Related papers: Probabilistic Parallels in the Classical Limit of …
Based on a geometric picture, the example of free particle motion for both classical and quantum domains is considered in the tomographic probability representation. Wave functions and density operators as well as optical and symplectic…
Conditions under which a quantum particle is described using classical quantities are studied. The one-dimensional (1D) and three-dimensional (3D) problems are considered. It is shown that the sum of the contributions from all quantum…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…
In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like "point" particle, motion "on the line", "smooth" observables, wave…
The conceptual problems in quantum mechanics -- related to the collapse of the wave function, the particle-wave duality, the meaning of measurement -- arise from the need to ascribe particle character to the wave function. As will be shown,…
A complete solution to the long standing problem of basing Schroedinger quantum theory on standard stochastic theory is given. The solution covers all "single" particle three-dimensional Schroedinger theory linear or nonlinear and with any…
We discuss recent results of the replica approach to statistical mechanics of a single classical particle placed in a random N(>>1)-dimensional Gaussian landscape. The particular attention is paid to the case of landscapes with…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
A scenario is outlined for quantum measurement, assuming that self-sustaining classicality is the consequence of an attractive gravitational self-interaction acting on massive bodies, and randomness arises already in the classical domain. A…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
We study the behavior of a quantum particle trapped in a confining potential in one dimension under multiple sudden changes of velocity and/or acceleration. We develop the appropriate formalism to deal with such situation and we use it to…
A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
It is often stated that complex numbers are essential in quantum theory. In this article, the need for complex numbers in quantum theory is motivated using the results of tandem Stern-Gerlach experiments
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
We consider the product of infinitely many copies of a spin-$1\over 2$ system. We construct projection operators on the corresponding nonseparable Hilbert space which measure whether the outcome of an infinite sequence of $\sigma^x$…