian RMT with quartic and sextic potentials, and RMT with Gaussian noise. We compute and analyze the quantum Krylov complexity and the spectral form factor for both of these models. We find that both models show suppression of the spectral form factor at short times due to decoherence effects, but they differ in their long-time behavior. In particular, we show that the Krylov complexity for the non-Gaussian RMT and RMT with noise deviates from that of a Gaussian RMT. We discuss the implications and limitations of our results for quantum chaos and quantum information in open quantum systems. Our study reveals the distinct sensitivities of the spectral form factor and complexity to non-Gaussianity and noise, which contribute to the observed differences in the different time domains.

Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models

TL;DR

Problem: how decoherence and non-Gaussianity influence spectral statistics and quantum information metrics in random-matrix models. Approach: compute spectral form factor and Krylov (spread) complexity for two modified RMT classes—non-Gaussian quartic/sextic and Gaussian-noise models—using ensemble averaging and Krylov basis methods, with Lindblad dynamics for the open system. Key findings: decoherence suppresses the SFF early-time dip in both models; non-Gaussianity and noise produce distinct long-time and complexity behaviors; Krylov complexity deviates from Gaussian RMT for both models, with g_c and γ_c controlling transitions. Significance: shows SFF and Krylov complexity provide complementary insights into quantum chaos in open systems and suggests extensions to non-Hermitian ensembles and analytical treatment.

Abstract

We study the spectral properties of two classes of random matrix models: non-Gaussian RMT with quartic and sextic potentials, and RMT with Gaussian noise. We compute and analyze the quantum Krylov complexity and the spectral form factor for both of these models. We find that both models show suppression of the spectral form factor at short times due to decoherence effects, but they differ in their long-time behavior. In particular, we show that the Krylov complexity for the non-Gaussian RMT and RMT with noise deviates from that of a Gaussian RMT. We discuss the implications and limitations of our results for quantum chaos and quantum information in open quantum systems. Our study reveals the distinct sensitivities of the spectral form factor and complexity to non-Gaussianity and noise, which contribute to the observed differences in the different time domains.
Paper Structure (8 sections, 21 equations, 11 figures, 1 table)

This paper contains 8 sections, 21 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Our Models
  3. Spectral Form Factor
  4. SFF for Non-Gaussian Models
  5. Krylov Complexity
  6. Krylov Complexity for Non-Gaussian RMT
  7. Krylov Complexity for RMT with Noise
  8. Discussion

Figures (11)

  • Figure 1: SFF for quartic potential for various values of the coupling.
  • Figure 2: SFF for Sextic potential for various values of the coupling.
  • Figure 3: SFF for Non-Gaussian RMT with both quartic and sextic potential for different values of parameters.
  • Figure 4: SFF for Gaussian random matrix model with Gaussian noise.
  • Figure 5: SFF for Non-Gaussian RMT with Gaussina noise.
  • ...and 6 more figures