1,325 research outputs found
Exact Markovian kinetic equation for a quantum Brownian oscillator
We derive an exact Markovian kinetic equation for an oscillator linearly
coupled to a heat bath, describing quantum Brownian motion. Our work is based
on the subdynamics formulation developed by Prigogine and collaborators. The
space of distribution functions is decomposed into independent subspaces that
remain invariant under Liouville dynamics. For integrable systems in
Poincar\'e's sense the invariant subspaces follow the dynamics of uncoupled,
renormalized particles. In contrast for non-integrable systems, the invariant
subspaces follow a dynamics with broken-time symmetry, involving generalized
functions. This result indicates that irreversibility and stochasticity are
exact properties of dynamics in generalized function spaces. We comment on the
relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.Comment: A few typos in the published version are correcte
Phenomenological approach to the critical dynamics of the QCD phase transition revisited
The phenomenological dynamics of the QCD critical phenomena is revisited.
Recently, Son and Stephanov claimed that the dynamical universality class of
the QCD phase transition belongs to model H. In their discussion, they employed
a time-dependent Ginzburg-Landau equation for the net baryon number density,
which is a conserved quantity. We derive the Langevin equation for the net
baryon number density, i.e., the Cahn-Hilliard equation. Furthermore, they
discussed the mode coupling induced through the {\it irreversible} current.
Here, we show the {\it reversible} coupling can play a dominant role for
describing the QCD critical dynamics and that the dynamical universality class
does not necessarily belong to model H.Comment: 13 pages, the Curie principle is discussed in S.2, to appear in
J.Phys.
Star-unitary transformations. From dynamics to irreversibility and stochastic behavior
We consider a simple model of a classical harmonic oscillator coupled to a
field. In standard approaches Langevin-type equations for {\it bare} particles
are derived from Hamiltonian dynamics. These equations contain memory terms and
are time-reversal invariant. In contrast the phenomenological Langevin
equations have no memory terms (they are Markovian equations) and give a time
evolution split in two branches (semigroups), each of which breaks time
symmetry. A standard approach to bridge dynamics with phenomenology is to
consider the Markovian approximation of the former. In this paper we present a
formulation in terms of {\it dressed} particles, which gives exact Markovian
equations. We formulate dressed particles for Poincar\'e nonintegrable systems,
through an invertible transformation operator \Lam introduced by Prigogine
and collaborators. \Lam is obtained by an extension of the canonical
(unitary) transformation operator that eliminates interactions for
integrable systems. Our extension is based on the removal of divergences due to
Poincar\'e resonances, which breaks time-symmetry. The unitarity of is
extended to ``star-unitarity'' for \Lam. We show that \Lam-transformed
variables have the same time evolution as stochastic variables obeying Langevin
equations, and that \Lam-transformed distribution functions satisfy exact
Fokker-Planck equations. The effects of Gaussian white noise are obtained by
the non-distributive property of \Lam with respect to products of dynamical
variables. Therefore our method leads to a direct link between dynamics of
Poincar\'e nonintegrable systems, probability and stochasticity.Comment: 24 pages, no figures. Made more connections with other work.
Clarified ideas on irreversibilit
Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws
In this and a companion paper we outline a general framework for the
thermodynamic description of open chemical reaction networks, with special
regard to metabolic networks regulating cellular physiology and biochemical
functions. We first introduce closed networks "in a box", whose thermodynamics
is subjected to strict physical constraints: the mass-action law, elementarity
of processes, and detailed balance. We further digress on the role of solvents
and on the seemingly unacknowledged property of network independence of free
energy landscapes. We then open the system by assuming that the concentrations
of certain substrate species (the chemostats) are fixed, whether because
promptly regulated by the environment via contact with reservoirs, or because
nearly constant in a time window. As a result, the system is driven out of
equilibrium. A rich algebraic and topological structure ensues in the network
of internal species: Emergent irreversible cycles are associated to
nonvanishing affinities, whose symmetries are dictated by the breakage of
conservation laws. These central results are resumed in the relation between the number of fundamental affinities , that of broken
conservation laws and the number of chemostats . We decompose the
steady state entropy production rate in terms of fundamental fluxes and
affinities in the spirit of Schnakenberg's theory of network thermodynamics,
paving the way for the forthcoming treatment of the linear regime, of
efficiency and tight coupling, of free energy transduction and of thermodynamic
constraints for network reconstruction.Comment: 18 page
Causality, delocalization and positivity of energy
In a series of interesting papers G. C. Hegerfeldt has shown that quantum
systems with positive energy initially localized in a finite region,
immediately develop infinite tails. In our paper Hegerfeldt's theorem is
analysed using quantum and classical wave packets. We show that Hegerfeldt's
conclusion remains valid in classical physics. No violation of Einstein's
causality is ever involved. Using only positive frequencies, complex wave
packets are constructed which at are real and finitely localized and
which, furthemore, are superpositions of two nonlocal wave packets. The
nonlocality is initially cancelled by destructive interference. However this
cancellation becomes incomplete at arbitrary times immediately afterwards. In
agreement with relativity the two nonlocal wave packets move with the velocity
of light, in opposite directions.Comment: 14 pages, 5 figure
Quantum properties of a cyclic structure based on tripolar fields
The properties of cyclic structures (toroidal oscillators) based on classical
tripolar (colour) fields are discussed, in particular, of a cyclic structure
formed of three colour-singlets spinning around a ring-closed axis. It is shown
that the helicity and handedness of this structure can be related to the
quantum properties of the electron. The symmetry of this structure corresponds
to the complete cycle of -rotations of its constituents, which leads
to the exact overlapping of the paths of its three complementary coloured
constituents, making the system dynamically colourless. The gyromagnetic ratio
of this system is estimated to be g, which agrees with the Land\'e
g-factor for the electron.Comment: 11 pages, 4 figures, journal versio
Non-trivial stably free modules over crossed products
We consider the class of crossed products of noetherian domains with
universal enveloping algebras of Lie algebras. For algebras from this class we
give a sufficient condition for the existence of projective non-free modules.
This class includes Weyl algebras and universal envelopings of Lie algebras,
for which this question, known as noncommutative Serre's problem, was
extensively studied before. It turns out that the method of lifting of
non-trivial stably free modules from simple Ore extensions can be applied to
crossed products after an appropriate choice of filtration. The motivating
examples of crossed products are provided by the class of RIT algebras,
originating in non-equilibrium physics.Comment: 13 page
Slow, Steady-State Transport with "Loading" and Bulk Reactions: the Mixed Ionic Conductor LaCuO
We consider slow, steady transport for the normal state of the superconductor
LaCuO in a one-dimensional geometry, with surface fluxes
sufficiently general to permit oxygen to be driven into the sample (``loaded'')
either by electrochemical means or by high oxygen partial pressure. We include
the bulk reaction OO, where neutral atoms () go into ions
() and holes (). For slow, steady transport, the transport equations
simplify because the bulk reaction rate density and the bulk loading rates
then are uniform in space and time. All three fluxes must be
specified at each surface, which for a uniform current density corresponds
to five independent fluxes. These fluxes generate two types of static modes at
each surface and a bulk response with a voltage profile that varies
quadratically in space, characterized by and the total oxygen flux
(neutral plus ion) at each surface. One type of surface mode is associated with
electrical screening; the other type is associated both with diffusion and
drift, and with chemical reaction (the {\it diffusion-reaction mode}). The
diffusion-reaction mode is accompanied by changes in the chemical potentials
, and by reactions and fluxes, but it neither carries current (J=0) nor
loads the system chemically (). Generation of the diffusion-reaction
mode may explain the phenomenon of ``turbulence in the voltage'' often observed
near the electrodes of other mixed ionic electronic conductors (MIECs).Comment: 11 pages, 1 figur
Numerical Investigation of a Mesoscopic Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process
In this paper a spatial homogeneous vehicular traffic flow model based on a
stochastic master equation of Boltzmann type in the acceleration variable is
solved numerically for a special driver interaction model. The solution is done
by a modified direct simulation Monte Carlo method (DSMC) well known in non
equilibrium gas kinetic. The velocity and acceleration distribution functions
in stochastic equilibrium, mean velocity, traffic density, ACN, velocity
scattering and correlations between some of these variables and their car
density dependences are discussed.Comment: 23 pages, 10 figure
The thermodynamic dual structure of linear-dissipative driven systems
The spontaneous emergence of dynamical order, such as persistent currents, is
sometimes argued to require principles beyond the entropy maximization of the
second law of thermodynamics. I show that, for linear dissipation in the
Onsager regime, current formation can be driven by exactly the Jaynesian
principle of entropy maximization, suitably formulated for extended systems and
nonequilibrium boundary conditions. The Legendre dual structure of equilibrium
thermodynamics is also preserved, though it requires the admission of
current-valued state variables, and their correct incorporation in the entropy
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