Quantum Trajectory Approach to Molecular Dynamics Simulation with Surface Hopping

In this work we propose a quantum trajectory approach to the powerful molecular dynamics simulation with surface hopping,from an insight that an efectiveobservationis actually implied in the simulation through tracking the forces experienced,just like checking the meter’s result in quantum measurement process.This treatment can build the nonadiabatic surface hopping on a physical foundation,instead of the usual fictitious and conceptually inconsistent hopping algorithms.The efects and advantages of the proposed scheme are preliminarily illustrated by a two-surface model system.     

Symmetric Surface Momentum and Centripetal Force for a Particle on a Curved Surface

The Hermitian surface momentum operator for a particle confined to a 2D curved surface spanned by orthogonal coordinates and embedded in 3D space is expressed as a symmetric expression in derivatives with respect to the surface coordinates and so is manifestly along the surface. This is an alternative form to the one reported in the literature and usually named geometric momentum, which has a term proportional to the mean curvature along the direction normal to the surface, and so"apparently"not along the surface. The symmetric form of the momentum is the sum of two symmetric Hermitian operators along the two orthogonal directions defined by the surface coordinates.The centripetal force operator for a particle on the surface of a cylinder and a sphere is calculated by taking the time derivative of the momentum and is seen to be a symmetrization of the well-known classical expressions.     

Chaotic Dynamics of Test Particle in the Gravitational Field with Magnetic Dipoles

We investigate the dynamics of the test particle in the gravitational field with magnetic dipoles in thispaper. At first we study the gravitational potential by numerical simulations. We find, for appropriate parameters, thatthere are two different cases in the potential curve, one of which is the one-well case with a stable critical point, and theother is the three-well case with three stable critical points and two unstable ones. As a consequence, the chaotic motionwill rise. By performing the evolution of the orbits of the test particle in the phase space, we find that the orbits of thetest particle randomly oscillate without any periods, even sensitively depending on the initial conditions and parameters.chaotic motion of the test particle in the field with magnetic dipoles becomes even obvious as the value of the magneticdipoles increases.     

The Phase of a Quantum Mechanical Particle in Curved Spacetime

We investigate the quantum mechanical wave equations for free particles of spin 0, 1/2, 1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is S/ = p dx /, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple manageable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has exactly the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin 1 wave equations yield the above phase only to lowest order in . We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in . For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations.     

Quantum Phase Dynamics of Interaction between Photon Field and Magnetic System: Effects of Magnetic Quantum Tunnelling

We investigate the dynamics of probability distributions of an initially one-mode coherent field interacting with a four-state molecular system, which is a single magnet with a tunneling across an anisotropic barrier, using a numerically exact approach. The population for each state, the phase properties of and , and ), the entropy are calculated for a model system. The model predicts that the molecule and field become asymptotically disentangled at half of the revival time, and that optical Schrödinger-cat and magnetic Schrödinger-cat states are generated.This paper was originally presented at the 5th International Conference on NEAR FIELD OPTICS and RELATED TECHNOLOGIES (NFO-5), which was held on December 6–10, 1998 at Coganoi Bay Hotel, Shirahama, Japan, in cooperation with the Japan Society of Applied Physics and Mombusho Grant-in Aid for Scientific Research on Priority Areas “Near-field Nano-optics” Project, sponsored by Japan Society for the Promotion of Science.     

Zitterbewegung in External Magnetic Field: Classic versus Quantum Approach

We investigate variations of the Zitterbewegung frequency of electron due to an external static and uniform magnetic field employing the expectation value quantum approach, and compare our results with the classical model of spinning particles. We demonstrate that these two so far compatible approaches are not in agreement in the presence of an external uniform static magnetic field, in which the classical approach breaks the usual symmetry of free particles and antiparticles states, i.e. it leads to CP violation. Hence, regarding the Zitterbewegung frequency of electron, the classical approach in the presence of an external magnetic field is unlikely to correctly describe the spin of electron, while the quantum approach does, as expected. We also show that the results obtained via the expectation value are in close agreement with the quantum approach of the Heisenberg picture derived in the literature. However, the method we use is capable of being compared with the classical approach regarding the spin aspects. The classical interpretation of spin produced by the altered Zitterbewegung frequency, in the presence of an external magnetic field, are discussed.     

Geometric and Algebraic Approach to Classical Dynamics of a Particle with Spin

We investigate the Frenkel equation and alternative approaches aimed to describe classically the dynamics of a particle with a spin degree of freedom. For all those theories unphysical solutions are shown to exist but to be removable via formal use of geometric perturbation theory. With an Clifford algebraic representation of the employed geometric concepts we put forward the modified Frenkel equation as more intuitive as alternative approaches.     

Four-Electron Quantum Ring in a Magnetic Field

We study a quantum ring （QR） with four electrons in a perpendicular external magnetic field B by exact diagonalization. The low-lying spectra of the QR as a function orb are obtained. A phase diagram is presented indicating that the angular momentum and the spin of the ground state of the QR may jump when B and/or the radius of the QR vary, and a corresponding analysis is performed. By plotting the density functions of the QR, the ground-state configuration is found to be a regular quadrangle. Furthermore, the features of the ground-state persistent current are revealed.     

A Quantum Particle in a One-Dimensional Fractal Field

Algorithms have been obtained for calculating reflection coefficients for a particle incident on a fractal potential barrier or on a fractal potential well. It has been investigated how these coefficients vary with the energy of the particle and with the fractal dimension and other parameters of the barrier or well. The energies of the bound states of fractal potential wells have been calculated.     

Ground State of a Quantum Particle Coupled to a Scalar Bose Field

We use methods from functional integration to prove the existence and uniqueness of the ground state of a confined quantum particle coupled to a scalar massless Bose field. For an external potential growing at infinity, the ground state exists under fairly general conditions while, for a decaying potential, an unphysical condition on the coupling strength is still needed.     

New Approach to Quantum Scattering Near the Lowest Landau Threshold for a Schrödinger Operator with a Constant Magnetic Field

 For a fixed magnetic quantum number m results on spectral properties and scattering theory are given for the three-dimensional Schr?dinger operator with a constant magnetic field and an axisymmetrical electric potential V. Asymptotic expansions for the resolvent of the Hamiltonian H _m  = H _om  + V are deduced as the spectral parameter tends to the lowest Landau threshold E ₀. In particular it is shown that E ₀ can be an eigenvalue of H _m . Furthermore, asymptotic expansions of the scattering matrix associated with the pair (H _m , H _om ) are derived as the energy parameter tends to E ₀. Received December 11, 2000; accepted in final form June 16, 2001 Published online June 10, 2002     

Coulomb Interaction in Quantum Dot with a Precessing Magnetic Field

We study electronic transport through a quantum dot （QD） with a precessing magnetic field. By using the Keldysh nonequilibrium Green function method, formulas of local density of states （LDOS） and conductance of QD are derived self-consistently. It shows that the LDOS and conductance have obvious changes with the Coulomb blockade interaction. The intensity and angle of the magnetic field or temperatures, which reflect the mesoscopic structure of the QD are derived. The superiority of this device is that the QD can be controlled easily by the magnetic field, so it is valuable to apply in generating, manipulating and probing spin state.     

Particle Distribution in Quantum Field Theory

The change of the particle distribution in space-time is analysed in the framework of quantum field theory. The formalism is turned out to be thermo field dynamics. The formulation suggests a unification of quantum field theory and statistical physics.     

System Plus Reservoir Approach to Quantum Brownian Motion of a Rod-Like Particle

Quantum Brownian motion of a rod-like particle is investigated in the frame work of system plus reservoir model. The quantum mechanical and classical limit for both translational and rotational motions are discussed. Correlation functions, fluctuation-dissipation relations and mean squared values of translational and rotational motions are obtained.     

Particle Trajectories for Quantum Field Theory

The formulation of quantum mechanics developed by Bohm, which can generate well-defined trajectories for the underlying particles in the theory, can equally well be applied to relativistic quantum field theories to generate dynamics for the underlying fields. However, it does not produce trajectories for the particles associated with these fields. Bell has shown that an extension of Bohm’s approach can be used to provide dynamics for the fermionic occupation numbers in a relativistic quantum field theory. In the present paper, Bell’s formulation is adopted and elaborated on, with a full account of all technical detail required to apply his approach to a bosonic quantum field theory on a lattice. This allows an explicit computation of (stochastic) trajectories for massive and massless particles in this theory. Also particle creation and annihilation, and their impact on particle propagation, is illustrated using this model.     

Particle Correlation in Quantum Field Theory

The paper deals with studies of the angular correlation of two mono-energetic particles produced in several fundamental processes in quantum field theory. The angular correlation is defined as the average (expectation value) of the cosine of the angle between the momenta of the two outgoing particles. A positive correlation indicates, in a statistical sense, that the particles tend to travel in the same directions (as in beam formation) while a negative one indicates that they tend to travel in opposing directions. The angular correlations for photons and electrons produced by sources, and in quantum eletrodynamics, to lowest order, γγ produced in e⁺e⁻ collision (annihilation), e⁺e⁻ pair production in γγ collision, and finally e⁺e⁻ pair production by a Nambu string are studied in detail.