Related papers: Time-dependent quantum graph
In the Schr{\"o}dinger picture, the state of a quantum system evolves in time and the quantum speed limit describes how fast the state of a quantum system evolves from an initial state to a final state. However, in the Heisenberg picture…
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a…
We address continuous-time quantum walks on graphs in the presence of time- and space-dependent noise. Noise is modeled as generalized dynamical percolation, i.e. classical time-dependent fluctuations affecting the tunneling amplitudes of…
We consider a quantum particle under the dynamical confinement caused by PT-symmetric box with a moving wall. The latter is described in terms of the time-dependent Schr\"{o}dinger equation obeying the time-dependent PT-symmetric boundary…
We prove a global well-posedness result for defocusing nonlinear Schrodinger equations with time dependent potential. We then focus on time dependent harmonic potentials. This aspect is motivated by Physics (Bose--Einstein condensation),…
We perform numerical studies of the wave packet propagation through open quantum billiards whose classical counterparts exhibit regular and chaotic dynamics. We show that for t less or similar to tau (tau being the Heisenberg time), the…
The energy levels of a quantum graph with time reversal symmetry and unidirectional classical dynamics are doubly degenerate and obey the spectral statistics of the Gaussian Unitary Ensemble. These degeneracies, however, are lifted when the…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
We derive an exact analytical solution to the time-dependent Schr\"odinger equation for transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet…
We consider a hydrogen atom confined in time-dependent trap created by a spherical impenetrable box with time-dependent radius. For such model we study the behavior of atomic electron under the (non-adiabatic) dynamical confinement caused…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
The structure of time-dependent Gaussian solutions for the Kostin equation in dissipative quantum mechanics is analyzed. Expanding the generic external potential near the center of mass of the wave packet, one conclude that: the center of…
We use the Fourier operator to transform a time dependent mass quantum harmonic oscillator into a frequency dependent one. Then we use Lewis-Ermakov invariants to solve the Schr\"odinger equation by using squeeze operators. Finally we give…
In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schr\"odinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which…
We study relativistic stars in the scale-dependent scenario, which is one of the approaches to quantum gravity, and where Newton's constant is promoted to a scale-dependent quantity. First, the generalized structure equations are derived…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
The dynamics associated with a measurement-based master equation for quantum Brownian motion are investigated. A scheme for obtaining time evolution from general initial conditions is derived. This is applied to analyze dissipation and…