16,438 research outputs found
Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
For a general class of linear collisional kinetic models in the torus,
including in particular the linearized Boltzmann equation for hard spheres, the
linearized Landau equation with hard and moderately soft potentials and the
semi-classical linearized fermionic and bosonic relaxation models, we prove
explicit coercivity estimates on the associated integro-differential operator
for some modified Sobolev norms. We deduce existence of classical solutions
near equilibrium for the full non-linear models associated, with explicit
regularity bounds, and we obtain explicit estimates on the rate of exponential
convergence towards equilibrium in this perturbative setting. The proof are
based on a linear energy method which combines the coercivity property of the
collision operator in the velocity space with transport effects, in order to
deduce coercivity estimates in the whole phase space
Passage-time distributions from a spin-boson detector model
The passage-time distribution for a spread-out quantum particle to traverse a
specific region is calculated using a detailed quantum model for the detector
involved. That model, developed and investigated in earlier works, is based on
the detected particle's enhancement of the coupling between a collection of
spins (in a metastable state) and their environment. We treat the continuum
limit of the model, under the assumption of the Markov property, and calculate
the particle state immediately after the first detection. An explicit example
with 15 boson modes shows excellent agreement between the discrete model and
the continuum limit. Analytical expressions for the passage-time distribution
as well as numerical examples are presented. The precision of the measurement
scheme is estimated and its optimization discussed. For slow particles, the
precision goes like , which improves previous estimates,
obtained with a quantum clock model.Comment: 11 pages, 6 figures; minor changes, references corrected; accepted
for publication in Phys. Rev.
A Theory of Errors in Quantum Measurement
It is common to model random errors in a classical measurement by the normal
(Gaussian) distribution, because of the central limit theorem. In the quantum
theory, the analogous hypothesis is that the matrix elements of the error in an
observable are distributed normally. We obtain the probability distribution
this implies for the outcome of a measurement, exactly for the case of 2x2
matrices and in the steepest descent approximation in general. Due to the
phenomenon of `level repulsion', the probability distributions obtained are
quite different from the Gaussian.Comment: Based on talk at "Spacetime and Fundamental Interactions: Quantum
Aspects" A conference to honor A. P. Balachandran's 65th Birthda
Probing of the Kondo peak by the impurity charge measurement
We consider the real-time dynamics of the Kondo system after the local probe
of the charge state of the magnetic impurity. Using the exactly solvable
infinite-degeneracy Anderson model we find explicitly the evolution of the
impurity charge after the measurement.Comment: 4 pages, 1 eps figure, revte
Weak Measurements with Arbitrary Pointer States
The exact conditions on valid pointer states for weak measurements are
derived. It is demonstrated that weak measurements can be performed with any
pointer state with vanishing probability current density. This condition is
found both for weak measurements of noncommuting observables and for -number
observables. In addition, the interaction between pointer and object must be
sufficiently weak. There is no restriction on the purity of the pointer state.
For example, a thermal pointer state is fully valid.Comment: 4 page
Classical, quantum and total correlations
We discuss the problem of separating consistently the total correlations in a
bipartite quantum state into a quantum and a purely classical part. A measure
of classical correlations is proposed and its properties are explored.Comment: 10 pages, 3 figure
Relative momentum for identical particles
Possible definitions for the relative momentum of identical particles are
considered
Universal scaling dynamics in a perturbed granular gas
We study the response of a granular system at rest to an instantaneous input
of energy in a localised region. We present scaling arguments that show that,
in dimensions, the radius of the resulting disturbance increases with time
as , and the energy decreases as , where the
exponent is independent of the coefficient of restitution. We
support our arguments with an exact calculation in one dimension and event
driven molecular dynamic simulations of hard sphere particles in two and three
dimensions.Comment: 5 pages, 5 figure
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