393 research outputs found
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
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
Deterministic models of quantum fields
Deterministic dynamical models are discussed which can be described in
quantum mechanical terms. -- In particular, a local quantum field theory is
presented which is a supersymmetric classical model. The Hilbert space approach
of Koopman and von Neumann is used to study the classical evolution of an
ensemble of such systems. Its Liouville operator is decomposed into two
contributions, with positive and negative spectrum, respectively. The unstable
negative part is eliminated by a constraint on physical states, which is
invariant under the Hamiltonian flow. Thus, choosing suitable variables, the
classical Liouville equation becomes a functional Schroedinger equation of a
genuine quantum field theory. -- We briefly mention an U(1) gauge theory with
``varying alpha'' or dilaton coupling where a corresponding quantized theory
emerges in the phase space approach. It is energy-parity symmetric and,
therefore, a prototype of a model in which the cosmological constant is
protected by a symmetry.Comment: 6 pages; synopsis of hep-th/0510267, hep-th/0503069, hep-th/0411176 .
Talk at Constrained Dynamics and Quantum Gravity - QG05, Cala Gonone
(Sardinia, Italy), September 12-16, 2005. To appear in the proceeding
General linear dynamics - quantum, classical or hybrid
We describe our recent proposal of a path integral formulation of classical
Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics,
which concerns the direct coupling of classical and quantum mechanical degrees
of freedom. This is of practical as well as of foundational interest and no
fully satisfactory solution of this problem has been established to date.
Related aspects will be observed in a general linear ensemble theory, which
comprises classical and quantum dynamics in the form of Liouville and von
Neumann equations, respectively, as special cases. Considering the simplest
object characterized by a two-dimensional state-space, we illustrate how
quantum mechanics is special in several respects among possible linear
generalizations.Comment: 17 pages; based on invited talks at the conferences DICE2010
(Castiglioncello, Italia, Sept 13-17, 2010) and Quantum Field Theory and
Gravity (Regensburg, Germany, Sept 28 - Oct 1, 2010
Quantum fields, cosmological constant and symmetry doubling
Energy-parity has been introduced by Kaplan and Sundrum as a protective
symmetry that suppresses matter contributions to the cosmological constant
[KS05]. It is shown here that this symmetry, schematically Energy --> - Energy,
arises in the Hilbert space representation of the classical phase space
dynamics of matter. Consistently with energy-parity and gauge symmetry, we
generalize the Liouville operator and allow a varying gauge coupling, as in
"varying alpha" or dilaton models. In this model, classical matter fields can
dynamically turn into quantum fields (Schroedinger picture), accompanied by a
gauge symmetry change -- presently, U(1) --> U(1) x U(1). The transition
between classical ensemble theory and quantum field theory is governed by the
varying coupling, in terms of a one-parameter deformation of either limit.
These corrections introduce diffusion and dissipation, leading to decoherence.Comment: Replaced by published version, no change in contents - Int. J. Theor.
Phys. (2007
Color singlet suppression of quark-gluon plasma formation
The rate of quark-gluon plasma droplet nucleation in superheated hadronic
matter is calculated within the MIT bag model. The requirements of color
singletness and (to less extent) fixed momentum suppress the nucleation rate by
many orders of magnitude, making thermal nucleation of quark-gluon plasma
droplets unlikely in ultrarelativistic heavy-ion collisions if the transition
is first order and reasonably described by the bag model.Comment: 9 pages, 3 ps figures. To appear in PhysRevC (April 1996
A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide
The Liouville equation differs from the von Neumann equation 'only' by a
characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in
general, and for the Jaynes-Cummings model, in particular. -- Employing
superspace (instead of Hilbert space), we describe time evolution of density
matrices in terms of path integrals which are formally identical for quantum
and classical mechanics. They only differ by the interaction contributing to
the action. This allows to import tools developed for Feynman path integrals,
in order to deal with superoperators instead of quantum mechanical commutators
in real time evolution. Perturbation theory is derived. Besides applications in
classical statistical physics, the "classical path integral" and the parallel
study of classical and quantum evolution indicate new aspects of (dynamically
assisted) entanglement (generation). Our findings suggest to distinguish
'intra'- from 'inter-space' entanglement.Comment: 22 pages; based on invited talk at Quantum 2010 - Advances in
Foundations of Quantum mechanics and Quantum Information with Atoms and
Photons (Torino, May 2010). To appear in Int. J. Qu. Inf
Entropy Production in Relativistic Hydrodynamics
The entropy production occurring in relativistic hydrodynamical systems such
as the quark-gluon plasma (QGP) formed in high-energy nuclear collisions is
explored. We study mechanisms which change the composition of the fluid, i.e.
particle production and/or chemical reactions, along with chemo- and
thermo-diffusion. These effects complement the conventional dissipative effects
of shear viscosity, bulk viscosity, and heat conductivity.Comment: 15 pages; LaTex. Accepted for publication in Physics Letters B. - Two
typos corrected and one reference adde
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