Related papers: Establishment of the conserved operators using var…
"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a…
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
The principle of energy conservation leads to a generalized choice of transition probability in a piecewise adiabatic representation of quantum(-classical) dynamics. Significant improvement (almost an order of magnitude, depending on the…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
For any transfer operator we establish the equivalence of variational principles for $t$-entropy, the spectral potential and entropy statistic theorem and give new proofs for all these statements.
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism from a set of physically comprehensible assumptions. In this paper, we formulate a…
We show that the correct mathematical foundation of quantum decision theory, dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of the projection-valued measure. The latter is…
We propose in this work a concept of integrability for quantum systems, which corresponds to the concept of noncommutative integrability for systems in classical mechanics. We determine a condition for quantum operators which can be a…
In their constructions of system of quantum stochastic differential equations, mathematicians and/or several physicists interpret that the function of random force operator is to preserve the canonical commutation relation in time, i.e., to…
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…
Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that in principle, the real and imaginary parts of the weak value of any operator may be elucidated from…
The quantum kinetic equation used in the study of weak turbulence is reconsidered in the context of a theory with a generic quartic interaction. The expectation value of the time derivative of the mode number operators is computed in a…
The position operator (defined within Schroedinger representation as usual) becomes meaningless when the usual Born-von Karman periodic boundary conditions are adopted: this fact is at the root of the polarization problem. I show how to…
We propose a non-commutative extension of the Pauli stabilizer formalism. The aim is to describe a class of many-body quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are…
In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
For a very general class of unbounded self-adjoint operator function we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find…
We formulate a variational principle for non-relativistic quantum mechanics inspired by Gauss's principle of least constraint. We define a quantum constraint functional as the probability-weighted square deviation between the actual motion…
In quantum logic there is well-known arbitrariness in choosing a binary operation for conditional. Currently, we have at least three candidates, called the Sasaki conditional, the contrapositive Sasaki conditional, and the relevance…