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Superexponential diffusion in nonlinear non-Hermitian systems

Physical Review A 2020年第6期102卷 062213-062213页

作者： Wen-Lei Zhao Longwen Zhou Jie Liu Peiqing Tong Kaiqian Huang School of Science Jiangxi University of Science and Technology Ganzhou 341000 China Department of Physics College of Information Science and Engineering Ocean University of China Qingdao 266100 China Graduate School of China Academy of Engineering Physics Beijing 100193 China CAPT HEDPS and IFSA Collaborative Innovation Center of the Ministry of Education Peking University Beijing 100871 China Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing 210023 China Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing Jiangsu 210023 China Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials SPTE South China Normal University Guangzhou 510006 China

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 〈p2(t)〉∝exp[βexp(αt)], 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.

关键词： Anderson localization Atomic, optical & lattice clocks Diffusion Nonlinear optics Quantum transport Spatiotemporal chaos Wave chaos

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Reanalysis of the most strange dibaryon within constituent quark models

arXiv

引用

arXiv 2019年

作者： Huang, Hongxia Zhu, Xinmei Ping, Jialun Department of Physics Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China Department of Physics Yangzhou University Yangzhou225009 China

The most strange dibaryon ΩΩ with quantum numbers S = −6, I = 0, and JP = 0+, 1−, 2+, 3− is reanalyzed in the framework of quark delocalization color screening model (QDCSM) and chiral quark model (ChQM). The ΩΩ dibaryon with JP = 0+ is bound, and the one with other quantum numbers JP = 1−, 2+, 3− are all unbound in our calculation. The low-energy scattering phase shifts, the scattering length, and the effective range of the ΩΩ dibaryon with JP = 0+ also support the existence of such strange dibaryon. This dibaryon is showed to be a shallow bound state in QDCSM, while the binding energy becomes much larger in the ChQM by including the effect of the hidden-color channel coupling. And the scalar nonet meson-exchange in the ChQM also provides more attraction for the ΩΩ system. Experimental search for such most strange dibaryon will provide much information for understanding the hadron-hadron interactions in different quark models. Copyright © 2019, The Authors. All rights reserved.

关键词： Quantum theory

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Influences of weak disorder on dynamical quantum phase transitions of anisotropic XY chain

arXiv

引用

arXiv 2019年

作者： Cao, Kaiyuan Li, Wenwen Zhong, Ming Tong, Peiqing Department of Physics Institute of Theoretical Physics Nanjing Normal University Nanjing210023 China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China

In this paper, the effects of disorder on the dynamical quantum phase transitions (DQPTs) in the transverse-field anisotropic XY chain are studied by numerically calculating the Loschmidt echo after quench. We obtain the formula for calculating the Loschmidt echo of the inhomogeneous system in real space. By comparing the results with that of the homogeneous chain, we find that when the quench crosses the Ising transition, the small disorder will cause a new critical point. As the disorder increases, more critical points of the DQPTs will occur, constituting a critical region. In the quench across the anisotropic transition, the disorder will cause a critical region near the critical point, and the width of the critical region increases by the disordered strength. In the case of quench passing through two critical lines, the small disorder leads to the system to have three additional critical points. When the quench is in the ferromagnetic phase, the large disorder causes the two critical points of the homogeneous case to become a critical region. And for the quench in the paramagnetic phase, the DQPTs will disappear for large disorder. Copyright © 2019, The Authors. All rights reserved.

关键词： Phase transitions

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Mass- and energy-preserving exponential Runge-Kutta methods for the nonlinear Schrödinger equation

arXiv

引用

arXiv 2020年

作者： Cui, Jin Xu, Zhuangzhi Wang, Yushun Jiang, Chaolong Department of Basic Sciences Nanjing Vocational College of Information Technology Nanjing210023 China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems School of Mathematical Sciences Nanjing Normal University Nanjing210023 China Department of Mathematics College of Liberal Arts and Science National University of Defense Technology Changsha410073 China School of Statistics and Mathematics Yunnan University of Finance and Economics Kunming650221 China

In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods is developed for the nonlinear Schrödinger equation by combing the scalar auxiliary variable approach and the exponential Runge-Kutta method. By introducing an auxiliary variable, we first transform the original model into an equivalent system which admits both mass and modified energy. Then applying the Lawson method and the symplectic Runge-Kutta method in time, we derive a class of mass- and energy-conserving time-discrete schemes. numerical experiments are addressed to demonstrate the accuracy and effectiveness of the newly proposed schemes. Copyright © 2020, The Authors. All rights reserved.

关键词： Runge Kutta methods

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Dynamical energy equipartition of the Toda model with additional on-site potentials

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Chinese Physics B 2017年第10期26卷 107-111页

作者：张振俊唐春梅康静童培庆 College of Science Hohai University School of Physics and Technology Nanjing Normal University Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University

We study the dynamical energy equipartition properties in the integrable Toda model with additional uniform or disordered on-site energies by extensive numerical simulations. The total energy is initially equidistributed among some of the lowest frequency linear modes. For the Toda model with uniform on-site potentials, the energy spectrum keeps its profile nearly unchanged in a relatively short time scale. On a much longer time scale, the energies of tail modes increase slowly with time. Energy equipartition is far away from being attached in our studied time scale. For the Toda model with disordered on-site potentials, the energy transfers continuously to the high frequency modes and eventually towards energy equipartition. We further perform a systematic study of the equipartition time teq depending on the energy density ε and the nonlinear parameter α in the thermodynamic limit for the Toda model with disordered on-site potentials. We find teq∝ （1/ε）^a（1/α）^b, where b≈ 2a. The values of a and b are increased when increasing the strengths of disordered on-site potentials or decreasing the number of initially excited modes.

关键词： energy transport behaviors Toda model uniform or disordered on-site potentials

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Directed momentum current induced by the PT-symmetric driving

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Physical Review E 2019年第4期99卷 042201-042201页

作者： Wen-Lei Zhao Jiaozi Wang Xiaohui Wang Peiqing Tong School of Science Jiangxi University of Science and Technology Ganzhou 341000 China Department of Modern Physics University of Science and Technology of China Hefei 230026 China School of Information Engineering Jiangxi University of Science and Technology Ganzhou 341000 China Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing 210023 China Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing Jiangsu 210023 China

We investigate the directed momentum current in the quantum kicked rotor model with PT-symmetric deriving potential. For the quantum nonresonance case, the values of quasienergy become complex when the strength of the imaginary part of the kicking potential exceeds a threshold value, which demonstrates the appearance of the spontaneous PT symmetry breaking. In the vicinity of the transition point, the momentum current exhibits a staircase growth with time. Each platform of the momentum current corresponds to the mean momentum of some eigenstates of the Floquet operator whose imaginary parts of the quasienergy are significantly large. Above the transition point, the momentum current increases linearly with time. Interestingly, its acceleration rate exhibits a kind of “quantized” increment with the kicking strength. We propose a modified classical acceleration mode of the kicked rotor model to explain such an intriguing phenomenon. Our theoretical prediction is in good agreement with numerical results.

关键词： Coherent control Cold atoms & matter waves Light-matter interaction Wave chaos

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Chaotic diffusion of complex trajectory and its quantum signature

arXiv

引用

arXiv 2019年

作者： Zhao, Wen-Lei Wang, Jiaozi Wang, Qian Tong, Peiqing School of Science Jiangxi University of Science and Technology Ganzhou341000 China Department of Modern Physics University of Science and Technology of China Hefei230026 China Department of Physics Zhejiang Normal University Jinhua321004 China Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing210023 China Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing Jiangsu210023 China

We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with PT symmetry. In non-Hermitian case, the classical trajectory is assumed to be complex. We find the normal diffusion for the real part of momentum and the exponentially-fast diffusion for the imaginary part of momentum. Due to the exponentially-fast increase of some trajectories, there is a threshold time for the breakdown of classical diffusion. Our theoretical prediction of such a threshold 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. We find that the growth of the OTOC exhibits a sharp transition to infinitely large at a critical time which exponentially increases with the increase of the threshold time of the classical diffusion. For the quantum dynamics, both the mean momentum and mean square of momentum exhibits the staircase growth with time when the system parameter is in the neighborhood of the PT symmetry breaking. If the system parameter is very larger than the PT symmetry breaking point, the acceleration mode results in the directed spreading of the wavepackets as well as the ballistic diffusion in momentum space. Copyright © 2019, The Authors. All rights reserved.

关键词： Momentum

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Directed momentum current induced by the PT -symmetric driving

arXiv

引用

arXiv 2019年

作者： Zhao, Wen-Lei Wang, Jiaozi Wang, Xiaohui Tong, Peiqing School of Science Jiangxi University of Science and Technology Ganzhou341000 China Department of Modern Physics University of Science and Technology of China Hefei230026 China School of Information Engineering Jiangxi University of Science and Technology Ganzhou341000 China Department of Physics Institute of Theoretical Physics Nanjing Normal University Nanjing210023 China Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing Jiangsu210023 China

We investigate the directed momentum current in the quantum kicked rotor model with PT symmetric deriving potential. For the quantum non-resonance case, the values of quasi-energy become to be complex when the strength of imaginary part of the kicking potential exceeds a threshold value, which demonstrates the appearance of the spontaneous PT symmetry breaking. In the vicinity of the transition point, the momentum current exhibits a staircase growth with time. Each platform of the momentum current corresponds to the mean momentum of some eigenstates of the Floquet operator whose imaginary parts of the quasi-energy are significantly large. Above the transition point, the momentum current increases linearly with time. Interestingly, its acceleration rate exhibits a kind of "quantized" increment with the kicking strength. We propose a modified classical acceleration mode of the kicked rotor model to explain such an intriguing phenomenon. Our theoretical prediction is in good agreement with numerical results. Copyright © 2019, The Authors. All rights reserved.

关键词： Momentum

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Detection of Picric Acid by Terpy-Based Metallo- Supramolecular Fluorescent Coordination Polymers in Aqueous Media

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Chinese Journal of Chemistry 2017年第4期35卷 447-456页

作者： Zhongyu Ding Hongqing Li Wanqing Gao Yiquan Zhang Chunhua Liu Yuanyuan Zhu School of Chemistry and Chemical Engineering Hefei University of Technology and Anhui Key Laboratory of Advanced Functional Materials and Devices Hefei Anhui 230009 China Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems (NSLSCS) School of Physical Science and Technology Nanjing Normal University Nanjing Jiangsu 210023 China

The synthesis of two linear terpy-based metallo-supramolecular fluorescent coordination polymers through 1 ： 1 complexation of Zn^2＋ and Cd^2＋ ions with ditopic terpyridine ligand was reported. The dispersibility of P1 and P2 was significantly improved in organic solvent and water through the introduction of hydrophilic oligo-ethyoxy side chain. Two polymers displayed yellow light emission both in solution and the solid state due to the intra-ligand charge transfer （ILCT） between the d^10 metal ions and the conjugated spacer unit. These coordination polymers were explored as fluorescent chemosensors for detecting picric acid in aqueous media, displaying high sensitivity and good selectivity. In addition, test strips were prepared from these polymers and exhibited the practical potential of detecting the NACs pollutants in the outdoor water for public safety and security.

关键词： coordination polymer fluorescent chemosensors nitroaromatic explosives picric acid aqueous media

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An LQP-Based Two-Step Method for Structured Variational Inequalities

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Journal of the Operations Research Society of China 2017年第3期5卷 301-317页

作者： Hong-Jin He Kai Wang Xing-Ju Cai De-Ren Han Department of Mathematics School of ScienceHangzhou Dianzi UniversityHangzhou 310018China School of Mechanical and Aerospace Engineering Nanyang Technological UniversitySingapore 639798Singapore School of Mathematical Sciences Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex SystemsNanjing Normal UniversityNanjing 210023China

t The logarithmic quadratic proximal(LQP)regularization is a popular and powerful proximal regularization technique for solving monotone variational inequalities with nonnegative *** this paper,we propose an implementable two-step method for solving structured variational inequality problems by combining LQP regularization and projection *** proposed algorithm consists of two *** first step generates a pair of predictors via inexactly solving a system of nonlinear ***,the second step updates the iterate via a simple correction *** establish the global convergence of the new method under mild *** improve the numerical performance of our new method,we further present a self-adaptive version and implement it to solve a traffic equilibrium *** numerical results further demonstrate the efficiency of the proposed method.

关键词： Logarithmic quadratic proximal Projection method Variational inequality problem Traffic equilibrium problem

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