相关论文: Feynman Integrals with Absorbing Boundaries

A theory of quantum jumps is developed by using a new asymmetric equation, which is complementary to the Schr\"odinger equation. The new equation displays Bohr's rules for quantum jumps, and its solutions demonstrate that once a quantum…

We consider the gravitational analogue of Lyman-alpha absorption lines in astronomical spectroscopy. If Einstein gravity with minimally coupled matter is valid up to the Planck scale, quantum bound states absorb gravitons of a specific…

The Feynman path integral approach to quantum mechanics is examined in the case where the configuration space is curved. It is shown how the ambiguity that is present in the choice of path integral measure may be resolved if, in addition to…

A complete theoretical treatment in many problems relevant to physics, chemistry, and biology requires considering the action of the environment over the system of interest. Usually the environment involves a relatively large number of…

Early Wheeler-Feynman absorber theories invoke both retarded and advanced electromagnetic waves for photon emission and absorption in order to remove problems involving lack of radiative damping during electron acceleration. Subsequent…

Negative refractive index materials have attracted significant research attention due to their unique electromagnetic response characteristics. In this paper, we employ the complementing boundary condition to establish rigorous a priori…

We consider subdiffusion of a particle in a one-dimensional system with a thin partially permeable wall. Passing through the wall, the particle can be absorbed with a certain probability. We call such a wall partially permeable partially…

Feynman integrands are constructed as Hida distributions. For our approach we first have to construct solutions to a corresponding Schroedinger equation with time-dependent potential. This is done by a generalization of the Doss approach to…

In this paper we analyze the behavior of quantum random walks. In particular we present several new results for the absorption probabilities in systems with both one and two absorbing walls for the one-dimensional case. We compute these…

We present a prescription for choosing orthogonal bases of differential $n$-forms belonging to quadratic twisted period integrals, with respect to the intersection number inner product. To evaluate these inner products, we additionally…

The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non--relativistic quantum mechanics. The long--range part of pair potentials is assumed to be pure Coulomb and no restriction…

Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most…

The logical consistency of a description of Quantum Theory in the context of General Relativity, which includes Minimal Coupling Principle, is analyzed from the point of view of Feynman's formulation in terms of path integrals. We will…

The very early universe is understood in terms of quantum field theories on curved spacetime, where the classical background spacetime is typically an FLRW cosmology and the quantum fields which propagate on it include gravitational waves…

Consider a particle which is randomly accelerated by Gaussian white noise on the line segment $0<x<1$ and is absorbed as soon as it reaches $x=0$ or $x=1$. The mean absorption time $T(x,v)$, where $x$ and $v$ denote the initial position and…

We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point…

We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard…

Spacetime foam is analyzed within the simplistic model of a set of scalar fields on a flat background. We suggest the formula for the path integral which allows to account for the all possible topologies of spacetime. We show that the…

Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary 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…