J. L. Sánchez-Gómez

On the probabilistic postulate of quantum mechanics

We study whether the probabilistic postulate could be derived from basic principles. Through the analysis of the Strong Law of Large Numbers and its formulation in quantum mechanics, we show, contrary to the claim of the many-worlds interpretation defenders and the arguments of some other authors, the impossibility of obtaining the probabilistic postulate by means of the frequency analysis of an ensemble of infinite copies of a single system. It is shown, though, how the standard form of the probability as the square of the scalar product follows from Gleasons theorem.

Non-linear Schrödinger equation coming from the action of the particle's gravitational field on the quantum potential

Abstract The effect of the gravitational field of a particle on its own wave function is analyzed by obtaining the “stochastic” metric induced by the quantum potential when such an effect is taken into account.Upon going to the non-relativistic limit, a non-linear Schrodinger equation is derived in which the non-linear term is related to gravity. This term is completely negligible for “microscopic” systems, yet some arguments are given which suggest that it must be important for macroscopic systems; in the latter case it would produce an appreciable deviation from the strict quantum behaviour, in the sense that one would get classical trajectories for the motion of the systems centre of mass.

A Simple Proof of the Jamiołkowski Criterion for Complete Positivity of Linear Maps

We give a simple direct proof of the Jamiołkowski criterion to check whether a linear map between matrix algebras is completely positive or not. This proof is more accessible for physicists than other ones found in the literature and provides a systematic method to give any set of Kraus matrices of the Kraus decomposition.

ON THE ABSENCE OF THE ZENO EFFECT IN RELATIVISTIC QUANTUM FIELD THEORY

Abstract We study the time evolution of decaying particles in renormalizable models of relativistic quantum field theory (RQFT). Significant differences between the latter and nonrelativistic quantum mechanics are found - in particular, the Zeno effect seems to be absent in such RQFT models. Conventional renormalization yields finite time behaviour in some cases but fails to produce finite survival probabilities in others.

Conformal metric fluctuations and quantum mechanics

Abstract Some general properties of conformal (classical) metric fluctuations are studied in this paper. It is argued that there is a profound relationship between such fluctuations and the quantum fluctuations, at least in the case of an isolated scalar particle dealt with here.

A note on some physical and cosmological implications of conformal metric fluctuations

Abstract We show that stochastic fluctuations of the space-time metric - which various authors invoke as a possible physical agent of decoherence in macroscopic systems - must be conformal in order to avoid some bizarre physical and cosmological implications.

Gravitationally Induced Decoherence in Macroscopic Systems

A quantum master equation for the time evolution of the center of mass (CM) of a macroscopic body is derived which takes into account the influence of the system’s gravitational field over the CM wave function. As a consequence, all the relevant phenomenological features of the so-called GRW (Ghirardi, Rimini, and Weber) model are reproduced with no free parameters. The model presented here predicts also the existence of a transition region for the mass of the system—a kind of frontier between quantum (coherent) and classical (decoherent) behavior.

A formula for the Bloch vector of some Lindblad quantum systems

Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators.

QSES's and the Quantum Jump

Abstract The stochastic methods in Hilbert space have been used both from a fundamental and a practical point of view. The result reported here concerns the application of these methods to model the evolution of quantum systems and does not enter into the question of their fundamental or practical status. It can easily be stated as follows: Once a quantum stochastic evolution scheme is assumed, the incompatibility of the Markov property with the notion of quantum jumps is easily established

Short Time Behavior and Zeno Effect in Relativistic Quantum Field Theory

We study the short-time evolution of decaying particles in the framework of relativistic quantum field theory. Significant differences between the relativistic and non-relativistic (that is, non-relativistic quantum mechanics) cases are found; in particular the so-called quantum Zeno effect is not present in relativistic quantum field theory, at least in the models studied herein.