arXiv subjects

Alberto Montina

Publications and source records attributed to Alberto Montina.

21 records · Page 2Linked to original sources

arXiv2008

Exponential complexity and ontological theories of quantum mechanics

Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We consider the general class of ontological theories describing a quantum system by a set of variables with Markovian (either deterministic or stochastic) evolution. We provide the first proof that the number of continuous variables can not be smaller than 2N-2, N being the Hilbert space dimension. Thus, any ontological Markovian theory of quantum mechanics requires a number of variables which grows exponentially with the physical size. This result is relevant also in the framework of quantum Monte Carlo methods.

quant-ph↗

arXiv2007

A condition for any realistic theory of quantum systems

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 quantum states and events with classical probability distributions and conditional probabilities and prove that the distributions can not be quadratic functions of the quantum state. Some examples are considered. Finally, we deal with the exponential complexity problem of quantum physics and introduce the concept of classical dimension for a quantum system.

quant-ph↗

arXiv2005

Exact BCS stochastic schemes for a time dependent many-body fermionic system

The exact quantum state evolution of a fermionic gas with binary interactions is obtained as the stochastic average of BCS-state trajectories. We find the most general Ito stochastic equations which reproduce exactly the dynamics of the system and we obtain some conditions to minimize the stochastic spreading of the trajectories in the Hilbert space. The relation between the optimized equations and mean-field equations is analyzed. The method is applied to a simple two-site model. The simulations display effects that cannot be obtained in the mean-field approximation.

cond-mat.other↗