133 research outputs found

### Models of Passive and Reactive Tracer Motion: an Application of Ito Calculus

By means of Ito calculus it is possible to find, in a straight-forward way,
the analytical solution to some equations related to the passive tracer
transport problem in a velocity field that obeys the multidimensional Burgers
equation and to a simple model of reactive tracer motion.Comment: revised version 7 pages, Latex, to appear as a letter to J. of
Physics

### Preheating after N-flation

We study preheating in N-flation, assuming the Mar\v{c}enko-Pastur mass
distribution, equal energy initial conditions at the beginning of inflation and
equal axion-matter couplings, where matter is taken to be a single, massless
bosonic field. By numerical analysis we find that preheating via parametric
resonance is suppressed, indicating that the old theory of perturbative
preheating is applicable. While the tensor-to-scalar ratio, the non-Gaussianity
parameters and the scalar spectral index computed for N-flation are similar to
those in single field inflation (at least within an observationally viable
parameter region), our results suggest that the physics of preheating can
differ significantly from the single field case.Comment: 14 pages, 14 figures, references added, fixed typo

### Equation-Free Dynamic Renormalization: Self-Similarity in Multidimensional Particle System Dynamics

We present an equation-free dynamic renormalization approach to the
computational study of coarse-grained, self-similar dynamic behavior in
multidimensional particle systems. The approach is aimed at problems for which
evolution equations for coarse-scale observables (e.g. particle density) are
not explicitly available. Our illustrative example involves Brownian particles
in a 2D Couette flow; marginal and conditional Inverse Cumulative Distribution
Functions (ICDFs) constitute the macroscopic observables of the evolving
particle distributions.Comment: 7 pages, 5 figure

### Non-intrusive and structure preserving multiscale integration of stiff ODEs, SDEs and Hamiltonian systems with hidden slow dynamics via flow averaging

We introduce a new class of integrators for stiff ODEs as well as SDEs. These
integrators are (i) {\it Multiscale}: they are based on flow averaging and so
do not fully resolve the fast variables and have a computational cost
determined by slow variables (ii) {\it Versatile}: the method is based on
averaging the flows of the given dynamical system (which may have hidden slow
and fast processes) instead of averaging the instantaneous drift of assumed
separated slow and fast processes. This bypasses the need for identifying
explicitly (or numerically) the slow or fast variables (iii) {\it
Nonintrusive}: A pre-existing numerical scheme resolving the microscopic time
scale can be used as a black box and easily turned into one of the integrators
in this paper by turning the large coefficients on over a microscopic timescale
and off during a mesoscopic timescale (iv) {\it Convergent over two scales}:
strongly over slow processes and in the sense of measures over fast ones. We
introduce the related notion of two-scale flow convergence and analyze the
convergence of these integrators under the induced topology (v) {\it Structure
preserving}: for stiff Hamiltonian systems (possibly on manifolds), they can be
made to be symplectic, time-reversible, and symmetry preserving (symmetries are
group actions that leave the system invariant) in all variables. They are
explicit and applicable to arbitrary stiff potentials (that need not be
quadratic). Their application to the Fermi-Pasta-Ulam problems shows accuracy
and stability over four orders of magnitude of time scales. For stiff Langevin
equations, they are symmetry preserving, time-reversible and Boltzmann-Gibbs
reversible, quasi-symplectic on all variables and conformally symplectic with
isotropic friction.Comment: 69 pages, 21 figure

### The quantum theory of measurement within dynamical reduction models

We analyze in mathematical detail, within the framework of the QMUPL model of
spontaneous wave function collapse, the von Neumann measurement scheme for the
measurement of a 1/2 spin particle. We prove that, according to the equation of
the model: i) throughout the whole measurement process, the pointer of the
measuring device is always perfectly well localized in space; ii) the
probabilities for the possible outcomes are distributed in agreement with the
Born probability rule; iii) at the end of the measurement the state of the
microscopic system has collapsed to the eigenstate corresponding to the
measured eigenvalue. This analysis shows rigorously how dynamical reduction
models provide a consistent solution to the measurement problem of quantum
mechanics.Comment: 24 pages, RevTeX. Minor changes mad

### Cosmological Inflation and the Quantum Measurement Problem

According to cosmological inflation, the inhomogeneities in our universe are
of quantum mechanical origin. This scenario is phenomenologically very
appealing as it solves the puzzles of the standard hot big bang model and
naturally explains why the spectrum of cosmological perturbations is almost
scale invariant. It is also an ideal playground to discuss deep questions among
which is the quantum measurement problem in a cosmological context. Although
the large squeezing of the quantum state of the perturbations and the
phenomenon of decoherence explain many aspects of the quantum to classical
transition, it remains to understand how a specific outcome can be produced in
the early universe, in the absence of any observer. The Continuous Spontaneous
Localization (CSL) approach to quantum mechanics attempts to solve the quantum
measurement question in a general context. In this framework, the wavefunction
collapse is caused by adding new non linear and stochastic terms to the
Schroedinger equation. In this paper, we apply this theory to inflation, which
amounts to solving the CSL parametric oscillator case. We choose the
wavefunction collapse to occur on an eigenstate of the Mukhanov-Sasaki variable
and discuss the corresponding modified Schroedinger equation. Then, we compute
the power spectrum of the perturbations and show that it acquires a universal
shape with two branches, one which remains scale invariant and one with nS=4, a
spectral index in obvious contradiction with the Cosmic Microwave Background
(CMB) anisotropy observations. The requirement that the non-scale invariant
part be outside the observational window puts stringent constraints on the
parameter controlling the deviations from ordinary quantum mechanics...
(Abridged).Comment: References added, minor corrections, conclusions unchange

### Differentiable potentials and metallic states in disordered one-dimensional systems

We provide evidence that as a general rule Anderson localization effects
become weaker as the degree of differentiability of the disordered potential
increases. In one dimension a band of metallic states exists provided that the
disordered potential is sufficiently correlated and has some minimum degree of
differentiability. Several examples are studied in detail. In agreement with
the one parameter scaling theory the motion in the metallic region is ballistic
if the spectral density is smooth. Finally, we study the most promising
settings to observe these results in the context of cold atoms.Comment: 5 pages, 3 figures, journal versio

### Stochastic Gravity

Gravity is treated as a stochastic phenomenon based on fluctuations of the
metric tensor of general relativity. By using a (3+1) slicing of spacetime, a
Langevin equation for the dynamical conjugate momentum and a Fokker-Planck
equation for its probability distribution are derived. The Raychaudhuri
equation for a congruence of timelike or null geodesics leads to a stochastic
differential equation for the expansion parameter $\theta$ in terms of the
proper time $s$. For sufficiently strong metric fluctuations, it is shown that
caustic singularities in spacetime can be avoided for converging geodesics. The
formalism is applied to the gravitational collapse of a star and the
Friedmann-Robertson-Walker cosmological model. It is found that owing to the
stochastic behavior of the geometry, the singularity in gravitational collapse
and the big-bang have a zero probability of occurring. Moreover, as a star
collapses the probability of a distant observer seeing an infinite red shift at
the Schwarzschild radius of the star is zero. Therefore, there is a vanishing
probability of a Schwarzschild black hole event horizon forming during
gravitational collapse.Comment: Revised version. Eq. (108) has been modified. Additional comments
have been added to text. Revtex 39 page

### STOCHASTIC DYNAMICS OF LARGE-SCALE INFLATION IN DE~SITTER SPACE

In this paper we derive exact quantum Langevin equations for stochastic
dynamics of large-scale inflation in de~Sitter space. These quantum Langevin
equations are the equivalent of the Wigner equation and are described by a
system of stochastic differential equations. We present a formula for the
calculation of the expectation value of a quantum operator whose Weyl symbol is
a function of the large-scale inflation scalar field and its time derivative.
The unique solution is obtained for the Cauchy problem for the Wigner equation
for large-scale inflation. The stationary solution for the Wigner equation is
found for an arbitrary potential. It is shown that the large-scale inflation
scalar field in de Sitter space behaves as a quantum one-dimensional
dissipative system, which supports the earlier results. But the analogy with a
one-dimensional model of the quantum linearly damped anharmonic oscillator is
not complete: the difference arises from the new time dependent commutation
relation for the large-scale field and its time derivative. It is found that,
for the large-scale inflation scalar field the large time asymptotics is equal
to the `classical limit'. For the large time limit the quantum Langevin
equations are just the classical stochastic Langevin equations (only the
stationary state is defined by the quantum field theory).Comment: 21 pages RevTex preprint styl

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