相关论文: Quantum Dot Potentials: Symanzik Scaling, Resurgen…
Certain quantum mechanical potentials give rise to a vanishing perturbation series for at least one energy level (which as we here assume is the ground state), but the true ground-state energy is positive. We show here that in a typical…
In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton…
We generalize the notion of an asymptotic weak coupling expansion about an exactly solvable model in quantum mechanics and quantum field theory to an all positive value coupling convergent expansion. This is done by rescaling the variables…
It is known that there exist a limited number of analytic potentials with the unusual property that any bound quantum state therein will be periodic in time. This is known as a perfect quantum state revival. Examples of such potentials are…
The analytic properties of the ground state resonance energy E(g) of the cubic potential are investigated as a function of the complex coupling parameter g. We explicitly show that it is possible to analytically continue E(g) by means of a…
We study a Fokker-Planck equation with double-well potential that is nonlocally driven by a dynamical constraint and involves two small parameters. Relying on formal asymptotics we identify several parameter regimes and derive reduced…
The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important…
We provide an analytical solution for the time-dependent Fokker-Planck equation for a two-dimensional active Brownian particle trapped in an isotropic harmonic potential. Using the passive Brownian particle as basis states we show that the…
We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width, which goes beyond the usual techniques applied to quasi-exactly solvable…
A macroscopic, self-propelled wave-particle entity (WPE) that emerges as a walking droplet on the surface of a vibrating liquid bath exhibits several hydrodynamic quantum analogs. We explore the rich dynamical and quantum-like features…
A series of informal seminars at graduate-student level on the subject of coupling dependence in quantum field theory, with an elementary introduction to the notion of resurgent function that forms the appropriate framework for the coupling…
Fokker-Planck equations have been applied in the past to field theory topics such as the stochastic quantization and the stabilization of bottomless action theories. In this paper we give another application of the FP-techniques in a way…
We study the relaxation to equilibrium for a class linear one-dimensional Fokker-Planck equations characterized by a particular subcritical confinement potential. An interesting feature of this class of Fokker-Planck equations is that, for…
In quantum theory, physical amplitudes are usually presented in the form of Feynman perturbation series in powers of coupling constant $\al .$ However, it is known that these amplitudes are not regular functions at $\alpha=0 .$ For QCD, we…
A basic theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions. This model postulates an extension of the Schrodinger equation to include a 4th and…
In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time asymptotics for the quantum Fokker-Planck…
The full set of resonant states in double and triple quantum well/barrier structures is investigated. This includes bound, anti-bound and normal resonant states which are all eigensolutions of Schrodinger's equation with generalized…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
A simple model of a two-mode non-resonant parametric amplifier is studied with special regard to non-classical features such as revivals and squeezing. The methods used apply for an arbitrary pump parameter. Detailed analytical and explicit…
We consider specific quantum mechanical model problems for which perturbation theory fails to explain physical properties like the eigenvalue spectrum even qualitatively, even if the asymptotic perturbation series is augmented by…