Related papers: Complexified quantum and classical mechanics
Among the many perplexing results of quantum mechanics is one that contradicts a result from introductory physics: the possibility of finding a quantum particle in a region that would be forbidden classically by energy conservation. An…
The anti self-adjoint operators of imaginary coordinate and momentum, together with the self-adjoint operators of real coordinate, momentum, energy and time are used in construction of the quantum field theory in operator form. This…
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…
It was proposed recently that the Schr\"odinger wave function can be reconstructed exactly from a discrete superposition of classical action branches weighted by associated classical densities, without semiclassical approximations. We…
Classical mechanics is a singular theory in that real-energy classical particles can never enter classically forbidden regions. However, if one regulates classical mechanics by allowing the energy E of a particle to be complex, the particle…
A classical representation of an extended body over barriers of height greater than the energy of the incident body is shown to have many features in common with quantum tunneling as the center-of-mass literally goes through the barrier. It…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We study quantum mechanical tunneling using complex solutions of the classical field equations. Simple visualization techniques allow us to unify and generalize previous treatments, and straightforwardly show the connection to the standard…
Quantum tunneling is considered from the point of view of local realism. It is concluded that a quantum object tunneling through a potential barrier cannot be interpreted as a point-like particle because such an interpretation generates a…
We revisit the path integral description of quantum tunneling and lay the groundwork for its generalization to excites states through real-time path integral techniques. For clarity, we focus on the simple toy model of a point particle in a…
The problem of inter-band tunneling in a semiconductor (Zener breakdown) in a nonstationary and homogeneous electric field is solved exactly. Using the exact analytical solution, the approximation based on classical trajectories is studied.…
We use an one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of the…
We consider a minisuperspace model for a closed universe with small and positive cosmological constant, filled with a massive scalar field conformally coupled to gravity. In the quantum version of this model, the universe may undergo a…
The boundary between the classical and quantum worlds has been intensely studied. It remains fascinating to explore how far the quantum concept can reach with use of specially fabricated elements. Here we employ a tunable flux qubit with…
By using techniques developed in quantum cosmology, it is found that a tunneling particle spends purely imaginary time on a barrier region. The {\it imaginary} time is associated with the stochastic acausal behaviour of a state, while the…
We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution…
Quantum memory effects are essential in understanding and controlling open quantum systems, yet distinguishing them from classical memory remains challenging. We introduce a convex geometric framework to analyze quantum memory propagating…
By allowing the light cones to tip over on hypersurfaces according to the conservation laws of an one-kink in static, Schwarzschild and five-dimensional black hole metrics, we show that in the quantum regime there also exist instantons…
Real numbers provide a sufficient description of classical physics and all measurable phenomena; however, complex numbers are occasionally utilized as a convenient mathematical tool to aid our calculations. On the other hand, the formalism…
Quantum tunneling, a phenomenon which has no counterpart in classical physics, is the quantum-mechanical process by which a microscopic particle can transition through a potential barrier even when the energy of the incident particle is…