Scrambling and quantum chaos indicators from long-time properties of operator distributions

• URL: http://arxiv.org/abs/2211.15872v2
• Date: Thu, 13 Apr 2023 08:46:07 GMT
• Title: Scrambling and quantum chaos indicators from long-time properties of operator distributions
• Authors: Sivaprasad Omanakuttan, Karthik Chinni, Philip Daniel Blocher, Pablo M. Poggi
• Abstract summary: Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. We study the structure of the expansion coefficients treated as a coarse-grained probability distribution in the space of operators. We show that the long-time properties of the operator distribution display common features across these cases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. Most studies focus on its characterization via out-of-time-ordered correlation functions (OTOCs), particularly through the early-time decay of the OTOC. However, scrambling is a complex process which involves operator spreading and operator entanglement, and a full characterization requires one to access more refined information on the operator dynamics at several timescales. In this work we analyze operator scrambling by expanding the target operator in a complete basis and studying the structure of the expansion coefficients treated as a coarse-grained probability distribution in the space of operators. We study different features of this distribution, such as its mean, variance, and participation ratio, for the Ising model with longitudinal and transverse fields, kicked collective spin models, and random circuit models. We show that the long-time properties of the operator distribution display common features across these cases, and discuss how these properties can be used as a proxy for the onset of quantum chaos. Finally, we discuss the connection with OTOCs and analyze the cost of probing the operator distribution experimentally using these correlation functions.

Related papers

• The role of conjugacy in the dynamics of time of arrival operators [0.0]
  We provide an exact analytic solution of the time kernel equation (TKE) for a special class of potentials satisfying a specific separability condition. We show that the eigenfunctions of the constructed operator exhibit unitary arrival at the intended arrival point at a time equal to their corresponding eigenvalue. We find that the CPTOA operator possesses better unitary dynamics over the Weyl-quantized one within numerical accuracy.
  arXiv  Detail & Related papers  (2024-04-25T02:40:14Z)
• Identifiable Latent Neural Causal Models [82.14087963690561]
  Causal representation learning seeks to uncover latent, high-level causal representations from low-level observed data. We determine the types of distribution shifts that do contribute to the identifiability of causal representations. We translate our findings into a practical algorithm, allowing for the acquisition of reliable latent causal representations.
  arXiv  Detail & Related papers  (2024-03-23T04:13:55Z)
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective [0.0]
  We analytically establish the linear growth of two sets of coefficients for any generic jump operators. We find that the Krylov complexity saturates inversely with the dissipation strength, while the dissipative timescale grows logarithmically.
  arXiv  Detail & Related papers  (2023-11-01T18:00:06Z)
• Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model [11.353329565587574]
  Quantum scrambling plays an important role in understanding thermalization in closed quantum systems. We show that scrambling is absent for disorder-averaged expectation values of observables. We develop a cumulant expansion approach to approximate the evolution of equal-time observables.
  arXiv  Detail & Related papers  (2022-10-05T17:47:52Z)
• Eigen Analysis of Self-Attention and its Reconstruction from Partial Computation [58.80806716024701]
  We study the global structure of attention scores computed using dot-product based self-attention. We find that most of the variation among attention scores lie in a low-dimensional eigenspace. We propose to compute scores only for a partial subset of token pairs, and use them to estimate scores for the remaining pairs.
  arXiv  Detail & Related papers  (2021-06-16T14:38:42Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
  The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy. In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
  arXiv  Detail & Related papers  (2020-07-31T19:23:26Z)
• Generalization Properties of Optimal Transport GANs with Latent Distribution Learning [52.25145141639159]
  We study how the interplay between the latent distribution and the complexity of the pushforward map affects performance. Motivated by our analysis, we advocate learning the latent distribution as well as the pushforward map within the GAN paradigm.
  arXiv  Detail & Related papers  (2020-07-29T07:31:33Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• On operator growth and emergent Poincar\'e symmetries [0.0]
  We consider operator growth for generic large-N gauge theories at finite temperature. The algebra of these modes allows for a simple analysis of the operators with whom the initial operator mixes over time. We show all these approaches have a natural formulation in terms of the Gelfand-Naimark-Segal (GNS) construction.
  arXiv  Detail & Related papers  (2020-02-10T15:29:50Z)

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.