Abstract We study quantum particle dynamics in a box and driven by a parity-time (PT)-symmetric, delta-kicking complex potential. The dynamical characteristics, identified by the average kinetic energy as a function of time, and quasi-energy are computed for different values of the kicking parameters. Breaking of the PT-symmetry at certain values of the non-Hermitian kicking parameter is shown. Experimental realization of the model is also discussed.
Abstract We study quantum particle dynamics in a box and driven by a parity-time (PT)-symmetric, delta-kicking complex potential. The dynamical characteristics, identified by the average kinetic energy as a function of time, and quasi-energy are computed for different values of the kicking parameters. Breaking of the PT-symmetry at certain values of the non-Hermitian kicking parameter is shown. Experimental realization of the model is also discussed.
We study quantum dynamics of a kicked relativistic spin-half particle in a one dimensional box. Time-dependence of the average kinetic energy and evolution of the wave packet are explored. Kicking potential is introduced as the Lorentz-scalar, i.e., through the mass-term in the Dirac equation. It is found that depending on the values of the kicking parameters E(t) can be periodic, monotonically growing and non-periodic function of time. Particle transport in the system is studied by considering spatio-temporal evolution of the Gaussian wave packet.Splitting of the packet into two symmetric parts and restoration of the profile of the packet is found.
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.
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.
We consider a quantum particle under the dynamical confinement caused by PT-symmetric box with a moving wall. The latter is described in terms of the time-dependent Schr\"odinger equation obeying the time-dependent PT-symmetric boundary conditions. The class of the functions, describing time dependence of the wall's position and keeping the system as PT-symmetric is found. Physically observable characteristics, such as average kinetic energy and the average quantum force are calculated as a function of time. It is found that the behavior of the average kinetic energy as a function of time is completely different than that for of Hermitian counterpart of the model, while the average quantum force behaves similarly to that for Hermitian system. Also, geometric phase is calculated for the harmonically oscillating wall regime. The experimental realization of the proposed model is discussed.
We study kicked particle dynamics in a rectangular quantum billiard.The kicking potential is chosen as localized at the center of the billiard.The exact solution for the time-dependent Schrödinger equation for a single kicking period is derived.Using this solution, the time-dependence of the average kinetic energy and probability density as a function of spatial coordinates are computed.Different regimes for trapping of the particle in kicking area are analyzed.It is found that depending of the values of kicking parameters, the average kinetic energy can be a periodic or a monotonically growing function of time or can be suppressed.Such behavior is explained in terms of particle trapping regimes.Wave packet dynamics are also studied.
We investigate the quantum diffusion of a periodically kicked particle subjected to both nonlinearity-induced self-interactions and 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 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 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.