Related papers: Multi-Instantons and Exact Results II: Specific Ca…
Instanton theory has arisen as a practical tool for calculating tunneling splittings in molecular systems. Unfortunately, the original formulation of instanton theory fundamentally breaks down when trying to calculate the level splitting in…
The aim of Part II of this paper is to try to describe wave functions on q-deformed versions of position and momentum space. This task is done within the framework developed in Part I of the paper. In order to make Part II self-contained…
Using the idea of the instanton approach to quantum tunneling we try to obtain a method of calculating spontaneous fission rates for nuclei with the odd number of neutrons or protons. This problem has its origin in the failure of the…
The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the…
Quantum theory of conformal factor coupled with matter fields is investigated. The more simple case of the purely classical scalar matter is considered. It is calculated the conformal factor contribution to the effective potential of scalar…
We discuss various aspects of multi-instanton configurations in generic multi-cut matrix models. Explicit formulae are presented in the two-cut case and, in particular, we obtain general formulae for multi-instanton amplitudes in the…
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the…
Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the…
This is the first of a sequence of papers that address the non-perturbative origin of the central, and spin-dependent forces between quarks. Its main thrust is a focus on meson spectroscopy in the center of mass frame. We suggest a "dense…
We present a new six-parameter family of potentials whose solutions are expressed in terms of the hypergeometric functions 3F2, 2F2 and 1F2. Both the scattering data and the bound states of these potentials are explicitly computed and the…
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…
We study the quantum-mechanical tunneling phenomenon in models which include the existence of non-equivalent vacua. For such a purpose we evaluate the euclidean propagator between two minima of the potential at issue in terms of the…
In this paper we present results of computations for the ground energy of weakly coupled double well potential in quantum mechanics. We give a numerical evidence for cancelation of imaginary contributions to energy coming from Borel…
In this paper we present a generating function approach to two counting problems in elementary quantum mechanics. The first is to find the total ways of distributing identical particles among different states. The second is to find the…
The confluent second-order supersymmetric quantum mechanics, in which the factorization energies tend to a common value, is used to generate Hamiltonians with known spectra departing from the hyperbolic Rosen-Morse and Eckart potentials.…
Instantons and their quantisation in pure Yang-Mills theory formulated in the background of de Sitter spacetime represented by spatially-closed ($k = 1$) Friedmann-Robertson-Walker metric are discussed. As for the classical treatment of the…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
We consider the time-independent Wigner functions of phase-space quantum mechanics (a.k.a. deformation quantization) for a Morse potential. First, we find them by solving the $\ast$-eigenvalue equations, using a method that can be applied…
Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…