Related papers: Limits of reductionism and the measurement problem
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
The problem of a particle localized in a ultra-short potential in one dimension is considered. By proposing a general solution to Schrodinger;s equation we show that the energy spectra and the probability of the particle have definite…
In this letter we present an analytic evidence of the non-integrability of the discrete nonlinear Schroedinger equation, a well-known discrete evolution equation which has been obtained in various contexts of physics and biology. We use a…
We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness…
Absorbing boundaries are frequently employed in real-time propagation of the Schr\"odinger equation to remove spurious reflections and efficiently emulate outgoing boundary conditions. These conditions are a fundamental ingredient for an…
The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The…
There exist limits of self-inspection due to self-referential paradoxes, incompleteness and fixed point theorems. As quantum mechanics dictates the exchange of discrete quanta, measurements and self-inspection of quantized systems are…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
We consider the inverse conductivity problem of identifying embedded objects in unbounded domains. The main tool is a set of special solutions to the Schroedinger equation, the complex spherical waves, which are constructed by a Carleman…
Certain solutions to a gravitational form of Schrodinger's equation can yield stable, macroscopic eigenstate solutions having no classical analogue, with properties resembling those of dark matter. Some more tractable solutions show: (1)…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
The interface problem for the linear Schr\"odinger equation in one-dimensional piecewise homogeneous domains is examined by providing an explicit solution in each domain. The location of the interfaces is known and the continuity of the…
Left on its own, a quantum state evolves deterministically under the Schr\"odinger Equation, forming superpositions. Upon measurement, however, a stochastic process governed by the Born rule collapses it to a single outcome. This dual…
It is argued that the occurrence of disproportionately ("un-natural") large (or small) numbers, as well as deep cancellations, are comparatively natural traits of the way Nature is geared to operate in most complex systems. The idea is…
A general system constrained with {\it several} initial constraint conditions is quantized based on the Dirac formalism and the Schr\"{o}dinger equation for this system is obtained. These constraint conditions are now allowed to depend not…
A nonlinear Schrodinger equation, that had been obtained within the context of the maximum uncertainty principle, has the form of a difference-differential equation and exhibits some interesting properties. Here we discuss that equation in…
A satisfactory resolution of the persistent quantum measurement problem remains stubbornly unresolved in spite of an overabundance of efforts of many prominent scientists over the decades. Among others, one key element is considered yet to…
This work is concerned with existence and uniqueness of solutions to the reflection problem for linear parabolic equation with multiplicative Gaussian noise.
We consider the Schrodinger equation with a logarithmic nonlinearity and a repulsive harmonic potential. Depending on the parameters of the equation, the solution may or may not be dispersive. When dispersion occurs, it does with an…
Various aspects of the Cauchy problem for the Einstein equations are surveyed, with the emphasis on local solutions of the evolution equations. Particular attention is payed to giving a clear explanation of conceptual issues which arise in…