REVIEW 43 cited by
Quantum chaos and the complexity of spread of states
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Quantum chaos and the complexity of spread of states
read the original abstract
We propose a measure of quantum state complexity defined by minimizing the spread of the wave-function over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently computed in theories with discrete spectra. For continuous Hamiltonian evolution, it generalizes Krylov operator complexity to quantum states. We apply our methods to the harmonic and inverted oscillators, particles on group manifolds, the Schwarzian theory, the SYK model, and random matrix models. For time-evolved thermofield double states in chaotic systems our measure shows four regimes: a linear "ramp" up to a "peak" that is exponential in the entropy, followed by a "slope" down to a "plateau". These regimes arise in the same physics producing the slope-dip-ramp-plateau structure of the Spectral Form Factor. Specifically, the complexity slope arises from spectral rigidity, distinguishing different random matrix ensembles.
Forward citations
Cited by 43 Pith papers
-
Comments on holographic spread complexity
The momentum–spread-complexity relation requires generalized coherent states adapted to the spacetime symmetry algebra; semiclassical spreading alone cannot produce a momentum–complexity correspondence.
-
Polynomial Initial-State Jumps and Christoffel Transforms in Krylov Complexity
Polynomial changes of the initial state in Krylov complexity are solved exactly via Christoffel transforms of the spectral measure, yielding finite-band amplitude transfer and projected-kernel complexity formulas with...
-
Polynomial Initial-State Jumps and Christoffel Transforms in Krylov Complexity
Changing the initial state to Q(H)|K0⟩ is exactly a Christoffel reweighting of the spectral measure by |Q|²; Krylov complexity then transfers from the reference problem through finite-band connectors and finite-rank k...
-
Complexity Inequalities for Quantum Subsystems
Introduces tripartite complexity and complexity gap for three-region subsystems and reports that the gap has a definite sign in holographic volume complexity, Fisher-Rao Gaussian complexity, and Krylov-space approaches.
-
Complexity Inequalities for Quantum Subsystems
Defines tripartite complexity and complexity gap for three-subsystem states and reports that the gap has definite sign across holographic CV, Fisher-Rao, and Krylov measures, suggesting it as a building block for comp...
-
Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity
Exact Krylov correlators in sl(2,R) models are proportional to proper radial momenta of infalling particles in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
-
q-Askey Deformations of Double-Scaled SYK
q-Askey deformations of double-scaled SYK yield transfer matrices for orthogonal polynomials whose semiclassical chord dynamics map to ER bridges and new geometric transitions in sine dilaton gravity.
-
q-Askey Deformations of Double-Scaled SYK
q-Askey deformations of DSSYK produce transfer matrices from basic orthogonal polynomials whose chord numbers map to ER bridge lengths and signal geometric transitions with discrete spectra in sine dilaton gravity.
-
Holographic Krylov Complexity for Charged, Composite and Extended Probes
Holographic Krylov complexity for charged composite and extended probes retains universal leading large-time growth but acquires structure-dependent subleading corrections.
-
Towards a Refinement of Krylov Complexity: Scrambling, Classical Operator Growth and Replicas
LogK complexity via replicas distinguishes genuine scrambling from saddle effects in quantum and classical systems and refines the measure for integrable cases.
-
Krylov Subspace Dynamics as Near-Horizon AdS$_2$ Holography
In the continuum limit the discrete Krylov chain becomes a Klein-Gordon field in AdS2, with Lanczos growth rate α identified as πT, recovering the maximal chaos bound and requiring the Breitenlohner-Freedman bound for...
-
Universal Time Evolution of Holographic and Quantum Complexity
Holographic complexity measures show universal linear growth followed by late-time saturation, proven necessary and sufficient via pole structures in the energy basis using the residue theorem, arising from random mat...
-
Krylov-Space Memory Cores
Anomalous initial states in otherwise thermalizing models leave compact, stationary low-depth Krylov-space cores—regions with persistent fluctuations, Gibbs mismatch, and current activity—while generic states do not.
-
Non-perturbative saturation of Krylov complexity, and its implications in quantum gravity
Full-spectrum Krylov complexity provably saturates at ~e^{S(E)} log(1/λ) in every low-energy state — near the energy-dependent Heisenberg time, not the maximal e^{S_max} — because discrete-spectrum orthogonal polynomi...
-
The Normalised Wigner Negativity Rate as a Second-Moment Probe of Infall in AdS$_3$
Normalized Krylov-Wigner negativity rate matches Krylov variance growth and equals tidal stretch rate R ∝ C P_ρ if and only if Δ=1 in AdS3.
-
The Normalised Wigner Negativity Rate as a Second-Moment Probe of Infall in AdS$_3$
A rescaled Wigner negativity in Krylov space grows as sinh^{4Δ} and, at Δ=1, its rate matches the tidal momentum of infalling geodesics in AdS3.
-
Wigner negativity in Krylov space and emergent semiclassicality
Wigner negativity in Krylov space stays O(1) or grows as t^{1/2} (without Hilbert-space scaling) in 2d CFTs, one-cut matrix models, and double-scaled SYK, indicating emergent semiclassicality.
-
Holographic Spread Complexity from Branes and Strings
D0-branes in ABJM, rotating D3-branes, and wound strings realize holographic spread complexity via proper momentum and Routhian prescriptions that match short-time Krylov behavior.
-
Controlled Chaos in 4D SCFTs
Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.
-
Krylov complexity has it all
Krylov complexity's Taylor coefficients recursively determine all Lanczos coefficients, making it a complete descriptor of operator dynamics, with caveats for spread complexity.
-
Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity
Exact Krylov correlators in sl(2,R) models are proportional to radial momenta in BTZ black holes, extending the complexity-momentum correspondence to include fluctuations.
-
Krylov Correlators in $\mathfrak{sl}(2,\mathbb R)$ Models: Exact Results and Holographic Complexity
Exact Krylov correlators in sl(2,R) models are proportional to radial momenta of infalling particles in the BTZ black hole, providing a step toward generalizing the complexity-momentum correspondence.
-
Bridging Krylov Complexity and Universal Analog Quantum Simulator
Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.
-
Cosmological brick walls & quantum chaotic dynamics of de Sitter horizons
Brick-wall spectra in de Sitter space show long-range chaotic signatures via spectral form factor and Krylov complexity even when conventional level repulsion is absent.
-
Resolving Black Hole Singularities in Jackiw-Teitelboim Gravity
In JT gravity, the left confining potential required by spectral discreteness makes the wormhole length turn around and plateau, allowing boundary time to run past the would-be singularity and eliminating future horizons.
-
Deforming the Double-Scaled SYK & Reaching the Stretched Horizon From Finite Cutoff Holography
Deformations of the double-scaled SYK model via finite-cutoff holography produce Krylov complexity as wormhole length and realize Susskind's stretched horizon proposal through targeted T² deformations in the high-ener...
-
Black Hole States in Quantum Spin Chains
An equal-weight superposition of all non-crossing singlet pairings in a Heisenberg chain shows logarithmic entanglement growth (c≈5.2) and near-infinite-temperature thermalization.
-
Grand Canonical vs Canonical Krylov Complexity in Double-Scaled Complex SYK Model
In double-scaled complex SYK, grand-canonical Krylov complexity is the charge-weighted sum of canonical complexities, saturating a conjectured inequality.
-
Quantum Cosmology in Krylov Space: Complexity and Entropy
In a sharply peaked Gaussian state of a flat FLRW universe with a massless scalar clock, Krylov state complexity grows as σ²(φ−φ0)²/4 and operator complexity is exactly twice that, in both Wheeler-DeWitt and loop quan...
-
Cosmological Entanglement Entropy from the von Neumann Algebra of Double-Scaled SYK & Its Connection with Krylov Complexity
Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specif...
-
Toward Krylov-based holography in double-scaled SYK
Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-ge...
-
On the stabilizer complexity of Hawking radiation
In the PSSY model, the Wigner negativity (stabilizer magic) of Hawking radiation is O(1) before the Page time and grows as sqrt(2/pi) exp((S_max - S_2)/2) afterward; a similar formula is proposed for holographic state...
-
Holography of K-complexity: Switchbacks and Shockwaves
Operator Krylov complexity in triple-scaled DSSYK matches JT-gravity geodesic lengths with shockwaves and exhibits the switchback effect when the Lanczos algorithm is perturbed by two-sided operator insertions.
-
The Information Content of Krylov Observables: A Machine Learning Approach
Under chaos, the normalized Wigner negativity χ(t) carries information about the fine return dynamics that spread complexity C(t) cannot, with the asymmetry gap rising from +0.33 to +0.77 across the integrable-to-GUE ...
-
On the Universality of Probe Complexity in $\mathcal{N}=4$ SYM
Protected and few-body sectors in N=4 SYM exhibit integrable Krylov dynamics with a_n=2Mg and b_n→Mg, insufficient for testing gravitational universality of complexity growth; a finite-density program is proposed to t...
-
Holographic complexity of de-Sitter black holes
In SdS black hole holography, CV and CV2.0 complexities grow linearly while CA growth vanishes due to finite action, with matching rates between static patch and dS/CFT schemes.
-
Krylov complexity has it all
Krylov complexity is equivalent to Lanczos coefficients, return amplitude, and spectral density for operator dynamics, via an explicit recursive algorithm from its t=0 Taylor expansion.
-
Krylov complexity from a simple quantum mechanical model for a radiating black hole
A simplified mini-BMN matrix model for a radiating black hole exhibits early-time chaotic growth of Krylov complexity followed by late-time saturation to a plateau consistent with equilibration.
-
A Timelike Quantum Focusing Conjecture
A timelike quantum focusing conjecture implies a complexity-based quantum strong energy condition and a complexity bound analogous to the covariant entropy bound for suitable codimension-0 field theory complexity measures.
-
Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity
Reducing a graph walk to distance-layers reproduces Krylov/spread complexity, yielding analytic finite-q SYK Lanczos coefficients and hypercube complexity D sin²(t/D), with faster saturation than classical-walk circuits.
-
Probing the Chaos to Integrability Transition in Double-Scaled SYK
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-inte...
-
Krylov Complexity for Open Quantum System: Dissipation and Decoherence
Krylov complexity saturates in the full high-temperature Caldeira-Leggett system, reproduces dissipative features when decoherence is suppressed, shows oscillations when dissipation is suppressed, and remains insensit...
-
Complexity of Quadratic Quantum Chaos
Hard-core boson two-body models with random interactions exhibit chaotic spectral statistics, operator growth, and eigenstate properties approaching those of random matrices and the SYK model.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.