Motion Of Quantum Particles Research Articles

Quantumlike Dynamics of Classical Particles in Ponderomotive Potentials

The average dynamics of a classical particle under the action of a high-frequency radiation resembles quantum particle motion in a conservative field with an effective de Broglie wavelength lambda equal to the particle average displacement on the oscillation period. In a quasiclassical field, with a spatial scale large compared to lambda, the guiding-center motion is adiabatic. Otherwise, a particle exhibits quantized eigenstates in ponderomotive potential wells, tunnels through "classically forbidden" regions, and experiences stochastic reflection from attractive potentials.

On quantum particles

A new theory of quantum particles is explained, in which the equation of motion is a pair of evolution equations in duality. The existence of the equation of dynamics is shown. The equation of dynamics determines Markov processes, which enable us to analyze the motion of quantum particles.

Quantum mechanics with coordinate-dependent mass

We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed between two semiconductors. We predict a new type of electron states, localized at the interface. They appear whenever the two bulk dispersions intersect. These shallow states lie near the point of intersection and are restricted to a finite range of perpendicular momentum. The scattering of carriers by the interface is discussed.

Quantum motion of particles along one-dimensional pathways with static and dynamic energy disorder

We have theoretically studied the competitive effects of static and dynamic energy disorder on the quantum-mechanical propagation of charge carriers and excitations along one-dimensional pathways consisting of coupled classical oscillators. Both the probability to survive in the initially occupied state and the propagation along the chain were investigated. By using the simple tight-binding band approximation, we have demonstrated that the propagation proceeds in two stages. At short times the particles move ballistically, while at larger times their propagation becomes close to diffusive with increasing dispersion for a higher degree of static disorder. The existence of two stages is due to distinct effects of static and dynamic disorder on the particle motion. While the static disorder always creates a `friction' for the particle propagation, the dynamic disorder can either facilitate or suppress the inter-site transfer depending on the degree of static disorder. It has been shown that the competition of these effects gives rise to a behaviour of the particle diffusivity typical for the metal–insulator transition.

Quantum fluctuation and phase transition in a harmonic two-electron atomic model with variable dimensionality.

Witten's generalization to arbitrary dimension has afforded new insight into the correlated motion of quantum particles [Phys. Today 33, (7), 38 (1980)]. We have used a classically based method to understand the resultant dimensionality dependence of the ground-state energy of the helium atom in the approximation which regards the quantum fluctuations of the system as being harmonic oscillations about a classical, correlated state of minimum effective potential energy. Making an analogy with thermal systems, this provides a phase diagram'' of a single helium atom that features a first-order melting transition, with inverse dimensionality playing the role of temperature. Our approximation gives an understanding of the high-dimensionality behavior of the quantum solution found with a perturbation theory expansion in inverse dimensionality by Goodson and Herschbach [Phys. Rev. Lett. 58, 1628 (1987)]. From comparison with variational quantum ground-state solutions by Loeser and Herschbach [J. Chem. Phys. 84, 3882 (1986)] for atomic numbers 2, 3, and 6 we find that the harmonic description improves with decreasing nuclear charge.

Electron transport in disordered systems: A nonequilibrium quantum-molecular-dynamics approach.

For mixed systems of quantum and classical particles, a simulation approach is developed to calculate the transport coefficients of quantum particles. Simulating the real-time evolution by quantum molecular dynamics, the response is obtained by applying a subtraction technique to the motion of quantum particles at zero and finite fields. This approach is efficient and yields a good signal-to-noise ratio. Using an excess-electron-in-helium gas as a test system, the mobility of the electron is calculated at a finite temperature and the results are found to be in good agreement with experiments.

Quantum motion of particles in random dynamic fields and quantum dissipation: Schrodinger equation with Gaussian fluctuating potentials

The Schrodinger equation with Gaussian dynamic fluctuating potentials is considered. This model gives a convenient example of an open quantum system coupled to a given external environment. The evolution equations for averaged correlators are derived and it is shown that a system coupled to a thermoequilibrium environment tends asymptotically with time to a thermodynamic density matrix. At high temperatures the quantum evolution equation for the density matrix can be approximated by the quasiclassical Fokker-Planck equation. The generalisation for multiparticle systems is also given. The results are illustrated by the particular examples of coupling with phonons and of two-level systems. Finally, it is shown how the problem can be reformulated in terms of continuous stochastic evolution in the space of psi functions and a corresponding functional formalism based on the continuous Fokker-Planck equation in the space of psi functions.