Related papers: In-in formalism on tunneling background: multi-dim…
Recent developments in the understanding of real-time path integrals led to the development of the ``steadyon picture'' for the semi-classical calculation of quantum tunneling rates. We discuss tunneling out of a generic localized initial…
Quantum cosmology uses a wave function to model the universe, but finding solutions for this poses a problem as it is difficult to define the boundary conditions or identify the correct path for a path integral. We begin the discussion by…
We discuss quantum dynamics in multi-dimensional non-linear systems. It is well-known that wave functions are localized in a kicked rotor model. However, coupling with other degrees of freedom breaks the localization. In order to clarify…
We introduce a formulation of combined systems in orthodox non-relativistic quantum mechanics, mathematically equivalent to the usual one. For context and larger issues, see http://euclid.unh.edu/~jjohnson/axiomatics.html and…
Quantum tunneling between two potential wells in a magnetic field can be strongly increased when the potential barrier varies in the direction perpendicular to the line connecting the two wells and remains constant along this line. A…
We study tunneling in one-dimensional quantum mechanics using the path integral in real time, where solutions of the classical equation of motion live in the complex plane. Analyzing solutions with small (complex) energy, relevant for…
The concepts of quantile position, trajectory, and velocity are defined. For a tunneling quantum mechanical wave packet, it is proved that its quantile position always stays behind that of a free wave packet with the same initial…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…
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…
The tunneling wave function of the universe is investigated in a minisuperspace framework of a de Sitter universe with a quantum scalar field, treated as a perturbation. We consider three different approaches to defining the tunneling wave…
The Wheeler-DeWitt equation is investigated and used to examine a state after a quantum tunneling with gravity. To make arguments definite we treat a discretized version of the Wheeler-DeWitt equation and adopt the WKB method. We expand an…
It was recently shown that tunneling wavefunction proposal is consistent with loop quantum geometry corrections including both holonomy and inverse scale factor corrections in the gravitational part of a spatially closed isotropic model…
Tunneling is an iconic concept that captures the peculiarity of quantum dynamics but, despite its ubiquity, questions remain. We focus on strong-field tunneling, which is vital to all attosecond science. We find an unexpected optical…
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…
The new method for the simulation of nonstationary quantum processes is proposed. The method is based on the tomography representation of quantum mechanics, {\it i.e.}, the state of the system is described by the {\it nonnegative} function…
We compute tunneling in a quantum field theory in 1+1 dimensions for a field potential $U(\Phi)$ of the asymmetric double well type. The system is localized initially in the ``false vacuum''. We consider the case of a {\em compact space}…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
By viewing the non-equilibrium transport setup as a quantum open system, we propose a reduced-density-matrix based quantum transport formalism. At the level of self-consistent Born approximation, it can precisely account for the correlation…
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…
We revisit the problem of quantum tunneling for a particle moving in the continuum, and in the absence of a magnetic field. In all spatial dimensions, we extend previous results to the case where the single-well potential satisfies…