103 research outputs found
Discrete-time Quantum Walks in random artificial Gauge Fields
Discrete-time quantum walks (DTQWs) in random artificial electric and
gravitational fields are studied analytically and numerically. The analytical
computations are carried by a new method which allows a direct exact analytical
determination of the equations of motion obeyed by the average density
operator. It is proven that randomness induces decoherence and that the quantum
walks behave asymptotically like classical random walks. Asymptotic diffusion
coefficients are computed exactly. The continuous limit is also obtained and
discussed.Comment: 16 pages, 9 figures. Submitted to Physica
Central Limit Theorem for a Class of Relativistic Diffusions
Two similar Minkowskian diffusions have been considered, on one hand by
Barbachoux, Debbasch, Malik and Rivet ([BDR1], [BDR2], [BDR3], [DMR], [DR]),
and on the other hand by Dunkel and H\"anggi ([DH1], [DH2]). We address here
two questions, asked in [DR] and in ([DH1], [DH2]) respectively, about the
asymptotic behaviour of such diffusions. More generally, we establish a central
limit theorem for a class of Minkowskian diffusions, to which the two above
ones belong. As a consequence, we correct a partially wrong guess in [DH1].Comment: 20 page
Effective Dissipation and Turbulence in Spectrally Truncated Euler Flows
A new transient regime in the relaxation towards absolute equilibrium of the
conservative and time-reversible 3-D Euler equation with high-wavenumber
spectral truncation is characterized. Large-scale dissipative effects, caused
by the thermalized modes that spontaneously appear between a transition
wavenumber and the maximum wavenumber, are calculated using fluctuation
dissipation relations. The large-scale dynamics is found to be similar to that
of high-Reynolds number Navier-Stokes equations and thus to obey (at least
approximately) Kolmogorov scaling.Comment: 4 pages, 5 figures new version with only 4 figures; title changed;
manuscript changed; accepted by PR
Invariance of the relativistic one-particle distribution function
The one-particle distribution function is of importance both in
non-relativistic and relativistic statistical physics. In the relativistic
framework, Lorentz invariance is possibly its most fundamental property. The
present article on the subject is a contrastive one: we review, discuss
critically, and, when necessary, complete, the treatments found in the standard
literature
Discrete-time quantum walks: continuous limit and symmetries
The continuous limit of one dimensional discrete-time quantum walks with
time- and space-dependent coefficients is investigated. A given quantum walk
does not generally admit a continuous limit but some families (1-jets) of
quantum walks do. All families (1-jets) admitting a continuous limit are
identified. The continuous limit is described by a Dirac-like equation or,
alternately, a couple of Klein-Gordon equations. Variational principles leading
to these equations are also discussed, together with local invariance
properties
Curvature Diffusions in General Relativity
We define and study on Lorentz manifolds a family of covariant diffusions in
which the quadratic variation is locally determined by the curvature. This
allows the interpretation of the diffusion effect on a particle by its
interaction with the ambient space-time. We will focus on the case of warped
products, especially Robertson-Walker manifolds, and analyse their asymptotic
behaviour in the case of Einstein-de Sitter-like manifolds.Comment: 34 page
Fokker-Planck type equations for a simple gas and for a semi-relativistic Brownian motion from a relativistic kinetic theory
A covariant Fokker-Planck type equation for a simple gas and an equation for
the Brownian motion are derived from a relativistic kinetic theory based on the
Boltzmann equation. For the simple gas the dynamic friction four-vector and the
diffusion tensor are identified and written in terms of integrals which take
into account the collision processes. In the case of Brownian motion, the
Brownian particles are considered as non-relativistic whereas the background
gas behaves as a relativistic gas. A general expression for the
semi-relativistic viscous friction coefficient is obtained and the particular
case of constant differential cross-section is analyzed for which the
non-relativistic and ultra relativistic limiting cases are calculated.Comment: To appear in PR
Nonlocal observables and lightcone-averaging in relativistic thermodynamics
The unification of relativity and thermodynamics has been a subject of
considerable debate over the last 100 years. The reasons for this are twofold:
(i) Thermodynamic variables are nonlocal quantities and, thus, single out a
preferred class of hyperplanes in spacetime. (ii) There exist different,
seemingly equally plausible ways of defining heat and work in relativistic
systems. These ambiguities led, for example, to various proposals for the
Lorentz transformation law of temperature. Traditional 'isochronous'
formulations of relativistic thermodynamics are neither theoretically
satisfactory nor experimentally feasible. Here, we demonstrate how these
deficiencies can be resolved by defining thermodynamic quantities with respect
to the backward-lightcone of an observation event. This approach yields novel,
testable predictions and allows for a straightforward-extension of
thermodynamics to General Relativity. Our theoretical considerations are
illustrated through three-dimensional relativistic many-body simulations.Comment: typos in Eqs. (12) and (14) corrected, minor additions in the tex
Stationary Cylindrical Anisotropic Fluid
We present the whole set of equations with regularity and matching conditions
required for the description of physically meaningful stationary cylindrically
symmmetric distributions of matter, smoothly matched to Lewis vacuum spacetime.
A specific example is given. The electric and magnetic parts of the Weyl tensor
are calculated, and it is shown that purely electric solutions are necessarily
static. Then, it is shown that no conformally flat stationary cylindrical fluid
exits, satisfying regularity and matching conditions.Comment: 17 pages Latex. To appear in Gen.Rel.Gra
Improved Holographic QCD
We provide a review to holographic models based on Einstein-dilaton gravity
with a potential in 5 dimensions. Such theories, for a judicious choice of
potential are very close to the physics of large-N YM theory both at zero and
finite temperature. The zero temperature glueball spectra as well as their
finite temperature thermodynamic functions compare well with lattice data. The
model can be used to calculate transport coefficients, like bulk viscosity, the
drag force and jet quenching parameters, relevant for the physics of the
Quark-Gluon Plasma.Comment: LatEX, 65 pages, 28 figures, 9 Tables. Based on lectures given at
several Schools. To appear in the proceedinds of the 5th Aegean School
(Milos, Greece
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