Tunneling times for opaque barriers

We propose new criteria to evaluate the average time spent by particles in a tunneling barrier. First we construct asojourn time, on the basis of statistical information provided by quantum mechanics, which seems to be an appropriate measure of the time spent byall particles within the barrier. A simple, stochastic treatment is then used to deal with the particles that actually traverse the barrier, in order to study their interaction time. The results obtained show that opaque barriers have important effects on the particlesbefore they enter the potential region, confirming previously published numerical findings. No arbitrarily high effective velocities appear anywhere in the present treatment.     

Zwitters: Particles between quantum and classical

We describe both quantum particles and classical particles in terms of a classical statistical ensemble, with a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same quantum formalism. Quantum particles are characterized by a specific choice of observables and time evolution of the probability density. Then interference and tunneling are found within classical statistics. Zwitters are (effective) one-particle states for which the time evolution interpolates between quantum and classical particles. Experimental bounds on a small parameter can test quantum mechanics.     

Tunneling time in space fractional quantum mechanics

We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for $b\to \infty$ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.     

Tunneling time distribution by means of Nelson’s quantum mechanics and wave-particle duality

We construct a tunneling time distribution by means of Nelson’s quantum mechanics and investigate statistical properties of the tunneling time distribution. As a result, we find that the relationship between the average and the variance of the tunneling time shows ‘wave-particle duality’.     

Tunneling time based on the quantum diffusion process approach in multichannel and optical potential cases

We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson’s quantum mechanics. This generalization enables us to describe quantum system with channel couplings and optical potential in a real time stochastic approach, which seems to give us a new insight into quantum mechanics beyond Copenhagen interpretation     

Relativistic version of the imaginary-time formalism

A relativistic version of the quasiclassical imaginary-time formalism is developed. It permits calculation of the tunneling probability of relativistic particles through potential barriers, including barriers lacking spherical symmetry. Application of the imaginary-time formalism to concrete problems calls for finding subbarrier trajectories which are solutions of the classical equations of motion, but with an imaginary time (and thus cannot be realized in classical mechanics). The ionization probability of an s level, whose binding energy can be of the order of the rest energy, under the action of electric and magnetic fields of different configuration is calculated using the imaginary-time formalism. Besides the exponential factor, the Coulomb and pre-exponential factors in the ionization probability are calculated. The Hamiltonian approach to the tunneling of relativistic particles is described briefly. Scrutiny of the ionization of heavy atoms by an electric field provides an additional argument against the existence of the “Unruh effect.” Zh. éksp. Teor. Fiz. 114, 798–820 (September 1998)     

Reply to “quantum tunneling times: A crucial test for the causal program?”

Because Bohm’s Interpretation models particles with continuous trajectories, a natural property to attribute to a Bohmian particle is atunneling time, the time it takes for a particle to pass through a barrier. We also attribute a property-a different property-named ‘tunneling time’ to Copenhagen systems, systems that do not have particles with continuous trajectories. Cushing presents a discussion of the possibility of measuring Bohmian particle tunneling time; however, as becomes clear when considering the differences between properties named ‘tunneling time,’ he incorrectly argues that if such a measurement were possible, the measurement might constitute an empirical test between the Copenhagen interpretation and Bohm’s interpretation.     

Particle Dynamics of a Phase Space Distribution Function

No Heading A hydrodynamic analogy for quantum mechanics is used to develop a phase-space representation in terms of a quasi-probability distribution function. Averages over phase space using this approach agree with the usual expectation values of quantum mechanics for a certain class of observables. We also derive the equations of motion that particles in an ensemble would have in phase space in order to mimic the time development of this probability distribution, thus giving the position and momentum of particles in the ensemble as a function of time. The equations of motion separate into position and momentum components. The position component reproduces the de Broglie-Bohm equation of motion. As a simple example, we calculate the phase space trajectories and entropy of a free particle wave packet.     

Tunneling paths in multi-dimensional semiclassical dynamics

In light of the fundamental importance and renewed interest of the tunnel phenomena, we review the recent development of semiclassical tunneling theory, particularly from the view point of “tunneling path”, beginning from a simple one-dimensional formula to semiclassical theories making use of the analytic continuation, in time, coordinates, or momentum, which are the stationary solutions of semiclassical approximations to the Feynman path integrals. We also pay special attention to the instanton path and introduce various conventional and/or intuitive ideas to generate tunneling paths, to which one-dimensional tunneling theory is applied. Then, we review the recent progress in generalized classical mechanics based on the Hamilton–Jacobi equation, in which both the ordinary Newtonian solutions and the instanton paths are regarded as just special cases. Those new complex-valued solutions are generated along real-valued paths in configuration space. Such non-Newtonian mechanics is introduced in terms of a quantity called “parity of motion”. As many-body effects in tunneling, illustrative numerical examples are presented mainly in the context of the Hamilton chaos and chemical reaction dynamics, showing how the multidimensional tunneling is affected by the system parameters such as mass combination and anisotropy of potential functions.     

On Virtual Phonons,Photons, and Electrons

A macroscopic realization of the peculiar virtual particles is presented. The classical Helmholtz and the Schrödinger equations are differential equations of the same mathematical structure. The solutions with an imaginary wave number are called evanescent modes in the case of elastic and electromagnetic fields. In the case of non-relativistic quantum mechanical fields they are called tunneling solutions. The imaginary wave numbers point to strange consequences: The waves are non-local, they are not observable, and they are described as virtual particles. During the last two decades QED calculations of the solutions with an imaginary wave number have been experimentally confirmed for phonons, photons, and electrons. The experimental proofs of the predictions of non-relativistic quantum mechanics and the Wigner phase time approach for the elastic, electromagnetic and Schrödinger fields will be presented in this article. The results are zero time in the barrier and an interaction time (i.e. a phase shift) at the barrier interfaces. The measured tunneling time scales approximately inversely with the particle energy. Actually, the tunneling time is given only by the barrier boundary interaction time, as zero time is spent inside a barrier.     

黑洞量子隧穿过程的时间

讨论了弯曲时空中黑洞量子隧穿的时间.在假定了黑洞量子隧穿是一个瞬时过程的情况下,通过利用WKB法得出了有静止质量粒子的量子隧穿辐射谱.该辐射谱表明对于在黑洞视界处有静止质量粒子的出射也满足量子力学中的幺正性原理,支持Parikh-Wilczek的结论.结果的合理性表明,在黑洞视界处的量子隧穿过程可以看成是一个瞬时过程.     

Influence of dissipation on one- and two-dimensional quantum tunneling

The influence of low-frequency oscillations of the medium on the particle tunneling probability is investigated in a system with a selected tunneling coordinate, when the two-well tunnel potential takes the form of two parabolas of the same frequency. With parallel or antiparallel tunneling of two interacting particles, taking the interaction with the medium into account has no qualitative effect on the process. Quantitatively, however, the medium always influences the parallel motion of the tunneling particles and does not influence the action along the basic trajectory (R₁=−R₂) with antiparallel motion of the tunneling particles. Penzensk State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 103–107, July, 1998.     

冷原子穿越激光束的量子隧穿时间

原子通过激光冷却技术能够被制备在低温状态，这时冷原子云会展现出量子力学的波动性.研究了一束冷原子入射到一个蓝失谐的激光束上所表现出的量子力学隧穿效应.蓝失谐的激光束相对于冷原子而言等效于一个量子力学势垒.根据二能级模型，在理论上分析了具有内部结构的原子矢量物质波穿过激光束的量子力学反射与透射，特别是对原子穿越激光束所需的时间——量子隧穿时间进行了详细的研究.量子力学波动性使得冷原子穿越一个激光束时明显地展现出与经典粒子(热原子)不同的结果. 关键词： 冷原子 原子光学 量子隧穿     

Quantum control and entanglement using periodic driving fields

We propose a scheme for producing directed motion in a lattice system by applying a periodic driving potential. By controlling the dynamics by means of the effect known as coherent destruction of tunneling, we demonstrate a novel ratchetlike effect that enables particles to be coherently manipulated and steered without requiring local control. Entanglement between particles can also be controllably generated, which points to the attractive possibility of using this technique for quantum information processing.     

Features and states of microscopic particles in nonlinear quantum-mechanics systems

In this paper, we present the elementary principles of nonlinear quantum mechanics (NLQM), which is based on some problems in quantum mechanics. We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles. Concretely speaking, we study in this paper the wave-particle duality of the solution of the nonlinear Schr?dinger equation, the stability of microscopic particles described by NLQM, invariances and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles, and so on. We obtained the invariance and conservation laws of mass, energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions. We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics (LQM). They have a lot of new properties; for example, the particles possess the real wave-corpuscle duality, obey the classical rule of motion and conservation laws of energy, momentum and mass, satisfy minimum uncertainty relation, can be localized due to the nonlinear interaction, and its position and momentum can also be determined, etc. From these studies, we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM. Therefore, the NLQM is a new physical theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems, which can solve problems disputed for about a century by scientists in the LQM field. Hence, the NLQM built is very necessary and correct. The NLQM established can promote the development of physics and can enhance and raise the knowledge and recognition levels to the essences of microscopic matter. We can predict that nonlinear quantum mechanics has extensive applications in physics, chemistry, biology and polymers, etc.      

Features and states of microscopic particles in nonlinear quantum-mechanics systems

In this paper, we present the elementary principles of nonlinear quantum mechanics (NLQM), which is based on some problems in quantum mechanics. We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles. Concretely speaking, we study in this paper the wave-particle duality of the solution of the nonlinear Schrödinger equation, the stability of microscopic particles described by NLQM, invariances and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles, and so on. We obtained the invariance and conservation laws of mass, energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions. We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics (LQM). They have a lot of new properties; for example, the particles possess the real wave-corpuscle duality, obey the classical rule of motion and conservation laws of energy,momentum and mass, satisfy minimum uncertainty relation, can be localized due to the nonlinear interaction, and its position and momentum can also be determined, etc. From these studies, we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM. Therefore, the NLQM is a new physical theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems, which can solve problems disputed for about a century by scientists in the LQM field. Hence, the NLQM built is very necessary and correct. The NLQM established can promote the development of physics and can enhance and raise the knowledge and recognition levels to the essences of microscopic matter. We can predict that nonlinear quantum mechanics has extensive applications in physics, chemistry, biology and polymers, etc.     

Quantum mechanics as relativistic statistics. I: The two-particle case

It is shown that non-relativistic quantum mechanics can be treated as a kind of relativistic statistical theory, which describes the indeterministic motion of classical particles. The theory is relativistic in the sense that the relativistic notion of the state and two-time equations of motion are used. The principles and relations of quantum mechanics are obtained from the principles of statistics and those of classical mechanics.     

The research on the quantum tunneling characteristics and the radiation spectrum of the stationary axisymmetric black hole

At the event horizon and the cosmological horizon of the stationary axisymmetric Kerr-Newman black hole in the de Sitter space-time background, the tunneling rate of the charged particles is relevant with Bekenstein-Hawking entropy and the real radiation spectrum is not strictly pure thermal, but consistent with the underlying unitary theory in quantum mechanics. This is a feasible interpretation for the paradox of the black hole information loss. Taking the self-gravitation action, energy conservation, angular momentum conservation and charge conservation into account, the derived radiation spectrum is a correct amendment to the Hawking pure thermal spectrum.