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We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set…
Performing an nonperturbative path integral for the geometric part of a large class of 2d theories without kinetic term for the dilaton field, the quantum effects from scalar matter fields are treated as a perturbation. When integrated out…
It is pointed out that there are some fundamental difficulties with the frequently used continuous-time formalism of the spin-coherent-state path integral. They arise already in a single-spin system and at the level of the "classical…
The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…
We introduce a new method to analysis the many-body problem with disorder. The method is an extension of the real space renormalization group based on the operator product expansion. We consider the problem in the presence of interaction,…
Dynamical tunnelling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunnelling process is governed by nonlinear resonances that manifest within the regular…
Quantum walks constitute important tools in different applications, especially in quantum algorithms. To a great extent their usefulness is due to unusual diffusive features, allowing much faster spreading than their classical counterparts.…
Self-induced decoherence formalism and the corresponding classical limit are extended from quantum integrable systems to non-integrable ones.
In some spin tunneling problems, there are several different but symmetry-related tunneling paths that connect the same initial and final configurations. The topological phase factors of the corresponding tunneling amplitudes can lead to…
In this paper the Feynman path integral technique is applied to two-dimensional spaces of non-constant curvature: these spaces are called Darboux spaces $\DI$--$\DIV$. We start each consideration in terms of the metric and then analyze the…
I assume a universe whereby the speed of light and the planck constant are not constants but instead parameters that vary locally in time-and space. When describing motion, I am able to derive a modified path integral description at the…
We reconsider the problem of the enhancement of tunnelling of a quantum particle induced by disorder of a one-dimensional tunnel barrier of length $L$, using two different approximate analytic solutions of the invariant imbedding equations…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
Vacuum energy and other spectral functions of Laplace-type differential operators have been studied approximately by classical-path constructions and more fundamentally by boundary integral equations. As the first step in a program of…
Tunneling of fractionally charged quasi-particles (QPs) through a barrier is considered in the context of a multiply connected geometry. In this geometry global constraints do not prohibit such a tunneling process. The tunneling amplitude…
A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined.…
This work presents a theoretical framework for the safety-critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay-free systems, is extended to systems with state…
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
The semi-classical approximation to black hole partition functions is not well-defined, because the classical action is unbounded and the first variation of the uncorrected action does not vanish for all variations preserving the boundary…
Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a…