Chaos and Complexity for Inverted Harmonic Oscillators
arXiv:2111.07351 · doi:10.1103/PhysRevD.105.126015
Abstract
We investigate the circuit complexity and Loschmidt echo for the (inverted) harmonic oscillators. Focusing on the chaotic behaviors under the perturbation, we analytically derive the Lyapunov exponent and scrambling time of the inverted harmonic oscillators. We show that the circuit complexity and Loschmidt echo exhibit qualitatively similar behaviors, particularly the consistent Lyapunov exponent.
arXiv comment20 pages, 2 figures, references added
References in corpus (47)
- Gaussian Quantum Information
- A bound on chaos
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Comments on the Sachdev-Ye-Kitaev model
- Ultimate physical limits to computation
- Complexity Equals Action
- Complexity and Shock Wave Geometries
- Continuous variable quantum information: Gaussian states and beyond
- Chaos in quantum channels
- Complexity, action, and black holes
- Environment-independent decoherence rate in classically chaotic systems
- The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
- Chaos and complexity by design
- Circuit complexity in quantum field theory
- Towards Complexity for Quantum Field Theory States
- Quantum information with Gaussian states
- Chaos, Complexity, and Random Matrices
- Out-of-time-order correlators in quantum mechanics
- Circuit Complexity in Fermionic Field Theory
- Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
- Complexity and entanglement for thermofield double states
- Circuit complexity for free fermions
- Gaussian states in continuous variable quantum information
- Circuit complexity in interacting QFTs and RG flows
- Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
- Circuit Complexity for Coherent States
- Complexity as a novel probe of quantum quenches: universal scalings and purifications
- Time Evolution of Complexity: A Critique of Three Methods
- Black holes, complexity and quantum chaos
- Chaos and Complexity in Quantum Mechanics
- Quantum Complexity of Time Evolution with Chaotic Hamiltonians
- Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
- Complexity of Mixed States in QFT and Holography
- Renormalized Circuit Complexity
- The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
- The Black Hole S-Matrix from Quantum Mechanics
- Complexity growth rates for AdS black holes in massive gravity and gravity
- Thouless time for mass-deformed SYK
- Post-Quench Evolution of Complexity and Entanglement in a Topological System
- Thermal Emission from Semi-classical Dynamical Systems
- Complexity for Charged Thermofield Double States
- Circuit Complexity for Fermionic Thermofield Double states
- Complexity from the Reduced Density Matrix: a new Diagnostic for Chaos
- Circuit complexity for generalised coherent states in thermal field dynamics
- Butterflies from Information Metric
- Interactions resolve state-dependence in a toy-model of AdS black holes
- Quantum Complexity and Chaos in Young Black Holes
Cited by in corpus (15)
- Krylov complexity of density matrix operators
- Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model
- Spread complexity in saddle-dominated scrambling
- From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
- Angular momentum and chaos bound of charged particles around Einstein-Euler-Heisenberg AdS black holes
- Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields
- Chaos and multifold complexity for an inverted harmonic oscillator
- Spectral Properties of the Symmetry Generators of Conformal Quantum Mechanics: A Path-Integral Approach
- Holographic Complexity and Phase Transition for AdS Black Holes
- Duality between the quantum inverted harmonic oscillator and inverse square potentials
- Spatial regions, chaos bound and its violation
- Non-Markovian environment induced chaos in optomechanical system
- Out-of-Time-Order-Correlator for van der Waals potential
- Heat transport through an open coupled scalar field theory hosting stability-to-instability transition
- Quantum instability and Ehrenfest time for an inverted harmonic oscillator