In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and it...In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.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
We announce a result on quantum McKay correspondence for disc invariants of outer legs in toric Calabi-Yau 3-orbifolds, and illustrate our method in a special example [C^3/Z5（1, 1, 3）].
We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained ...We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10874174 the Specialized Reserach Fund for The Doctoral Progress of Higher Education of China under Grant No.20070358009
文摘In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.
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.
基金partially supported by China Scholarship Councilpartially supported by NSFC(Grant No.11171174)
文摘We announce a result on quantum McKay correspondence for disc invariants of outer legs in toric Calabi-Yau 3-orbifolds, and illustrate our method in a special example [C^3/Z5（1, 1, 3）].
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056
文摘We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too.
