Cosmological Krylov Complexity

• URL: http://arxiv.org/abs/2203.14330v5
• Date: Thu, 8 Jun 2023 02:03:01 GMT
• Title: Cosmological Krylov Complexity
• Authors: Kiran Adhikari, Sayantan Choudhury
• Abstract summary: We study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism. We show that the Krylov complexity ($K$) for this system is equal to average particle numbers suggesting it's relation to the volume.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism in the presence of an effective field having sound speed $c_s$. From our analysis, we obtain the explicit behavior of Krylov complexity ($K$) and lancoz coefficients ($b_n$) with respect to the conformal time scale and scale factor in the presence of effective sound speed $c_s$. Since lancoz coefficients ($b_n$) grow linearly with integer $n$, this suggests that universe acts like a chaotic system during this period. We also obtain the corresponding Lyapunov exponent $\lambda$ in presence of effective sound speed $c_s$. We show that the Krylov complexity ($K$) for this system is equal to average particle numbers suggesting it's relation to the volume. Finally, we give a comparison of Krylov complexity ($K$) with entanglement entropy (Von-Neumann) where we found that there is a large difference between Krylov complexity ($K$) and entanglement entropy for large values of squeezing amplitude. This suggests that Krylov complexity ($K$) can be a significant probe for studying the dynamics of the cosmological system even after the saturation of entanglement entropy.

Related papers

• Nearly Optimal Sample Complexity of Offline KL-Regularized Contextual Bandits under Single-Policy Concentrability [49.96531901205305]
  We propose the emphfirst algorithm with $tildeO(epsilon-1)$ sample complexity under single-policy concentrability for offline contextual bandits. Our proof leverages the strong convexity of the KL regularization, and the conditional non-negativity of the gap between the true reward and its pessimistic estimator. We extend our algorithm to contextual dueling bandits and achieve a similar nearly optimal sample complexity.
  arXiv  Detail & Related papers  (2025-02-09T22:14:45Z)
• Emptiness Instanton in Quantum Polytropic Gas [49.1574468325115]
  The problem involves determining the probability of the spontaneous formation of an empty interval in the ground state of the gas. By solving the hydrodynamic equations in imaginary time, we derive the analytic form of the emptiness instanton. This solution is expressed as an integral representation analogous to those used for correlation functions in Conformal Field Theory.
  arXiv  Detail & Related papers  (2024-12-16T11:58:51Z)
• Measuring quantum relative entropy with finite-size effect [53.64687146666141]
  We study the estimation of relative entropy $D(rho|sigma)$ when $sigma$ is known. Our estimator attains the Cram'er-Rao type bound when the dimension $d$ is fixed.
  arXiv  Detail & Related papers  (2024-06-25T06:07:20Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Inflationary complexity of thermal state [3.0346001106791323]
  We investigate inflationary complexity of the two-mode squeezed state with thermal effect for the single field inflation, modified dispersion relation, and non-trivial sound speed. Our investigations show the evolution of Krylov complexity will enhance upon some peaks factoring in the thermal effects. Our derivation for the Krylov complexity and Krylov entropy could nicely recover into the case of closed system.
  arXiv  Detail & Related papers  (2024-05-02T16:22:59Z)
• Dissecting Quantum Many-body Chaos in the Krylov Space [8.51823003676739]
  We introduce the Krylov metric $K_mn$, which probes the size of the Krylov basis. We show that $h=varkappa / 2alpha$ is a ratio between the quantum Lyapunov exponent $varkappa$ and the Krylov exponent $alpha$.
  arXiv  Detail & Related papers  (2024-04-12T02:40:29Z)
• Krylov complexity of density matrix operators [0.0]
  Krylov-based measures such as Krylov complexity ($C_K$) and Spread complexity ($C_S$) are gaining prominence. We investigate their interplay by considering the complexity of states represented by density matrix operators.
  arXiv  Detail & Related papers  (2024-02-14T19:01:02Z)
• Inflationary Krylov complexity [3.0346001106791323]
  We investigate the Krylov complexity of curvature perturbation for the modified dispersion relation in inflation. Our analysis could be applied to the most inflationary models.
  arXiv  Detail & Related papers  (2024-01-17T16:17:51Z)
• Krylov complexity as an order parameter for deconfinement phase transitions at large $N$ [0.0]
  Krylov complexity is an order parameter of confinement/deconfinement transitions in large $N$ quantum field theories. We show that Krylov complexity reflects the confinement/deconfinement phase transitions through the continuity of mass spectrum.
  arXiv  Detail & Related papers  (2024-01-09T07:04:17Z)
• Fast Rates for Maximum Entropy Exploration [52.946307632704645]
  We address the challenge of exploration in reinforcement learning (RL) when the agent operates in an unknown environment with sparse or no rewards. We study the maximum entropy exploration problem two different types. For visitation entropy, we propose a game-theoretic algorithm that has $widetildemathcalO(H3S2A/varepsilon2)$ sample complexity. For the trajectory entropy, we propose a simple algorithm that has a sample of complexity of order $widetildemathcalO(mathrmpoly(S,
  arXiv  Detail & Related papers  (2023-03-14T16:51:14Z)
• The Complexity of Adversarially Robust Proper Learning of Halfspaces with Agnostic Noise [67.27523616312428]
  We study the computational complexity of adversarially robust proper learning of halfspaces in the distribution-independent PAC model. We give a computationally efficient learning algorithm and a nearly matching computational hardness result for this problem.
  arXiv  Detail & Related papers  (2020-07-30T04:18:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.