Related papers: Complex Trajectories in a Classical Periodic Poten…
This paper reports a numerical study of complex classical trajectories of a particle in an elliptic potential. This study of doubly-periodic potentials is a natural sequel to earlier work on complex classical trajectories in trigonometric…
The energy of a quantum particle cannot be determined exactly unless there is an infinite amount of time in which to perform the measurement. This paper considers the possibility that $\Delta E$, the uncertainty in the energy, may be…
This paper revisits earlier work on complex classical mechanics in which it was argued that when the energy of a classical particle in an analytic potential is real, the particle trajectories are closed and periodic, but that when the…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
We consider a Parity-time (PT) invariant non-Hermitian quasi-exactly solvable (QES) potential which exhibits PT phase transition. We numerically study this potential in a complex plane classically to demonstrate different quantum effects.…
Periodic classical trajectories are of fundamental importance both in classical and quantum physics. Here we develop path integral techniques to investigate such trajectories in an arbitrary, not necessarily energy conserving hamiltonian…
Anderson $\textit{et al}$ have shown that for complex energies, the classical trajectories of $\textit{real}$ quartic potentials are closed and periodic only on a discrete set of eigencurves. Moreover, recently it was revealed that, when…
Consider any stationary Schroedinger wave equation (SWE) solution $psi (x)$ for a particle. The corresponding PDF on position QTR{em}{x} of the particle is QTR{em}{p}$_{X}(x)=|psi (x)|^{2}$. There is a classical trajectory QTR{em}{x(t)} for…
It has been found that complex non-Hermitian quantum-mechanical Hamiltonians may have entirely real spectra and generate unitary time evolution if they possess an unbroken $\cP\cT$ symmetry. A well-studied class of such Hamiltonians is $H=…
Complex trajectories for Hamiltonians of the form H=p^n+V(x) are studied. For n=2 time-reversal symmetry prevents trajectories from crossing. However, for n>2 trajectories may indeed cross, and as a result, the complex trajectories for such…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
In this numerical study, recurrence quantification analysis of chaotic trajectories is explored to detect atypical dynamical behaviour in non-linear Hamiltonian systems. An ensemble of initial conditions is evolved up to a maximum iteration…
Both the physical picture of the dynamics of atoms and molecules in intense infrared fields and its theoretical description use the concept of electron trajectories. Here we address a key question which arises in this context: Are…
This paper deals with the classical trajectories for two super-integrable systems: a system known in quantum chemistry as the Hartmann system and a system of potential use in quantum chemistry and nuclear physics. Both systems correspond to…
"Particle"-trajectories are defined as integrable $dx_\mu dp^\mu = 0$ paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalise in $(x, p)$ projection, the phase associated with the…
To comply with recent developments of path integrals in spaces with curvature and torsion we find the correct variational principle for the classical trajectories. Although the action depends only on the length, the trajectories are {\em…
In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic…
Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All…
We study the dynamics of a one-dimensional classical particle in a space and time dependent potential with randomly chosen parameters. The focus of this work is a quasi-periodic potential, which only includes a finite number of Fourier…