Related papers: When Is A Semiclassical Approximation Self-consist…
This dissertation investigates questions arising in the consistent histories formulation of the quantum mechanics of closed systems. Various criteria for approximate consistency are analysed. The connection between the Dowker-Halliwell…
Real atomic systems, like the hydrogen atom in a magnetic field or the helium atom, whose classical dynamics are chaotic, generally present both discrete and continuous symmetries. In this letter, we explain how these properties must be…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
Semiclassical results are usually expected to be valid in the semiclassical regime. An interesting question is, in models in which appropriate effective Planck constants can be introduced, to what extent will a semiclassical prediction stay…
The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting…
The standard notion of a classical limit, represented schematically by $\hbar\rightarrow 0$, provides a method for approximating a quantum system by a classical one. In this work we explain why the standard classical limit fails when…
We prove a double-inequality for the product of uncertainties for position and momentum of bound states for 1D quantum mechanical systems in the semiclassical limit.
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. This definition leads to statistical distributions of work that satisfy nonequilibrium work…
The mathematical possibility of coupling two quantum dynamic systems having two different Planck constants, respectively, is investigated. It turns out that such canonical dynamics are always irreversible. Semiclassical dynamics is obtained…
In the framework of semiparametric distribution regression, we consider the problem of comparing the conditional distribution functions corresponding to two samples. In contrast to testing for exact equality, we are interested in the (null)…
In this paper we develop the topics of Quantum Recurrences and of Quantum Fidelity which have attracted great interest in recent years. The return probability is given by the square modulus of the overlap between a given initial wavepacket…
An investigation of the validity of the semiclassical approximation to quantum electrodynamics in 1+1 dimensions is given. The criterion for validity used here involves the impact of quantum fluctuations introduced through a two-point…
We study smooth, caustic-free, chaotic semiclassical dynamics on two-dimensional phase space and find that the dynamics can be approached by an iterative procedure which constructs an approximation to the exact long-time semiclassical…
We discuss parameter dependent polynomial ordinary differential equations that model chemical reaction networks. By classical quasi-steady state (QSS) reduction we understand the following familiar heuristic: Set the rate of change for…
We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…
The usual semiclassical approximation for atom-field dynamics consists in substituting the field operators by complex numbers related to the (supposedly large enough) intensity of the field. We show that a semiclassical evolution for…
In this work we extend the results of [1] where, Semiclassical Selfconsistent Configurations (SSC) formalism was introduced. The scheme combines quantum field theory on a background space-time, semiclassical treatment of gravitation and…
In this work we present the results of a numerical and semiclassical analysis of high lying states in a Hamiltonian system, whose classical mechanics is of a generic, mixed type, where the energy surface is split into regions of regular and…
We address the task of active learning in the context of semantic segmentation and show that self-consistency can be a powerful source of self-supervision to greatly improve the performance of a data-driven model with access to only a small…