Related papers: Path integral predictions for pre-asymptotic false…
We follow up the work, where in light of the Picard-Lefschetz thimble approach, we split up the real-time path integral into two parts: the initial density matrix part which can be represented via an ensemble of initial conditions, and the…
Path integral techniques are used to understand the behaviour of a particle moving in a bistable potential well and acted upon by quasi-monochromatic external noise. In the limit of small diffusion coefficient, a steepest descent evaluation…
The semiclassical formalism for numerical calculation of the rate of tunneling transitions induced by N particles with total energy E of order or higher than the height of the barrier is developed. The formalism is applied to the induced…
In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space…
We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections. For this purpose, we use the well-known fact that Euclidean saddle points in…
This work establishes a firm relationship between classical nonlinear resonances and the phenomenon of dynamical tunneling. It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes…
We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior…
Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is…
The decay rates of quasistable states in quantum field theories are usually calculated using instanton methods. Standard derivations of these methods rely in a crucial way upon deformations and analytic continuations of the physical…
A general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic analysis implies that both types of saddles…
A standard approach to analyzing tunneling processes in various physical contexts is to use instanton or imaginary time path techniques. For systems in which the tunneling takes place in a time dependent setting, the standard methods are…
Process of quantum tunneling of particles in various physical systems can be effectively controlled even by a weak and slow varying in time electromagnetic signal if to adapt specially its shape to a particular system. During an…
We analyze vacuum tunneling in quantum field theory in a general formalism by using the Wigner representation. In the standard instanton formalism, one usually approximates the initial false vacuum state by an eigenstate of the field…
Dynamical tunnelling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunnelling process is governed by nonlinear resonances that manifest within the regular…
We consider the thermally activated escape of an overdamped Brownian particle over a potential barrier in the presence of periodic driving. A time-dependent path-integral formalism is developed which allows us to derive asymptotically exact…
We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as…
We frame the issue of pedestrian dynamics modeling in terms of path-integrals, a formalism originally introduced in quantum mechanics to account for the behavior of quantum particles, later extended to quantum field theories and to…
The strong enhancement of tunneling couplings typically observed in tunneling splittings in the quantum map is investigated. We show that the transition from instanton to noninstanton tunneling, which is known to occur in tunneling…
Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit…
We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description…