Decoherence on Quantum Tunneling in the Multi-Dimensional Wave Function Approach

Path-integral approach in imaginary and complex time has been proven successful in treating the tunneling phenomena in quantum mechanics and quantum field theories. Latest developments in this field, the proper valley method in imaginary time, its application to various quantum systems, complex time formalism, asympton theory for the large order analysis of the perturbation theory, are reviewed in a self-contained manner.

A simple model is considered to study the effects of finite size and internal structure in the tunneling of bound two-body systems through a potential barrier. It is demonstrated that these effects are able to increase the tunneling probability. Applications may include nuclear fusion,hydrogen atom and Cooper pair tunneling.

The tunneling probability for a system modelling macroscopic quantum tunneling is computed. We consider an open quantum system with one degree of freedom consisting of a particle trapped in a cubic potential interacting with an environment characterized by a dissipative and a diffusion parameter. A representation based on the energy eigenfunctions of the isolated system, i. e. the system uncoupled to the environment, is used to write the dynamical master equation for the redu...

Quantum tunneling is a fundamental quantum mechanical effect involved in plenty of physical phenomena. Its control would impact these phenomena and the technologies based on them. We show that the quantum tunneling probability through a potential barrier can be increased to approach unity in a quantum Zeno dynamics undergone by the tunneling particle in which the direction of the momentum is frequently monitored. We first model the measurements of the momentum direction as se...

Over the preceeding twenty years, the role of underlying classical dynamics in quantum mechanical tunneling has received considerable attention. A number of new tunneling phenomena have been uncovered that have been directly linked to the set of dynamical possibilities arising in simple systems that contain at least some chaotic motion. These tunneling phenomena can be identified by their novel $\hbar$-dependencies and/or statistical behaviors. We summarize a sampling of thes...

We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a semiclassical technique developed in the context of instanton-like transitions in quantum field theory. This latter technique is based on an analytic continuation of the degrees of freedom into a complex phase space, and the simultaneous analyt...

Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new experimental techniques revived the issue and ignited a debate with often contradictory results. This motivates the present study of an exactly solvable model for quantum tunneling induced by a strong field. We show that the tunneling dynamics can d...

We examine a fast decay process that arises in the transition period between the Gaussian and exponential decay processes in quantum decay systems. It is usually expected that the decay is decelerated by a confinement potential barrier. However, we find a case where the decay in the transition period is accelerated by tunneling through a confinement potential barrier. We show that the acceleration gives rise to an appreciable effect on the time evolution of the nonescape prob...

Traditionally quantum tunneling in a static SQUID is studied on the basis of a classical trajectory in imaginary time under a two-dimensional potential barrier. The trajectory connects a potential well and an outer region crossing their borders in perpendicular directions. In contrast to that main-path mechanism, a wide set of trajectories with components tangent to the border of the well can constitute an alternative mechanism of multi-path tunneling. The phenomenon is essen...

We develop a new numerical scheme which allows precise solution of coherent tunneling problems, i.e., problems with exponentially small transition amplitudes between quasidegenerate states. We explain how this method works for the single-particle (tunneling in the double-well potential) and many-body systems (e.g., vacuum-to-vacuum transitions), and gives directly the instanton shape and tunneling amplitude. Most importantly, transition amplitudes may be calculated to arbitra...