Speaker
Davide Cocco
(Università di Roma La Sapienza)
Description
In this contribution we explore the derivation
of quantum mechanics from a classical
field theory, or more precisely from a thermodynamic
approach involving two field phases. This attempt
is in line with the analysis of Laughlin and Pines on
the emergent characters of physical laws, including
quantum physics (PNAS, 97, 2000, 28).
The first
part of the presentation analyzes in detail the stochastic
interpretation of quantum physics
grounded on the "Advective Quantum Gauge" (AQG for
short), i.e., on the equivalence between the Schrodinger
and the advection diffusion equations in a Wick-rotated time.
Albeit this connection have been addressed by a huge and extensive
literature,
several implications
of the above equivalence are fairly novel and of physical interest.
Specifically:
(i) The AQG approach provides for quantum system a kinematic
equation of motion (complex Langevin equation) of the
form
$ d {\bf x}(t) = i \, {\bf v}_q({\bf x}(t)) \, d t + \sqrt{i \, 2 \, D_h } \, d{\bf w}(t) $ where $ d {\bf w}(t) $ the increments
of a $n$-dimensional real-valued Wiener process. In the
absence of stochastic fluctuations, from the above
model one recovers the semiclassical limit of
the Newton equations of motion.
(ii) The AQG furnishes an interesting interpretation
of Bohmian quantum dynamics, as a mean field theory in
which quantum fluctuations are accounted for by the
quantum potential which depends on the modulus of the
wavefunction.
(iii) The AQG provides a way to obtain
the wavefunction or the quantum propagators in a simple and efficient
way from random walk simulations. This is
particularly relevant for quantum problems
involving many degrees of freedom.
The stochastic interpretation of quantum mechanics, and
specifically the AQG approach, is essentially
a particle-based description of a physical system intrinsically
subjected to fluctuations. This approach shows some
limitations in the presence of time-dependent (and, a fortiori}
stochastic) potentials.
The second part of the presentation provides
a classical
field-theoretical interpretation of the Schrodinger
equation, in which quantum (field) fluctuations
still play a leading role, but a quantum system is
viewed as a statistical mechanical system in which
two field-phases coexist.
In the present thermodynamic model we assume that a quantum system
corresponds to a two-phase thermodynamic system in which
a "distributed" (radiating) field coexists with
a "condensed field phase". Quantum equation
of motion emerges from the interaction between the two
phases by assuming a quasi steady-state approximation.
As regards the condensed phase, it is at present
described in a particle-like way via position and momentum.
As mentioned above, from a quasi-state approximation on the
statistical description of the condensed field phase, Schrodinger
equation is recovered.
More precisely, a system of hyperbolic first-order
equations analogous to the statistical description
of Generalized Poisson-Kac processes is derived.
The Kac limit of these equations provides the classical
Schrodinger model containing the Laplacian operator
accounting for the kinetic energy.
Primary author
Davide Cocco
(Università di Roma La Sapienza)
Co-author
Massimiliano Giona
(Università di Roma La Sapienza)
