We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact...We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.展开更多
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 th...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.展开更多
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....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.展开更多
We investigate the quantum-classical transition in a system of two coupled kicked rotors. We lind that when the mass of one kicked rotor is much smaller than the other＇s, the influence of the light kicked rotor is st...We investigate the quantum-classical transition in a system of two coupled kicked rotors. We lind that when the mass of one kicked rotor is much smaller than the other＇s, the influence of the light kicked rotor is still able to make decoherence of the heavy one. This leads to the quantum-classical transition of the heavy kicked rotor. We demonstrate this by two different coupling potentials.展开更多
While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge t...While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny＇s transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semielassical Landauer Buttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.展开更多
We investigate the quantum-classical transition of a kicked rotor （KR） under perturbation by a second one. The influence of such a chaotic KR makes decoherence of the first one, resulting in the emergence of classic...We investigate the quantum-classical transition of a kicked rotor （KR） under perturbation by a second one. The influence of such a chaotic KR makes decoherence of the first one, resulting in the emergence of classical diffusion from its quantum dynamics. Such quantum-classical transition persists by decreasing the effective Planck＇s constant h, and at the same time, decreasing the mass of the second KR and the interaction strength proportionally. In the limit of h → 0, due to vanishing small mass and interaction, the second KR has almost no effect on the classieal dynamics of the first one. We demonstrate this via two different coupling potentials.展开更多
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 integrab...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.展开更多
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...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.展开更多
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 stairc...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.展开更多
The spectral form factor(SFF)can probe the eigenvalue statistic at different energy scales as its time variable varies.In closed quantum chaotic systems,the SFF exhibits a universal dip-ramp-plateau behavior,which ref...The spectral form factor(SFF)can probe the eigenvalue statistic at different energy scales as its time variable varies.In closed quantum chaotic systems,the SFF exhibits a universal dip-ramp-plateau behavior,which reflects the spectrum rigidity of the Hamiltonian.In this work,we explore the general properties of SFF in open quantum systems.We find that in open systems the SFF first decays exponentially,followed by a linear increase at some intermediate time scale,and finally decreases to a saturated plateau value.We derive general relations between(i)the early-time decay exponent and Lindblad operators;(ii)the long-time plateau value and the number of steady states.We also explain the effective field theory perspective of general behaviors.We verify our theoretical predictions by numerically simulating the Sachdev−Ye−Kitaev(SYK)model,random matrix theory(RMT),and the Bose−Hubbard model.展开更多
The spectra of Rydberg hydrogen atom in magnetic fields have been calculated using linear variational method with B-splines basis functions [Acta Phys. Sin. 55 （2006） 3380]. Based on these calculations we have done...The spectra of Rydberg hydrogen atom in magnetic fields have been calculated using linear variational method with B-splines basis functions [Acta Phys. Sin. 55 （2006） 3380]. Based on these calculations we have done some statistics analysis about the high Rydberg energy levels. The nearest-neighbor energy spacing distribution and the 3-statistics have been shown about diamagnetic Rydberg hydrogen atom with the magnetic field being 0.6 T and 6 T. The phenomena of multiply crossing, multiply anti-crossing, and the mixed of crossing and anti-crossing of energy levels have appeared in this paper. For both cases, in range of lower energy, the energy 1evel statistics properties close to Poisson distribution. With the increasing of the energy, the energy level statistics properties are away to Poisson distribution and tend to Wigner distribution step by step.展开更多
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 f...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.展开更多
The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstat...The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin?Wigner perturbation theory. The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.展开更多
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 attack...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).展开更多
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-li...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.展开更多
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?ding...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.展开更多
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 Fun...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.展开更多
We investigate the interference of a kicked harmonic oscillator in phase space.With the measure of interference defined in Lee and Jeong[Phys.Rev.Lett.106(2011)220401],we show that interference increases more rapidly ...We investigate the interference of a kicked harmonic oscillator in phase space.With the measure of interference defined in Lee and Jeong[Phys.Rev.Lett.106(2011)220401],we show that interference increases more rapidly in the chaotic regime than in the regular regime,and that the sub-Planck structure is of importance for the decoherence time in the chaotic regime.We also find that interference plays an important role in energy transport between the kicking fields and the kicked harmonic oscillator.展开更多
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...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.展开更多
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 elem...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).展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10575034the Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics of China under Grant No.T152504
文摘We study quantum motion around a classical heteroclinic point of a single trapped ion interacting with a strong laser standing wave. We construct a set of exact coherent states of the quantum system and from the exact solutions reveal that quantum signatures of chaos can be induced by the adiabatic interaction between the trapped ion and the laser standing wave, where the quantum expectation values of position and momentum correspond to the classically chaotic orbit. The chaotic region on the phase space is illustrated. The energy crossing and quantum resonance in time evolution and the exponentially increased Heisenberg uncertainty are found. The results suggest a theoretical scheme for controlling the unstable regular and chaotic motions.
基金Project supported by National Natural Science Foundation of China (Grant Nos. 11025527,10874151,and 10935010)
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11175064 and 11475060the Construct Program of the National Key Discipline of Chinathe Hunan Provincial Innovation Foundation for Postgraduates under Grant No CX2014B195
文摘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.
基金supported by National Natural Science Foundation of China under Grant No.10875087
文摘We investigate the quantum-classical transition in a system of two coupled kicked rotors. We lind that when the mass of one kicked rotor is much smaller than the other＇s, the influence of the light kicked rotor is still able to make decoherence of the heavy one. This leads to the quantum-classical transition of the heavy kicked rotor. We demonstrate this by two different coupling potentials.
基金Supported by the National Science Council at Taiwan through Grants No. NSC 97-2112-M-009-008-MY3
文摘While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny＇s transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semielassical Landauer Buttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.
基金Supported by National Science Foundation of China under Grant No.10875087
文摘We investigate the quantum-classical transition of a kicked rotor （KR） under perturbation by a second one. The influence of such a chaotic KR makes decoherence of the first one, resulting in the emergence of classical diffusion from its quantum dynamics. Such quantum-classical transition persists by decreasing the effective Planck＇s constant h, and at the same time, decreasing the mass of the second KR and the interaction strength proportionally. In the limit of h → 0, due to vanishing small mass and interaction, the second KR has almost no effect on the classieal dynamics of the first one. We demonstrate this via two different coupling potentials.
基金supported by the Natural Science Foundation of Zhejiang Province,China(Grant No.LY16A050004)the Fundamental Research Funds for the Central Universities,China(Grant No.2017FZA3005)the National Natural Science Foundation of China(Grant No.11475146)
文摘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.
基金the National Natural Science Foundation of China(Grant Nos.11864014 and 11804130).
文摘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.
基金Project partially supported by the National Natural Science Foundation of China(Grant Nos.12065009,11804130,and 11805165)Zhejiang Provincial Nature Science Foundation,China(Grant No.LY20A050001)。
文摘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.
文摘The spectral form factor(SFF)can probe the eigenvalue statistic at different energy scales as its time variable varies.In closed quantum chaotic systems,the SFF exhibits a universal dip-ramp-plateau behavior,which reflects the spectrum rigidity of the Hamiltonian.In this work,we explore the general properties of SFF in open quantum systems.We find that in open systems the SFF first decays exponentially,followed by a linear increase at some intermediate time scale,and finally decreases to a saturated plateau value.We derive general relations between(i)the early-time decay exponent and Lindblad operators;(ii)the long-time plateau value and the number of steady states.We also explain the effective field theory perspective of general behaviors.We verify our theoretical predictions by numerically simulating the Sachdev−Ye−Kitaev(SYK)model,random matrix theory(RMT),and the Bose−Hubbard model.
基金Supported by the National Natural Science Foundation of China under Grant No.10774042
文摘The spectra of Rydberg hydrogen atom in magnetic fields have been calculated using linear variational method with B-splines basis functions [Acta Phys. Sin. 55 （2006） 3380]. Based on these calculations we have done some statistics analysis about the high Rydberg energy levels. The nearest-neighbor energy spacing distribution and the 3-statistics have been shown about diamagnetic Rydberg hydrogen atom with the magnetic field being 0.6 T and 6 T. The phenomena of multiply crossing, multiply anti-crossing, and the mixed of crossing and anti-crossing of energy levels have appeared in this paper. For both cases, in range of lower energy, the energy 1evel statistics properties close to Poisson distribution. With the increasing of the energy, the energy level statistics properties are away to Poisson distribution and tend to Wigner distribution step by step.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11005053,11135001,and 11375074)the Air Force Office of Scientific Research (Grant No. FA9550-12-1-0095)the Office of Naval Research (Grant No. N00014-08-1-0627)
文摘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.
文摘The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin?Wigner perturbation theory. The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.
文摘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).
基金Project supported by the Science and Technology Development Fund(FDCT)of Macao,China(Grant Nos.0014/2022/A1 and 0042/2018/A2)the National Natural Science Foundation of China(Grant Nos.11761161001,12035011,and 11975167)
文摘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.
基金the Natural Science Foundation of China under Grant Nos.11275179,11535011 and 11775210the Deutsche Forschungsgemeinschaft(DFG)within the Research Unit FOR 2692 under Grant No.397107022(GE 1657/3-2)
文摘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.
文摘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.
基金Supported by Talent Introduction Foundation of Kunming University of Science and Technology under Grant No.kksy201207034
文摘We investigate the interference of a kicked harmonic oscillator in phase space.With the measure of interference defined in Lee and Jeong[Phys.Rev.Lett.106(2011)220401],we show that interference increases more rapidly in the chaotic regime than in the regular regime,and that the sub-Planck structure is of importance for the decoherence time in the chaotic regime.We also find that interference plays an important role in energy transport between the kicking fields and the kicked harmonic oscillator.
基金This paper was supported by the National Natural Science Foundation of China under Grant Nos.11535011 and 11775210.
文摘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.
基金This work is supported by the National Science Foundation(Grant Nos.1037504 and 10875087).
文摘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).
