Chaos and quantum Fisher information in the quantum kicked top

Quantum Fisher information is related to the problem of parameter estimation. Recently, a criterion has been proposed for entanglement in multipartite systems based on quantum Fisher information. This paper studies the behaviours of quantum Fisher information in the quantum kicked top model, whose classical correspondence can be chaotic. It finds that, first, detected by quantum Fisher information, the quantum kicked top is entangled whether the system is in chaotic or in regular case. Secondly, the quantum Fisher information is larger in chaotic case than that in regular case, which means, the system is more sensitive in the chaotic case.

Combined Effect of Classical Chaos and Quantum Resonance on Entanglement Dynamics

We use linear entropy of an exact quantum state to study the entanglement between internal electronic states and external motional states for a two-level atom held in an amplitude-modulated and tilted optical lattice. Starting from an unentangled initial state associated with the regular ＇island＇ of classical phase space, it is demonstrated that the quantum resonance leads to entanglement generation, the chaotic parameter region results in the increase of the generation speed, and the symmetries of the initial probability distribution determine the final degree of entanglement. The entangled initial states are associated with the classical ＇chaotic sea＇, which do not affect the final entanglement degree for the same initial symmetry. The results may be useful in engineering quantum dynamics for quantum information processing.

Identifying the closeness of eigenstates in quantum many-body systems

We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis （ETH） which explains the thermalization in quantum many-body systems.

Quantum to classical transition induced by a classically small influence

We investigate the quantum to classical transition induced by two-particle interaction via a system of periodically kicked particles.The classical dynamics of particle 1 is almost unaffected in condition that its mass is much larger than that of particle 2.Interestingly,such classically weak influence leads to the quantum to classical transition of the dynamical behavior of particle 1.Namely,the quantum diffusion of this particle undergoes the transition from dynamical localization to the classically chaotic diffusion with the decrease of the effective Planck constantħeff.The behind physics is due to the growth of entanglement in the system.The classically very weak interaction leads to the exponential decay of purity in condition that the classical dynamics of external degrees freedom is strongly chaotic.

Chaotic dynamics of complex trajectory and its quantum signature

We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with PT symmetry.For the quantum dynamics,both the mean momentum and mean square of momentum exhibit the staircase growth with time when the system parameter is in the neighborhood of the PT symmetry breaking point.If the system parameter is much larger than the PT symmetry breaking point,the accelerator mode results in the directed spreading of the wavepackets as well as the ballistic diffusion in momentum space.For the classical dynamics,the non-Hermitian kicking potential leads to the exponentially-fast increase of classical complex trajectories.As a consequence,the imaginary part of the trajectories exponentially diffuses with time,while the real part exhibits the normal diffusion.Our analytical prediction of the exponential diffusion of imaginary momentum and its breakdown time is in good agreement with numerical results.The quantum signature of the chaotic diffusion of the complex trajectories is reflected by the dynamics of the out-of-timeorder correlators(OTOC).In the semiclassical regime,the rate of the exponential increase of the OTOC is equal to that of the exponential diffusion of the complex trajectories.

Level spacing statistics for two-dimensional massless Dirac billiards

Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The search- ing for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation （or Weyl equation） and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different, rendering distinct level spacing statistics.

Image Encryption Using Multi-Scroll Attractor and Chaotic Logistic Map

In the current scenario,data transmission over the network is a challenging task as there is a need for protecting sensitive data.Traditional encryption schemes are less sensitive and less complex thus prone to attacks during transmission.It has been observed that an encryption scheme using chaotic theory is more promising due to its non-linear and unpredictable behavior.Hence,proposed a novel hybrid image encryption scheme with multi-scroll attractors and quantum chaos logistic maps(MSA-QCLM).The image data is classified as inter-bits and intra-bits which are permutated separately using multi scroll attractor&quantum logistic maps to generate random keys.To increase the encryption efficiency,a hybrid chaotic technique was performed.Experimentation is performed in a Qiskit simulation tool for various image sets.The simulation results and theoretical analysis show that the proposed method is more efficient than its classical counterpart,and its security is verified by the statistical analysis,keys sensitivity,and keyspace analysis.The Number of changing pixel rate(NPCR)&the Unified averaged changed intensity(UACI)values were observed to be 99.6%&33.4%respectively.Also,entropy oscillates from 7.9 to 7.901 for the different tested encrypted images.The proposed algorithm can resist brute force attacks well,owing to the values of information entropy near the theoretical value of 8.The proposed algorithm has also passed the NIST test(Frequency Monobit test,Run test and DFT test).

Resonance and antiresonance characteristics in linearly delayed Maryland model

The Maryland model is a critical theoretical model in quantum chaos.This model describes the motion of a spin-1/2particle on a one-dimensional lattice under the periodical disturbance of the external delta-function-like magnetic field.In this work,we propose the linearly delayed quantum relativistic Maryland model(LDQRMM)as a novel generalization of the original Maryland model and systematically study its physical properties.We derive the resonance and antiresonance conditions for the angular momentum spread.The“characteristic sum”is introduced in this paper as a new measure to quantify the sensitivity between the angular momentum spread and the model parameters.In addition,different topological patterns emerge in the LDQRMM.It predicts some additions to the Anderson localization in the corresponding tight-binding systems.Our theoretical results could be verified experimentally by studying cold atoms in optical lattices disturbed by a linearly delayed magnetic field.

Steady-state relation of a two-level system strongly coupled to a many-body quantum chaotic environment

We study the long-time average of the reduced density matrix(RDM)of a two-level system as the central system,which is locally coupled to a many-body quantum chaotic system as the environment,under an overall Schr?dinger evolution.A phenomenological relation among elements of the RDM is proposed for a dissipative interaction in the strong coupling regime and is tested numerically with the environment as a defect Ising chain,as well as a mixed-field Ising chain.

Semiclassical Husimi Function of Simple and Chaotic Systems

We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Function. The validity of the method is tested using Harmonic Oscillator, Morse Potential and Dikie’s Model as example, we found a good accuracy in the classical limit.

Sensitivity of energy eigenstates to perturbation in quantum integrable and chaotic systems

We study the sensitivity of energy eigenstates to small perturbation in quantum integrable and chaotic systems.It is shown that the distribution of rescaled components of perturbed states in unperturbed basis exhibits qualitative difference in these two types of systems:being close to the Gaussian form in quantum chaotic systems,while,far from the Gaussian form in integrable systems.

Simulation of Decoherence by Averaged Semiquantum Method

We investigate the dynamics of a system coupled to an environment by averaged semiquantum method. The theory origins from the time-dependent variationalprinciple (TDVP) formulation and contains nondiagonal matrix elements, thus it canbe applied to study dissipation, measurement and decoherence problems in the model.In the calculation, the influence of the environment governed by differential dynamical equation is incorporated using a mean field. We have performed averaged semiquantum method for a spin-boson model, which reproduces the results from stochasticSchrodinger equation method and Hierarchical approach quite accurately. Moreover,we validate our results with noninteracting-blip approximation (NIBA) and generalized Smoluchowski equation (GSE). The problem dynamics in nonequilibrium environments has also been studied by our method. When applied to the harmonic oscillator model coupled to a heat bath with different coupling strengths and dimensionalities of the bath, we find that the loss of coherence predicted by semiquantum methodis identical to the result of master equation with different initial state (Gaussian wavepacket and superposed wave packets).

Note on higher-point correlation functions of the TT or JT deformed CFTs

We investigate generic n-point correlation functions of conformal field theories(CFTs),with TT and JT deformations,in terms of the perturbative CFT approach.We systematically obtain the first order correction to the generic correlation functions of CFTs with TT or JT deformation.We compute the out of time ordered correlation function(OTOC)in the Ising model with TT or Jdeformation,which confirms that these deformations do not change the integrable property up to the first order level.

WAVE COMPUTATION ON THE HYPERBOLIC DOUBLE DOUGHNUT

We compute the waves propagating on the compact surface of constant negative curvature and genus 2 that is a toy model in quantum chaos theory and cosmic topology. We adopt a variational approach using finite elements. We have to implement the action of the fuchsian group by suitable boundary conditions of periodic type. Despite the ergodicity of the dynamics that is quantum weak mixing, the computation is very accurate. A spectral analysis of the transient waves allows to compute the spectrum and the eigenfunctions of the Laplace-Beltrami operator. We test the exponential decay due to a localized dumping satisfying the assumption of geometric control.