arXiv:2501.14507

Ballistic diffusion vs. damped oscillation of energy in a $\mathcal{PT}$-symmetric quantum kicked harmonic oscillator

Jianzheng Li

Published Jan 24, 2025• 0 citations

Abstract

We numerically study the quantum dynamics of a $\mathcal{PT}$-symmetric kicked harmonic oscillator. We observe that directed current of momentum and ballistic diffusion of energy coexist under the non-resonant conditions, whereas both the momentum and energy oscillate as damped cosine functions with identical frequencies under the resonant conditions. The research shows that the directed current of momentum and ballistic diffusion of energy arise from nearest-neighbor hopping between momentum eigenstates with the non-Hermitian driving, while the damped oscillations of momentum and energy originate from resonant coupling between the non-Hermitian driving and the harmonic oscillator. Our findings indicate that the non-Hermiticity and the frequency characteristic of this system collectively result in these distinctive dynamical behaviors.

DOI: 10.48550/arxiv.2501.14507

Related papers

Ballistic diffusion versus damped oscillation of energy in a P T -symmetric quantum kicked harmonic oscillator

J. S. Li

Physica ScriptaAug 18, 20250 citations

Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors

Jian-Zheng Li, Wen-Lei Zhao, Jie Liu

arXiv:2211.00831Physical Review AMar 13, 20236 citations

Dynamical Behavior of the Quantum Periodically Kicked Harmonic Oscillator

Zongfu Jiang

Communications in Theoretical PhysicsApr 1, 19930 citations

Superexponential diffusion in nonlinear non-Hermitian systems

Wen-Lei Zhao, Longwen Zhou, Jie Liu +2 more

arXiv:2010.01975Physical Review ADec 18, 202017 citations

Chaotic dynamics of complex trajectory and its quantum signature*

Wen-Lei Zhao, Pengkai Gong, Jiaozi Wang +1 more

arXiv:1906.01798Chinese Physics BOct 14, 202013 citations

Phase modulation of directed transport, energy diffusion, and quantum scrambling in a Floquet non-Hermitian system

Wen-Lei Zhao, Guanling Li, Jie Liu

arXiv:2312.08082Physical Review ResearchSep 4, 20244 citations

arXiv:2501.14507

Ballistic diffusion vs. damped oscillation of energy in a $\mathcal{PT}$ -symmetric quantum kicked harmonic oscillatorBallistic diffusion vs. damped oscillation of energy in a $\mathcal{PT}$-symmetric quantum kicked harmonic oscillator

Jianzheng Li

Published Jan 24, 2025• 0 citations

arXiv HTML PDF

Abstract

We numerically study the quantum dynamics of a

\mathcal{PT}

-symmetric kicked harmonic oscillator. We observe that directed current of momentum and ballistic diffusion of energy coexist under the non-resonant conditions, whereas both the momentum and energy oscillate as damped cosine functions with identical frequencies under the resonant conditions. The research shows that the directed current of momentum and ballistic diffusion of energy arise from nearest-neighbor hopping between momentum eigenstates with the non-Hermitian driving, while the damped oscillations of momentum and energy originate from resonant coupling between the non-Hermitian driving and the harmonic oscillator. Our findings indicate that the non-Hermiticity and the frequency characteristic of this system collectively result in these distinctive dynamical behaviors.

DOI: 10.48550/arxiv.2501.14507

Related papers

Ballistic diffusion versus damped oscillation of energy in a P T -symmetric quantum kicked harmonic oscillator

J. S. Li

Abstract We numerically study the quantum dynamics of a P T -symmetric kicked harmonic oscillator. The P T symmetry breaks spontaneously when the non-Hermitian driving strength surpasses the exceptional point. In the P T -broken phase, we observe that directed current of momentum and ballistic diffusion of energy coexist under the non-resonant conditions, whereas both the momentum and energy oscillate as damped cosine functions with identical frequencies under the resonant conditions. The research shows that the directed current of momentum and ballistic diffusion of energy arise from nearest-neighbor hopping between momentum eigenstates with the non-Hermitian driving, while the damped oscillations of momentum and energy originate from resonant coupling between the non-Hermitian driving and the harmonic oscillator. Our findings indicate that the non-Hermiticity and the frequency characteristic of this system collectively result in these distinctive dynamical behaviors.Abstract We numerically study the quantum dynamics of a P T -symmetric kicked harmonic oscillator. The P T symmetry breaks spontaneously when the non-Hermitian driving strength surpasses the exceptional point. In the P T -broken phase, we observe that directed current of momentum and ballistic diffusion of energy coexist under the non-resonant conditions, whereas both the momentum and energy oscillate as damped cosine functions with identical frequencies under the resonant conditions. The research shows that the directed current of momentum and ballistic diffusion of energy arise from nearest-neighbor hopping between momentum eigenstates with the non-Hermitian driving, while the damped oscillations of momentum and energy originate from resonant coupling between the non-Hermitian driving and the harmonic oscillator. Our findings indicate that the non-Hermiticity and the frequency characteristic of this system collectively result in these distinctive dynamical behaviors.

Physica ScriptaAug 18, 20250 citations

Coexistence of directed momentum current and ballistic energy diffusion in coupled non-Hermitian kicked rotors

Jian-Zheng Li, Wen-Lei Zhao, Jie Liu

We numerically investigate the quantum transport in coupled kicked rotors with $\mathcal{PT}$ -symmetric potential. We find that spontaneous $\mathcal{PT}$ -symmetry breaking of wave functions emerges when the amplitude of the imaginary part of the complex potential is beyond a threshold value, which can be modulated by the coupling strength effectively. In the regime of $\mathcal{PT}$ -symmetry breaking, the particles driven by the periodical kicks move unidirectionally in momentum space, indicating the emergence of a directed current. Meanwhile, with increasing the coupling strength, we find a transition from the ballistic energy diffusion to a kind of modified ballistic energy diffusion where the width of the wave packet also increases with time in a power law. Our findings suggest that the decoherence effect induced by the interplay between the interparticle coupling and the non-Hermitian driving potential is responsible for these particular transport behaviors.We numerically investigate the quantum transport in coupled kicked rotors with $\mathcal{PT}$-symmetric potential. We find that spontaneous $\mathcal{PT}$-symmetry breaking of wave functions emerges when the amplitude of the imaginary part of the complex potential is beyond a threshold value, which can be modulated by the coupling strength effectively. In the regime of $\mathcal{PT}$-symmetry breaking, the particles driven by the periodical kicks move unidirectionally in momentum space, indicating the emergence of a directed current. Meanwhile, with increasing the coupling strength, we find a transition from the ballistic energy diffusion to a kind of modified ballistic energy diffusion where the width of the wave packet also increases with time in a power law. Our findings suggest that the decoherence effect induced by the interplay between the interparticle coupling and the non-Hermitian driving potential is responsible for these particular transport behaviors.

arXiv:2211.00831Physical Review AMar 13, 20236 citations

Dynamical Behavior of the Quantum Periodically Kicked Harmonic Oscillator

Zongfu Jiang

We explore the properties of the quantum kicked harmonic oscillation governed by the Hamiltonian . The classical version of this model is known to exhibit certain type of stochastic behavior. We reduce the quantum equation of the model to quantum mapping equations. Numerical results of the mappings show that the behavior of the average energy as a function of time depends on the ration of the frequency of the external and that of the unperturbed system . The energy increases first very rapidly and then the energy growth saturates for irrational . The break time is independent of the strength of the external force, but is roughly proportional to . For a fixed rational the energy is damped oscillation for smaller T, and it is seemingly recurrent with time in the sense of Hogg and Huberman. In both cases, these behaviors of energy are independent of the strength of the external force and differ from the behavior of the quantum kicked rotator.We explore the properties of the quantum kicked harmonic oscillation governed by the Hamiltonian . The classical version of this model is known to exhibit certain type of stochastic behavior. We reduce the quantum equation of the model to quantum mapping equations. Numerical results of the mappings show that the behavior of the average energy as a function of time depends on the ration of the frequency of the external and that of the unperturbed system . The energy increases first very rapidly and then the energy growth saturates for irrational . The break time is independent of the strength of the external force, but is roughly proportional to . For a fixed rational the energy is damped oscillation for smaller T, and it is seemingly recurrent with time in the sense of Hogg and Huberman. In both cases, these behaviors of energy are independent of the strength of the external force and differ from the behavior of the quantum kicked rotator.

Communications in Theoretical PhysicsApr 1, 19930 citations

Superexponential diffusion in nonlinear non-Hermitian systems

Wen-Lei Zhao, Longwen Zhou, Jie Liu +2 more

We investigate the quantum diffusion of a periodically kicked particle subjected to both nonlinearity-induced self-interactions and $\mathcal{PT}$ -symmetric potentials. We find that, due to the interplay between the nonlinearity and non-Hermiticity, the expectation value of the mean square of momentum scales with time in a superexponential form $\ensuremath{\langle}{p}^{2}(t)\ensuremath{\rangle}\ensuremath{\propto}exp[\ensuremath{\beta}exp(\ensuremath{\alpha}t)]$, which is faster than any known rates of quantum diffusion. In the $\mathcal{PT}$ -symmetry-breaking phase, the intensity of a state increases exponentially with time, leading to the exponential growth of the interaction strength. The feedback of the intensity-dependent nonlinearity further turns the interaction energy into the kinetic energy, resulting in a superexponential growth of the mean energy. These theoretical predictions are in good agreement with numerical simulations in a $\mathcal{PT}$ -symmetric nonlinear kicked particle. Our discovery establishes a mechanism of diffusion in interacting and dissipative quantum systems. Important implications and possible experimental observations are discussed.We investigate the quantum diffusion of a periodically kicked particle subjected to both nonlinearity-induced self-interactions and $\mathcal{PT}$-symmetric potentials. We find that, due to the interplay between the nonlinearity and non-Hermiticity, the expectation value of the mean square of momentum scales with time in a superexponential form $\ensuremath{\langle}{p}^{2}(t)\ensuremath{\rangle}\ensuremath{\propto}exp[\ensuremath{\beta}exp(\ensuremath{\alpha}t)]$, which is faster than any known rates of quantum diffusion. In the $\mathcal{PT}$-symmetry-breaking phase, the intensity of a state increases exponentially with time, leading to the exponential growth of the interaction strength. The feedback of the intensity-dependent nonlinearity further turns the interaction energy into the kinetic energy, resulting in a superexponential growth of the mean energy. These theoretical predictions are in good agreement with numerical simulations in a $\mathcal{PT}$-symmetric nonlinear kicked particle. Our discovery establishes a mechanism of diffusion in interacting and dissipative quantum systems. Important implications and possible experimental observations are discussed.

arXiv:2010.01975Physical Review ADec 18, 202017 citations

Chaotic dynamics of complex trajectory and its quantum signature*

Wen-Lei Zhao, Pengkai Gong, Jiaozi Wang +1 more

We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with P T 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 P T symmetry breaking point. If the system parameter is much larger than the P T 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-time-order 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.We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with P T 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 P T symmetry breaking point. If the system parameter is much larger than the P T 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-time-order 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.

arXiv:1906.01798Chinese Physics BOct 14, 202013 citations

Phase modulation of directed transport, energy diffusion, and quantum scrambling in a Floquet non-Hermitian system

Wen-Lei Zhao, Guanling Li, Jie Liu

We investigate both analytically and numerically the wavepacket's dynamics in momentum space for a Floquet non-Hermitian system with a periodically kicked driven potential. We have deduced the exact expression of a time-evolving wavepacket under the condition of quantum resonance. With this analytical expression, we can investigate thoroughly the temporal behaviors of the directed transport, mean energy, and quantum scrambling. We find interestingly that, by tuning the relative phase between the real part and imaginary part of the kicking potential, one can manipulate the directed transport, mean energy, and quantum scrambling efficiently: When the phase equals to π / 2 , we observe a maximum directed transport and mean energy, while a minimum scrambling phenomenon protected by the PT symmetry; when the phase is π , both the directed transport and the time dependence of the energy are suppressed; in contrast, the quantum scrambling is enhanced by the non-Hermiticity. For the quantum nonresonance case, we numerically find that the quantum interference effects lead to dynamical localization, characterized by the suppression of the directed transport, the time dependence of the energy, and quantum scrambling. Interestingly, these suppression effects can be adjusted by the phase of the non-Hermitian kicking potential. Possible applications of our findings are discussed. Published by the American Physical Society 2024We investigate both analytically and numerically the wavepacket's dynamics in momentum space for a Floquet non-Hermitian system with a periodically kicked driven potential. We have deduced the exact expression of a time-evolving wavepacket under the condition of quantum resonance. With this analytical expression, we can investigate thoroughly the temporal behaviors of the directed transport, mean energy, and quantum scrambling. We find interestingly that, by tuning the relative phase between the real part and imaginary part of the kicking potential, one can manipulate the directed transport, mean energy, and quantum scrambling efficiently: When the phase equals to π / 2 , we observe a maximum directed transport and mean energy, while a minimum scrambling phenomenon protected by the PT symmetry; when the phase is π , both the directed transport and the time dependence of the energy are suppressed; in contrast, the quantum scrambling is enhanced by the non-Hermiticity. For the quantum nonresonance case, we numerically find that the quantum interference effects lead to dynamical localization, characterized by the suppression of the directed transport, the time dependence of the energy, and quantum scrambling. Interestingly, these suppression effects can be adjusted by the phase of the non-Hermitian kicking potential. Possible applications of our findings are discussed. Published by the American Physical Society 2024

arXiv:2312.08082Physical Review ResearchSep 4, 20244 citations

Ballistic diffusion vs. damped oscillation of energy in a

\mathcal{PT}

-symmetric quantum kicked harmonic oscillator

We numerically study the quantum dynamics of a

\mathcal{PT}

We numerically investigate the quantum transport in coupled kicked rotors with

\mathcal{PT}

-symmetric potential. We find that spontaneous

\mathcal{PT}

-symmetry breaking of wave functions emerges when the amplitude of the imaginary part of the complex potential is beyond a threshold value, which can be modulated by the coupling strength effectively. In the regime of

\mathcal{PT}

-symmetry breaking, the particles driven by the periodical kicks move unidirectionally in momentum space, indicating the emergence of a directed current. Meanwhile, with increasing the coupling strength, we find a transition from the ballistic energy diffusion to a kind of modified ballistic energy diffusion where the width of the wave packet also increases with time in a power law. Our findings suggest that the decoherence effect induced by the interplay between the interparticle coupling and the non-Hermitian driving potential is responsible for these particular transport behaviors.

We investigate the quantum diffusion of a periodically kicked particle subjected to both nonlinearity-induced self-interactions and

\mathcal{PT}

-symmetric potentials. We find that, due to the interplay between the nonlinearity and non-Hermiticity, the expectation value of the mean square of momentum scales with time in a superexponential form $\ensuremath{\langle}{p}^{2}(t)\ensuremath{\rangle}\ensuremath{\propto}exp[\ensuremath{\beta}exp(\ensuremath{\alpha}t)]$, which is faster than any known rates of quantum diffusion. In the

\mathcal{PT}

-symmetry-breaking phase, the intensity of a state increases exponentially with time, leading to the exponential growth of the interaction strength. The feedback of the intensity-dependent nonlinearity further turns the interaction energy into the kinetic energy, resulting in a superexponential growth of the mean energy. These theoretical predictions are in good agreement with numerical simulations in a

\mathcal{PT}

-symmetric nonlinear kicked particle. Our discovery establishes a mechanism of diffusion in interacting and dissipative quantum systems. Important implications and possible experimental observations are discussed.