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 2024
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 2024
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 numerically investigate the quantum transport in coupled kicked rotors with PT-symmetric potential. We find that spontaneous 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 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.
This work presents a comprehensive study of geometric transport in non-Hermitian Floquet lattices. We derive the non-Hermitian Berry curvature using the biorthogonal formalism and prove an exact algebraic no-go theorem: perfectly anti-correlated driving (φ=0) yields zero net displacement for any wavepacket. When driving symmetry is broken (φ=π/2), a Gaussian wavepacket acquires finite directional displacement per cycle. Using adaptive peak-centered quadrature with analytic derivatives and direct time-dependent wavepacket simulations on finite chains, we demonstrate transport enhancement near the exceptional-point manifold, accompanied by non-monotonic behavior due to moving curvature hotspots. The paper includes full analytical characterization of the EP manifold topology, explicit convergence tests, finite-size scaling, and clear separation between geometric pumping and non-Hermitian skin effect. All Python scripts, raw outputs, and high-resolution figures are provided for full reproducibility. Keywords: non-Hermitian Floquet systems, exceptional points, geometric transport, Berry curvature, no-go theorem, adiabaticity, wavepacket dynamics
In recent years, there have been intensive studies of non-Hermitian physics and parity–time (PT) symmetry due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric system is phase transition (spontaneous PT-symmetry breaking), i.e. an all-real energy spectrum changes into an all-complex one when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. The generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real energy spectra is a currently important endeavor. A simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for the realization of non-unitary single-qubit quantum gate. However, studies of the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system are still relatively rare. In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. According to these pseudo fixed points, we analytically construct a non-unitary evolution operator and then explore the dynamic behaviors of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although it is non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all-real to all-complex energy spectrum, just like the PT symmetric system. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system satisfies fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not meet such a PT symmetry, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the requirement for the PT symmetry.
The conventional time-dependent perturbation theory in quantum mechanics is established within the framework of Hermitian Hamiltonians, applicable for describing quantum transitions and associated energy level responses in such systems. However, this theory has fundamental limitations when applied to non-Hermitian systems. Consequently, researchers have systematically extended time-dependent perturbation theory to non-Hermitian systems, establishing a corresponding mature framework. Building on this foundation, this study extends the theory to investigate the transition dynamics induced by non-Hermitian interactions in non-Hermitian Hamiltonian systems. We employ a biorthogonal basis representation for a three-level non-Hermitian system. This work investigates a system comprising an unperturbed static non-Hermitian Hamiltonian and a periodically driven time-dependent perturbation Hamiltonian. Taking the three-level system as a concrete example, we combine analytical methods with numerical simulations to solve and analyze its dynamical evolution equations. These complementary approaches reveal that when system parameters complete a full cycle around an exceptional point, the transitional behavior exhibits specific evolutionary patterns. In this system, quantum transition probabilities exhibit significant asymmetry and non-conservation that depend on the initial and final states, revealing inherent directional characteristics in the dynamical process. Furthermore, for a three-level, periodically driven non-Hermitian system with time-dependent perturbations, this asymmetry is even more pronounced, manifesting as a distinct disparity between forward and reverse transition probabilities. The periodic driving actively amplifies the asymmetry in the transition process. By designing the perturbation spectrum, selective manipulation of specific quantum states can be achieved. Moreover, transition probabilities can be significantly enhanced under resonance conditions, while non-Hermiticity further breaks the system's inherent symmetry, leading to substantial amplification of transitions in a single direction. By precisely tuning the drive frequency, interactions between specific coupling channels can be selectively enhanced or suppressed. The amplification of channel asymmetry by non-Hermitian properties provides a novel mechanism for directional control of quantum states and opens new pathways for realizing related quantum technologies.
In recent years, there have been intensive studies on non-Hermitian physics and parity-time (PT) symmetry, due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric systems is phase transition (spontaneous PT-symmetry breaking), where the energy spectrum changes from all real to complex when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. Generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real spectra is a currently important endeavor. The simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for realization of non-unitary single-qubit quantum gate. However, studies on the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system still remain relatively rare. In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. Based on these pseudo fixed points, we analytically construct the non-unitary evolution operator and then explore the dynamics of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although being non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all real to complex, just as for PT symmetric systems. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system respects fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the PT symmetry requirement.