Krylov Complexity in early universe

• URL: http://arxiv.org/abs/2411.18405v2
• Date: Mon, 02 Dec 2024 14:15:32 GMT
• Title: Krylov Complexity in early universe
• Authors: Ke-Hong Zhai, Lei-Hua Liu,
• Abstract summary: We investigate Krylov complexity across different phases of the early universe, including the radiation-dominated period (RD), and the matter-dominated period (MD) We are the first to calculate the evolution equations for (r_k) and (phi_k) as they relate to the scale factor. This research provides new insights into exploring the universe from the perspective of quantum information.
• Score: 0.0
• License:
• Abstract: The Lanczos algorithm offers a method for constructing wave functions for both closed and open systems based on their Hamiltonians. Given that the entire early universe is fundamentally an open system, we apply the Lanczos algorithm to investigate Krylov complexity across different phases of the early universe, including inflation, the radiation-dominated period (RD), and the matter-dominated period (MD). Notably, we find that Krylov complexity differs between the closed and open system approaches. To effectively capture the impact of potentials during the RD and MD phases, we analyze various inflationary potentials, including the Higgs potential, the \(R^2\) inflationary potential, and chaotic inflationary potential, which is taking into account the violations of slow-roll conditions. This analysis is conducted in terms of conformal time through the preheating process. Our numerical results indicate that the evolution of Krylov complexity and Krylov entropy is remarkably similar within distinctive potentials in RD and MD. Additionally, we rigorously construct what is referred to as an open two-mode squeezed state, utilizing the second kind of Meixner polynomials. Based on this construction, we are the first to calculate the evolution equations for \(r_k\) and \(\phi_k\) as they relate to the scale factor. Our findings suggest that dissipative effects lead to a rapid decoherence-like behavior. Moreover, our results indicate that inflation behaves as a strongly dissipative system, while both the radiation-dominated and matter-dominated phases exhibit characteristics of weak dissipation. This research provides new insights into exploring the universe from the perspective of quantum information.

Related papers

• Probing the self-coherence of primordial quantum fluctuations with complexity [0.0]
  A recently-proposed novel phenomenon is that of textitrecoherence, wherein a specific interaction between the adiabatic and the entropic sector leads to the adiabatic mode retaining a coherent state after a transient increase in linear entropy. In this paper, we analyze the evolution of linear entropy, complexity of purification (COP), and complexity of formation (COF) to capture the interplay between decoherence and recoherence in this model.
  arXiv  Detail & Related papers  (2025-02-13T19:49:13Z)
• Krylov complexity of thermal state in early universe [3.0346001106791323]
  We perform a detailed study of the Krylov complexity of the thermal state across the entire early universe. To accurately calculate the Krylov complexity, we purified the thermal state, resulting in a pure state with two modes. Our findings reveal that inflation behaves as a strong dissipative system, while the radiation-dominated and matter-dominated periods act as weak dissipative systems.
  arXiv  Detail & Related papers  (2024-08-06T16:41:54Z)
• Krylov complexity of fermion chain in double-scaled SYK and power spectrum perspective [0.0]
  We investigate Krylov complexity of the fermion chain operator which consists of multiple Majorana fermions in the double-scaled SYK (DSSYK) model with finite temperature. Using the fact that Krylov complexity is computable from two-point functions, the analysis is performed in the limit where the two-point function becomes simple. We confirm the exponential growth of Krylov complexity in the very low temperature regime.
  arXiv  Detail & Related papers  (2024-07-18T08:47:05Z)
• 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)
• 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)
• Quantum Langevin Dynamics for Optimization [14.447963674485132]
  We utilize Quantum Langevin Dynamics (QLD) to solve optimization problems. Specifically, we examine the dynamics of a system coupled with an infinite heat bath. We demonstrate that the average energy of the system can approach zero in the low temperature limit.
  arXiv  Detail & Related papers  (2023-11-27T07:25:47Z)
• Krylov complexity in quantum field theory, and beyond [44.99833362998488]
  We study Krylov complexity in various models of quantum field theory. We find that the exponential growth of Krylov complexity satisfies the conjectural inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos.
  arXiv  Detail & Related papers  (2022-12-29T19:00:00Z)
• Indication of critical scaling in time during the relaxation of an open quantum system [34.82692226532414]
  Phase transitions correspond to the singular behavior of physical systems in response to continuous control parameters like temperature or external fields. Near continuous phase transitions, associated with the divergence of a correlation length, universal power-law scaling behavior with critical exponents independent of microscopic system details is found.
  arXiv  Detail & Related papers  (2022-08-10T05:59:14Z)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• An analytical theory of CEP-dependent coherence driven by few-cycle pulses [28.971848801529205]
  We present an analytical theory that describes a two-level atom driven by a far-off-resonance, few-cycle square pulse. Despite its mathematical simplicity, the relation is able to capture some of the key features of the interaction. The theory can potentially offer a general guidance in future studies of CEP-sensitive quantum coherence.
  arXiv  Detail & Related papers  (2021-01-13T05:16:12Z)
• Analog cosmological reheating in an ultracold Bose gas [58.720142291102135]
  We quantum-simulate the reheating-like dynamics of a generic cosmological single-field model in an ultracold Bose gas. Expanding spacetime as well as the background oscillating inflaton field are mimicked in the non-relativistic limit. The proposed experiment has the potential of exploring the evolution up to late times even beyond the weak coupling regime.
  arXiv  Detail & Related papers  (2020-08-05T18:00:26Z)

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.