Related papers: A note on spectrum and quantum dynamics
We investigate the quantum dynamics of a spin chain that implements a quantum analog of Conway's game of life. We solve the time-dependent Schr\"odinger equation starting with initial separable states and analyse the evolution of quantum…
We investigate the dependence of the escape rate on the position of a hole placed in uniformly hyperbolic systems admitting a finite Markov partition. We derive an exact periodic orbit formula for finite size Markov holes which differs from…
In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is…
In the following we are interested in the spectral gaps of discrete quasiperiodic Schr\"odinger operators when the frequency is Diophantine, the potential is analytic, and in the subcritical regime. The gap-labelling theorem asserts in this…
We prove that any spectral sequence obeying a certain growth law is the quantum spectrum of an equivalence class of classically integrable non-linear oscillators. This implies that exceptions to the Berry-Tabor rule for the distribution of…
The motion of a ball through an appropriate lattice of round obstacles models the behavior of a Brownian particle and can be used to describe measurement on a macro system. On another hand, such motion is chaotic and a known conjecture…
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of…
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…
These notes are intended as an introduction to the question of unique continuation for the wave operator, and some of its applications. The general question is whether a solution to a wave equation in a domain, vanishing on a subdomain has…
Mesoscopic systems and large molecules are often modeled by graphs of one-dimensional wires, connected at vertices. In this paper we discuss the solutions of the Schr\"odinger equation on such graphs, which have been named "quantum…
Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial…
The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length…
In this paper we demonstrate that Lindblad equations characterized by a random rate variable arise after tracing out a complex structured reservoir. Our results follows from a generalization of the Born-Markov approximation, which relies in…
The central limit theorem has been found to apply to random vectors in complex Hilbert space. This amounts to sufficient reason to study the complex valued Gaussian, looking for relevance to quantum mechanics. Here we show that the…
By a quantum speed limit one usually understands an estimate on how fast a quantum system can evolve between two distinguishable states. The most known quantum speed limit is given in the form of the celebrated Mandelstam-Tamm inequality…
The time slice axiom states that the observables which can be measured within an arbitrarily small time interval suffice to predict all other observables. While well known for free field theories where the validity of the time slice axiom…
Quantum confinement is studied by numerically solving time-dependent Schr\"odinger equation. An imaginary-time evolution technique is employed in conjunction with the minimization of an expectation value, to reach the global minimum.…
Using nonstandard methods, we show that the time dependent Fourier series of any smooth function F, solving the wave equation, on a finite closed interval, with vanishing boundary conditions, converges uniformly to F.
In this paper, we investigate the multi-marginal Schrodinger bridge (MSB) problem whose marginal constraints are marginal distributions of a stochastic differential equation (SDE) with a constant diffusion coefficient, and with time…
In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an absolute time-duration in the…