A Schwinger-Keldysh Formulation of Semiclassical Operator Dynamics

• URL: http://arxiv.org/abs/2602.02106v1
• Date: Mon, 02 Feb 2026 13:51:01 GMT
• Title: A Schwinger-Keldysh Formulation of Semiclassical Operator Dynamics
• Authors: Jeff Murugan, Hendrik J. R. van Zyl,
• Abstract summary: We develop a real-time Schwinger-Keldysh formulation of Krylov dynamics that treats Krylov complexity as an in-in observable generated by a closed time contour path integral path.<n>The resulting functional exposes an emergent phase-space description in which the Lanczos coefficients define an effective Hamiltonian governing operator motion along the Krylov chain.<n>This formulation reorganises Krylov complexity into a dynamical field-theoretic framework and identifies new fluctuation diagnostics of operator growth in closed quantum systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work we develop a real-time Schwinger-Keldysh formulation of Krylov dynamics that treats Krylov complexity as an in-in observable generated by a closed time contour path integral. The resulting generating functional exposes an emergent phase-space description in which the Lanczos coefficients define an effective Hamiltonian governing operator motion along the Krylov chain. In the semiclassical limit, exponential complexity growth arises from hyperbolic trajectories, and asymptotically linear Lanczos growth appears as a universal chaotic fixed point, with sub-leading deformations classified as irrelevant, marginal or relevant. Going beyond the saddle, the Schwinger-Keldysh framework provides controlled access to fluctuations and large deviations of Krylov complexity, revealing sharp signatures of integrability-chaos crossovers that are invisible at the level of the mean. This formulation reorganises Krylov complexity into a dynamical field-theoretic framework and identifies new fluctuation diagnostics of operator growth in closed quantum systems.

Related papers

• KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra [65.11254608352982]
  We introduce a generator-based neural Koopman framework that models dynamics through a structured, state-dependent representation of Koopman generators.<n>By exploiting the intrinsic Cartesian decomposition into skew-adjoint and self-adjoint components, KoopGen separates conservative transport from irreversible dissipation.
  arXiv  Detail & Related papers  (2026-02-15T06:32:23Z)
• Long-Range Pairing in the Kitaev Model: Krylov Subspace Signatures [0.0]
  We show that Lanczos coefficients generated from local boundary operators provide a quantitative diagnostic of excitation gap.<n>We derive an exact single-particle operator Lanczos algorithm that reduces the recursion from exponentially large operator space to a finite-dimensional linear problem.<n>These results establish Krylov diagnostics as operational probes of how low-energy excitations are localized along the chain.
  arXiv  Detail & Related papers  (2026-02-11T19:00:05Z)
• Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuits [72.0643009153473]
  We show that expressive variational ansatze enter a Haar-like universality class in which both observable expectation values and parameter gradients concentrate exponentially with system size.<n>As a consequence, the hypothesis class induced by such circuits collapses with high probability to a narrow family of near-constant functions.<n>We further show that this collapse is not unavoidable: tensor-structured VQCs, including tensor-network-based and tensor-hypernetwork parameterizations, lie outside the Haar-like universality class.
  arXiv  Detail & Related papers  (2026-01-05T08:04:33Z)
• Spin Glass Dynamics on Complex Hardware Topologies: A Bond-Correlated Percolation Approach [41.99844472131922]
  We study the non-exponential relaxation behavior of spin glasses on network architectures relevant to quantum annealing hardware.<n>This framework enables a more comprehensive characterization of spin-glass energy landscapes.
  arXiv  Detail & Related papers  (2025-10-28T18:16:59Z)
• Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity [10.451635171062017]
  We study the emergence of nonchaotic dynamics in a quantum spin chain with a local non-Hermitian disorder.<n>As the disorder strength increases, the emergence of nonchaotic dynamics is qualitatively captured through the growth of Krylov complexity.
  arXiv  Detail & Related papers  (2025-01-27T12:09:49Z)
• Dynamics of inhomogeneous spin ensembles with all-to-all interactions: breaking permutational invariance [49.1574468325115]
  We investigate the consequences of introducing non-uniform initial conditions in the dynamics of spin ensembles characterized by all-to-all interactions. We find that the dynamics of the spin ensemble now spans a more expansive effective Hilbert space.
  arXiv  Detail & Related papers  (2023-09-19T16:44:14Z)
• Krylov complexity in quantum field theory, and beyond [41.99844472131922]
  We study Krylov complexity in various models of quantum field theory.<n>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)
• Krylov complexity from integrability to chaos [0.0]
  We apply a notion of quantum complexity, called "Krylov complexity", to study the evolution of systems from integrability to chaos. We investigate the integrable XXZ spin chain, enriched with an integrability breaking deformation that allows one to interpolate between integrable and chaotic behavior. We find that the chaotic system indeed approaches the RMT behavior in the appropriate symmetry class.
  arXiv  Detail & Related papers  (2022-07-15T18:51:13Z)
• Krylov complexity in saddle-dominated scrambling [0.0]
  In semi-classical systems, the exponential growth of the out-of-time order correlator (OTOC) is believed to be the hallmark of quantum chaos. In this work, we probe such an integrable system exhibiting saddle dominated scrambling through Krylov complexity and the associated Lanczos coefficients.
  arXiv  Detail & Related papers  (2022-03-07T17:29:24Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Krylov Localization and suppression of complexity [0.0]
  We investigate Krylov complexity for the case of interacting integrable models at finite size. We find that complexity saturation is suppressed as compared to chaotic systems. We demonstrate this behavior for an interacting integrable model, the XXZ spin chain.
  arXiv  Detail & Related papers  (2021-12-22T18:45:32Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)
• Toda chain flow in Krylov space [77.34726150561087]
  We show that the singularity along the imaginary axis, which is a generic behavior for quantum non-integrable many-body system, is due to delocalization in Krylov space.
  arXiv  Detail & Related papers  (2019-12-27T16:40:10Z)

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.