Related papers: Forced quantum inverted oscillator
Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schr\"odinger-Langevin or Kostin quantum classical transition wave equation is used and applied resulting in a scaled…
We use the free evolution propagator to determine the quantum probability representation (i.e., the general expression of the tomogram) of any one-dimensional system described by a density state. The evolution operator for the considered…
A fundamentally different approach to path integral quantum mechanics in curved space-time is presented, as compared to the standard approaches currently available in the literature. Within the context of scalar particle propagation in a…
We consider the time-dependent electron transport through a quantum dot connected to multiple leads in the presence of the additional over-dot (bridge) tunnelling channels by using the evolution operator technique. Each terminal and quantum…
By using an exact solution to the time-dependent Schr\"{o}dinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source…
A known limitation of time-dependent mean-field approaches is a lack of quantum tunneling for collective motions such as in sub-barrier fusion reactions. As a first step toward a solution, a time-dependent model is considered using a…
Modulating macroscopic parameters of materials in time offers innovative avenues for manipulating electromagnetic waves. Due to such enticing prospects, the general research subject of time-varying systems is expanding today in different…
For Lindblad's master equation of open quantum systems with a general quadratic form of the Hamiltonian, the propagator of the density matrix is analytically calculated by using path integral techniques. The time-dependent density matrix is…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
We discuss the time development of Gaussian wave packet solutions of the quantum bouncer' (a quantum mechanical particle subject to a uniform downward force, above an impermeable flat surface). We focus on the evaluation and visualization…
The real- and imaginary-time evolution of quantum states are powerful tools in physics, chemistry, and beyond, to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. On near-term devices, variational…
In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. For instance, in the semi-classical regime, while the position and momentum expectation values follow the classical…
We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schr\"odinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted…
We consider a quantum linear oscillator coupled to a bath in equilibrium at an arbitrary temperature and then exposed to an external field arbitrary in form and strength. We then derive the reduced density operator in closed form of the…
In classical mechanics, a nonrelativistic particle constrained on an $N-1$ curved hypersurface embedded in $N$ flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of…
We review the random matrix description of electron transport through open quantum dots, subject to time-dependent perturbations. All characteristics of the current linear in the bias can be expressed in terms of the scattering matrix,…
In the present work, we have analyzed the motion of a structured matter wave in the presence of a constant magnetic field and under the influence of a time-dependent external force. We have introduced exact propagator kernels obtained from…
Following the paper by M. Combescure [Ann. Phys. (NY) 204, 113 (1990)], we apply the quantum singular time dependent oscillator model to describe the relative one dimensional motion of two ions in a trap. We argue that the model can be…
The exact propagators of two one-dimensional systems with time-dependent external fields are presented by following the path-integral method. It is shown that the Bloch acceleration theorem can be generalized to the impulse-momentum theorem…
The method proposed by Inomata and his collaborators allows us to transform a damped Caldiroli-Kanai oscillator with time-dependent frequency to one with constant frequency and no friction by redefining the time variable, obtained by…