Semiclassical Density Matrix Near the Top of a Barrier

Effective quantum tunneling from semiclassical momentous approach

We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution of the system is given in terms of a dynamical system for which we are able to determine effective trajectories for individual particles, in a total resemblance of the Bohmian description of quantum mechanics. We obtain a type of semiclassical confinement for particles in a similar way as with the quantum potential, and also determine a semiclassical transmis…

Semiclassical analysis of the quantum instanton approximation

We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths and find that two such paths dominate the expression. For symmetric barriers, these two paths join together to describe the semiclassical instanton periodic orbit. However, for asymmetric barriers, one of the two paths takes an unphysically low energy and dominates the expression, leading to order-of-magnitude errors in the rate predictions. Nevertheless, s…

Dynamical tunneling of bound systems through a potential barrier: complex way to the top

A semiclassical method of complex trajectories for the calculation of the tunneling exponent in systems with many degrees of freedom is further developed. It is supplemented with an easily implementable technique, which enables one to single out the physically relevant trajectory from the whole set of complex classical trajectories. The method is applied to semiclassical transitions of a bound system through a potential barrier. We find that the properties of physically relevant complex trajectories are qualitatively different in the cases of potential tunneling at low energy and dynamical tun…

Reconciling Semiclassical and Bohmian Mechanics: II. Scattering states for discontinuous potentials

In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, …

Quantum-wave evolution in a step potential barrier

By using an exact solution to the time-dependent Schrödinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source with energy below the barrier height, and for distances larger than the penetration length, the probability density exhibits a {\it forerunner} associated with a non-tunneling process, which propagates in space at exactly the semiclassical group velocity. We show that the time of arrival of the maximum of the {\it forerunner} at a given fixed position inside the po…

输运的半经典理论

Semiclassical theory of transport

研究量子混沌系统中输运问题的半经典近似，通过传输矩阵和时间延迟矩阵的矩来评估性能，并通过轨迹求和得到图示公式，适用于微扰计算。

Extended WKB method, resonances and supersymmetric radial barriers

Semiclassical approximations are implemented in the calculation of position and width of low energy resonances for radial barriers. The numerical integrations are delimited by t/T<<8, with t the period of a classical particle in the barrier trap and T the resonance lifetime. These energies are used in the construction of `haired' short range potentials as the supersymmetric partners of a given radial barrier. The new potentials could be useful in the study of the transient phenomena which give rise to the Moshinsky's diffraction in time.

Feynman Integral in Quantum Walk, Barrier-top Scattering and Hadamard Walk

The aim of this article is to relate the discrete quantum walk on $\mathbb{Z}$ with the continuous Schrödinger operator on $\mathbb{R}$ in the scattering problem. Each point of $\mathbb{Z}$ is associated with a barrier of the potential, and the coin operator of the quantum walk is determined by the transfer matrix between bases of WKB solutions on the classically allowed regions of both sides of the barrier. This correspondence enables us to represent each entry of the scattering matrix of the Schrödinger operator as a countable sum of probability amplitudes associated with the paths of the qu…

带隧穿势垒的Wigner-Smith矩阵的精确有限通道Schur矩

Exact Finite-Channel Schur Moments of the Wigner-Smith Matrix with a Tunnel Barrier

本文针对带隧穿势垒的混沌腔，将Wigner-Smith矩阵的Schur矩分解为理想耦合值与CUE平均势垒因子，导出精确有限通道时延矩公式及对半经典猜想的指数小修正。

Transmission through a potential barrier in quantum mechanics of multiple degrees of freedom: complex way to the top

A semiclassical method for the calculation of tunneling exponent in systems with many degrees of freedom is developed. We find that corresponding classical solution as function of energy form several branches joint by bifurcation points. A regularization technique is proposed, which enables one to choose physically relevant branches of solutions everywhere in the classically forbidden region and also in the allowed region. At relatively high energy the physical branch describes tunneling via creation of a classical state, close to the top of the barrier. The method is checked against exact sol…

Induced tunneling in QFT: soliton creation in collisions of highly energetic particles

We consider tunneling transitions between states separated by an energy barrier in a simple field theoretical model. We analyse the case of soliton creation induced by collisions of a few highly energetic particles. We present semiclassical, but otherwise first principle, study of this process at all energies of colliding particles. We find that direct tunneling to the final state occurs at energies below the critical value E_c, which is slightly higher than the barrier height. Tunneling probability grows with energy in this regime. Above the critical energy, the tunneling mechanism is differe…

利用动力学势垒测量电子波包的到达时间

Measuring the arrival time of an electron wave packet using a dynamical potential barrier

本文研究时变势垒测量热电子波包到达时间时因有限上升速度导致的误差，区分半经典与准静态区域并给出精确检测的时间尺度条件。

半经典方法中配对涨落的纳入：约瑟夫森效应的研究案例

Inclusion of pairing fluctuations in a semiclassical approach: The case of study of the Josephson effect

本研究综述了纳入平均场外配对涨落、可描述非平凡几何下非均匀局域能隙的改进半经典方法，并将其应用于匹配超冷费米气体实验条件的约瑟夫森效应研究。