22,090 research outputs found
An embedding theorem for regular Mal'tsev categories
In this paper, we obtain a non-abelian analogue of Lubkin's embedding theorem
for abelian categories. Our theorem faithfully embeds any small regular
Mal'tsev category in an -th power of a particular locally
finitely presentable regular Mal'tsev category. The embedding preserves and
reflects finite limits, isomorphisms and regular epimorphisms, as in the case
of Barr's embedding theorem for regular categories. Furthermore, we show that
we can take to be the (cardinal) number of subobjects of the terminal
object in
A three-dimensional wavelet based multifractal method : about the need of revisiting the multifractal description of turbulence dissipation data
We generalize the wavelet transform modulus maxima (WTMM) method to
multifractal analysis of 3D random fields. This method is calibrated on
synthetic 3D monofractal fractional Brownian fields and on 3D multifractal
singular cascade measures as well as their random function counterpart obtained
by fractional integration. Then we apply the 3D WTMM method to the dissipation
field issue from 3D isotropic turbulence simulations. We comment on the need to
revisiting previous box-counting analysis which have failed to estimate
correctly the corresponding multifractal spectra because of their intrinsic
inability to master non-conservative singular cascade measures.Comment: 5 pages, 3figures, submitted to Phys. Rev. Let
Robust open-loop stabilization of Fock states by time-varying quantum interactions
A quantum harmonic oscillator (spring subsystem) is stabilized towards a
target Fock state by reservoir engineering. This passive and open-loop
stabilization works by consecutive and identical Hamiltonian interactions with
auxiliary systems, here three-level atoms (the auxiliary ladder subsystem),
followed by a partial trace over these auxiliary atoms. A scalar control input
governs the interaction, defining which atomic transition in the ladder
subsystem is in resonance with the spring subsystem. We use it to build a
time-varying interaction with individual atoms, that combines three
non-commuting steps. We show that the resulting reservoir robustly stabilizes
any initial spring state distributed between 0 and 4n+3 quanta of vibrations
towards a pure target Fock state of vibration number n. The convergence proof
relies on the construction of a strict Lyapunov function for the Kraus map
induced by this reservoir setting on the spring subsystem. Simulations with
realistic parameters corresponding to the quantum electrodynamics setup at
Ecole Normale Superieure further illustrate the robustness of the method
Deterministic submanifolds and analytic solution of the stochastic differential master equation describing a qubit
This paper studies the stochastic differential equation (SDE) associated to a
two-level quantum system (qubit) subject to Hamiltonian evolution as well as
unmonitored and monitored decoherence channels. The latter imply a stochastic
evolution of the quantum state (density operator), whose associated probability
distribution we characterize. We first show that for two sets of typical
experimental settings, corresponding either to weak quantum non demolition
measurements or to weak fluorescence measurements, the three Bloch coordinates
of the qubit remain confined to a deterministically evolving surface or curve
inside the Bloch sphere. We explicitly solve the deterministic evolution, and
we provide a closed-form expression for the probability distribution on this
surface or curve. Then we relate the existence in general of such
deterministically evolving submanifolds to an accessibility question of control
theory, which can be answered with an explicit algebraic criterion on the SDE.
This allows us to show that, for a qubit, the above two sets of weak
measurements are essentially the only ones featuring deterministic surfaces or
curves
Contraction and stability analysis of steady-states for open quantum systems described by Lindblad differential equations
For discrete-time systems, governed by Kraus maps, the work of D. Petz has
characterized the set of universal contraction metrics. In the present paper,
we use this characterization to derive a set of quadratic Lyapunov functions
for continuous-time systems, governed by Lindblad differential equations, that
have a steady-state with full rank. An extremity of this set is given by the
Bures metric, for which the quadratic Lyapunov function is obtained by
inverting a Sylvester equation. We illustrate the method by providing a strict
Lyapunov function for a Lindblad equation designed to stabilize a quantum
electrodynamic "cat" state by reservoir engineering. In fact we prove that any
Lindblad equation on the Hilbert space of the (truncated) harmonic oscillator,
which has a full-rank equilibrium and which has, among its decoherence
channels, a channel corresponding to the photon loss operator, globally
converges to that equilibrium.Comment: Submitted (10 pages, 1 figure
The random-lags approach: application to a microfounded model
It is well known that a one-dimensional discrete-time model may yield endogenous fluctuations while this is impossible in a one-dimensional continuous-time model. Invernizzi and Medio (1991) recast this time-modeling issue into an aggregation issue. They have proposed a "random-lags approach" as a way of preserving fluctuations while relaxing the discrete-time assumption. The present paper applies this approach to the model of Aghion, Bacchetta and Banerjee (2000), and shows that their result that economies at an intermediate level of financial development may be prone to economic fluctuations continues to hold when the discrete-time assumption is relaxed.continuous time; discrete time; fluctuations; aggregation
Small price change response to a large devaluation in a menu cost model
In an empirical paper based on five large devaluation episodes in Argentina, Brazil, Korea, Mexico and Thailand, Burstein and al. (2005a) find a very slow adjustment in the prices of non-tradable goods and services after large devaluations. Burnstein and al. (2005b) develop a quantitative general-equilibrium model that can account for this phenomenon. I consider an alternative, simpler model and explore under which conditions moderate menu costs can explain the muted response of the prices of non-tradables. The key new element in this alternative model is a nominal friction in wage-setting (generated by menu costs for changing wages). I find, for example, that although my model is based on menu costs, it is able to deliver not only constant prices of non-tradables, but also small price changes (in reality these prices do change, albeit by far less than the exchange rate). I also discuss the existence of multiple equilibria and the role of central-bank credibility.large devaluation; exchange rate; pass-through; sticky prices; sticky wages
- …