597 research outputs found
Quantum features in statistical observations of "timeless" classical systems
We pursue the view that quantum theory may be an emergent structure related
to large space-time scales. In particular, we consider classical Hamiltonian
systems in which the intrinsic proper time evolution parameter is related
through a probability distribution to the discrete physical time. This is
motivated by studies of ``timeless'' reparametrization invariant models, where
discrete physical time has recently been constructed based on coarse-graining
local observables. Describing such deterministic classical systems with the
help of path-integrals, primordial states can naturally be introduced which
follow unitary quantum mechanical evolution in suitable limits.Comment: 7 pages. Invited talk at Int. Workshop Trends and Perspectives on
Extensive and Non-Extensive Statistical Mechanics, Angra dos Reis (Brazil),
Nov. 2003. To appear in Physica
Relativistic Quantum Transport Theory
Relativistic quantum transport theory has begun to play an important role in
the space-time description of matter under extreme conditions of high energy
density in out-of-equilibrium situations. The following introductory lectures
on some of its basic concepts and methods comprise the sections: 1.
Introduction; 2. Aims of transport theory (classical); 3. Quantum mechanical
distribution functions - the density matrix and the Wigner function; 4.
Transport theory for quantum fields; 5. Particle production by classical
fields; 6. Fluid dynamics of relativistic quantum dust.Comment: Lectures presented at PASI "New States of Matter in Hadronic
Interactions", Campos do Jordao, Brazil, Jan.7-18, 2002. - 19 pages; LaTe
Quantum Mechanics and Discrete Time from "Timeless" Classical Dynamics
We study classical Hamiltonian systems in which the intrinsic proper time
evolution parameter is related through a probability distribution to the
physical time, which is assumed to be discrete. - This is motivated by the
``timeless'' reparametrization invariant model of a relativistic particle with
two compactified extradimensions. In this example, discrete physical time is
constructed based on quasi-local observables. - Generally, employing the
path-integral formulation of classical mechanics developed by Gozzi et al., we
show that these deterministic classical systems can be naturally described as
unitary quantum mechanical models. The emergent quantum Hamiltonian is derived
from the underlying classical one. It is closely related to the Liouville
operator. We demonstrate in several examples the necessity of regularization,
in order to arrive at quantum models with bounded spectrum and stable
groundstate.Comment: 24 pages, 1 figure. Lecture given at DICE 2002. To be published in:
Decoherence and Entropy in Complex Systems, Lecture Notes in Physics
(Springer-Verlag, Berlin 2003). - Comprises quant-ph/0306096 and
gr-qc/0301109, additional reference
Is there a relativistic nonlinear generalization of quantum mechanics?
Yes, there is. - A new kind of gauge theory is introduced, where the minimal
coupling and corresponding covariant derivatives are defined in the space of
functions pertaining to the functional Schroedinger picture of a given field
theory. While, for simplicity, we study the example of an U(1) symmetry, this
kind of gauge theory can accommodate other symmetries as well. We consider the
resulting relativistic nonlinear extension of quantum mechanics and show that
it incorporates gravity in the (0+1)-dimensional limit, where it leads to the
Schroedinger-Newton equations. Gravity is encoded here into a universal
nonlinear extension of quantum theory. The probabilistic interpretation, i.e.
Born's rule, holds provided the underlying model has only dimensionless
parameters.Comment: 10 pages; talk at DICE 2006 (Piombino, September 11-15, 2006); to
appear in Journal of Physics: Conference Series (2007
Time without time: a stochastic clock model
We study a classical reparametrization-invariant system, in which ``time'' is
not a priori defined. It consists of a nonrelativistic particle moving in five
dimensions, two of which are compactified to form a torus. There, assuming a
suitable potential, the internal motion is ergodic or more strongly irregular.
We consider quasi-local observables which measure the system's ``change'' in a
coarse-grained way. Based on this, we construct a statistical timelike
parameter, particularly with the help of maximum entropy method and Fisher-Rao
information metric. The emergent reparametrization-invariant ``time'' does not
run smoothly but is simply related to the proper time on the average. For
sufficiently low energy, the external motion is then described by a unitary
quantum mechanical evolution in accordance with the Schr\"odinger equation.Comment: 18 pages; LaTeX. 4 (.ps) plus 2 (.gif) figure file
Does quantum mechanics tell an atomistic spacetime?
The canonical answer to the question posed is "Yes." -- tacitly assuming that
quantum theory and the concept of spacetime are to be unified by `quantizing' a
theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics
arise as a coarse-grained reflection of the atomistic nature of spacetime? --
We speculate that this may indeed be the case. We recall the similarity between
evolution of classical and quantum mechanical ensembles, according to Liouville
and von Neumann equation, respectively. The classical and quantum mechanical
equations are indistinguishable for objects which are free or subject to
spatially constant but possibly time dependent, or harmonic forces, if
represented appropriately. This result suggests a way to incorporate anharmonic
interactions, including fluctuations which are tentatively related to the
underlying discreteness of spacetime. Being linear and local at the quantum
mechanical level, the model offers a decoherence and natural localization
mechanism. However, the relation to primordial deterministic degrees of freedom
is nonlocal.Comment: Based on invited talks at Fourth International Workshop DICE2008,
held at Castello Pasquini / Castiglioncello, Italy, 22-26 September 2008 and
at DISCRETE'08 - Symposium on Prospects in the Physics of Discrete
Symmetries, held at IFIC, Valencia, Spain, 11-16 December 2008 - to appear in
respective volumes of Journal of Physics: Conference Serie
The Attractor and the Quantum States
The dissipative dynamics anticipated in the proof of 't Hooft's existence
theorem -- "For any quantum system there exists at least one deterministic
model that reproduces all its dynamics after prequantization" -- is constructed
here explicitly. We propose a generalization of Liouville's classical phase
space equation, incorporating dissipation and diffusion, and demonstrate that
it describes the emergence of quantum states and their dynamics in the
Schroedinger picture. Asymptotically, there is a stable ground state and two
decoupled sets of degrees of freedom, which transform into each other under the
energy-parity symmetry of Kaplan and Sundrum. They recover the familiar Hilbert
space and its dual. Expectations of observables are shown to agree with the
Born rule, which is not imposed a priori. This attractor mechanism is
applicable in the presence of interactions, to few-body or field theories in
particular.Comment: 14 pages; based on invited talk at 4th Workshop ad memoriam of Carlo
Novero "Advances in Foundations of Quantum Mechanics and Quantum Information
with Atoms and Photons", Torino, May 2008; submitted to Int J Qu Inf
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