Ichiro Ohba

Modified Fowler-Nordheim field emission formulae from a nonplanar emitter model

Field emission formulae, current–voltage characteristics and energy distribution of emitted electrons, are derived analytically for a nonplanar (hyperboloidal) metallic emitter model. The traditional Fowler–Nordheim (F–N) formulae, which are derived from a planar emitter model, are modified, and the assumption of the planar emitter in the F–N model is reconsidered. Our analytical calculation also reveals the backgrounds of the previous numerical discussion by He et al. on the effect of the geometry of emitter on field emission. The new formulae contain a parameter which characterizes the sharpness of the hyperboloidal emitter, and experimental data of field emissions from clean tungsten emitters and nanotip emitters are analyzed by making use of this feature.

Sthochastic Quantization of Constrained Systems General Theory and Nonlinear Sigma Model

On etend la methode de quantification stochastique a un systeme dynamique decrit par un lagrangien regulier sous contraintes holonomes additionnelles

Tunneling time based on the quantum diffusion process approach

Abstract We present a time-dependent description of tunneling phenomena, using Nelsons stochastic approach. It appears to be capable to describe individual experimental runs, and provides a new insight into quantum measurement processes. We propose a new way to evaluate the tunneling time in this approach and give the results of numerical simulations.

On the assumption of initial factorization in the master equation for weakly coupled systems I: General framework

We analyze the dynamics of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. In the weak-coupling (van Hove) limit, the dynamics can be properly described in terms of a master equation, but a consistent application of Nakajima–Zwanzig’s projection method requires that the reference (not necessarily equilibrium) state of the reservoir be endowed with the mixing property.

Stochastic Quantization of Constrained Systems

The stochastic quantization method is extended to dynamical systems with constraints. We discuss the stochastic quantization of a system with holonomic constraints and a constraint Hamiltonian system

A derivation of the Dirac equation in an external field based on the Poisson process

Abstract The Dirac equation has been derived from the master equation of Poisson process by analytic continuation. We extend it to the case where a particle moves in an external field. Furthermore, we show that the generalized master equation is intimately connected with three-dimensional Dirac equation in an external field.

Stochastic quantization of bottomless systems based on a kerneled Langevin equation

Abstract We propose a new method for quantizing systems with bottomless action functionals. Our method is based on the kerneled Langevin equation of the stochastic quantization method. We prove that our kerneled Langevin equation describes a stochastic process with a thermal equilibrium state. The proof makes the relation between our method and the conventional path-integral quantization clear. We check numerically in a simple model that dynamical evolution leads to the desired equilibrium state. We also calculate convergent nonperturbative expectation values that are consistent with the perturbative results in the case of a small coupling constant. We also confirm that our method gives the same perturbative results as the conventional path-integral quantization method. Finally, to augment understanding, we discuss a ( d + 1)-dimensional path-integral representation of our method.

On the assumption of initial factorization in the master equation for weakly coupled systems II: Solvable models

We analyze some solvable models of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. We apply Nakajima–Zwanzig’s projection method by choosing a reference state of the reservoir endowed with the mixing property. In van Hove’s limit, the dynamics is described in terms of a master equation. We observe that Markovianity becomes a valid approximation for timescales that depend both on the form factors of the interaction and on the observables of the reservoir that can be measured.

Crossover from classical to quantum behavior of the Duffing oscillator through a pseudo-Lyapunov-exponent.

We discuss the quantum-classical correspondence (QCC) in a specific dissipative chaotic system, the Duffing oscillator. The quantum version of the Duffing oscillator is treated as an open quantum system and analyzed numerically by the use of quantum state diffusion (QSD). We consider a pseudo-Lyapunov exponent and investigate it in detail, varying the Planck constant effectively. We show that there exists a critical stage in which the crossover from classical to quantum behavior occurs. Furthermore, we find that a dissipation effect suppresses the occurrence of chaos in the quantum region, while it, combined with the periodic external force, plays a crucial role in the chaotic behavior of the classical system.

Stochastic derivation of the chiral anomaly based on the generalized langevin equation

Abstract A generalized Langevin equation for fermion field is first derived within the framework of the stochastic quantization. Based on it, the chiral anomaly is derived directly from the stationary property of the pseudoscalar density. This approach is convenient to observe the quantum origin of anomalies. The conservation law of the vector current is also derived in a similar way.