29 research outputs found
Transverse magnetization and transient oscillations in the quantum tunneling of molecular magnets
We calculate the response of a molecular magnet subject to a time-varying
magnetic field and coupled to a heat bath. We propose that observations of
calculated oscillations transverse to the field direction may be an effective
way of demonstrating quantum tunneling and thus probing the details of level
repulsion. The effective model of a triangle of Heisenberg spins and weak
anisotropies, as has been used to model the molecular magnets V15 and Cu3, is
used to illustrate this
Unfolding protein with an atomic force microscope: Force-fluctuation induced non-exponential kinetics
We show that in experimental atomic force microscopy studies of the lifetime
distribution of mechanically stressed folded proteins the effects of externally
applied fluctuations can not be distinguished from those of internally present
fluctuations. In certain circumstances this leads to artificially
non-exponential lifetime distributions which can be misinterpreted as a
signature of protein complexity. This work highlights the importance of fully
characterizing and controlling external sources of fluctuation in mechanical
studies of proteins before drawing conclusions on the physics at play on the
molecular level
Grassmann techniques applied to classical spin systems
We review problems involving the use of Grassmann techniques in the field of
classical spin systems in two dimensions. These techniques are useful to
perform exact correspondences between classical spin Hamiltonians and
field-theory fermionic actions. This contributes to a better understanding of
critical behavior of these models in term of non-quadratic effective actions
which can been seen as an extension of the free fermion Ising model. Within
this method, identification of bare masses allows for an accurate estimation of
critical points or lines and which is supported by Monte-Carlo results and
diagrammatic techniques
Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics
Fluctuations of global additive quantities, like total energy or
magnetization for instance, can in principle be described by statistics of sums
of (possibly correlated) random variables. Yet, it turns out that extreme
values (the largest value among a set of random variables) may also play a role
in the statistics of global quantities, in a direct or indirect way. This
review discusses different connections that may appear between problems of sums
and of extreme values of random variables, and emphasizes physical situations
in which such connections are relevant. Along this line of thought, standard
convergence theorems for sums and extreme values of independent and identically
distributed random variables are recalled, and some rigorous results as well as
more heuristic reasonings are presented for correlated or non-identically
distributed random variables. More specifically, the role of extreme values
within sums of broadly distributed variables is addressed, and a general
mapping between extreme values and sums is presented, allowing us to identify a
class of correlated random variables whose sum follows (generalized) extreme
value distributions. Possible applications of this specific class of random
variables are illustrated on the example of two simple physical models. A few
extensions to other related classes of random variables sharing similar
qualitative properties are also briefly discussed, in connection with the
so-called BHP distribution.Comment: 58 pages, final version, typo corrected in Theorem
The role of quantum measurement in stochastic thermodynamics
This article sets up a new formalism to investigate stochastic thermodynamics
in the quantum regime, where stochasticity and irreversibility primarily come
from quantum measurement. In the absence of any bath, we define a purely
quantum component to heat exchange, that corresponds to energy fluctuations
caused by measurement back-action. Energetic and entropic signatures of
measurement induced irreversibility are then investigated for canonical
experiments of quantum optics, and the energetic cost of counter-acting
decoherence is characterized on a simple state-stabilizing protocol. By placing
quantum measurement in a central position, our formalism contributes to bridge
a gap between experimental quantum optics and quantum thermodynamics
Criterion for universality class independent critical fluctuations: example of the 2D Ising model
Order parameter fluctuations for the two dimensional Ising model in the
region of the critical temperature are presented. A locus of temperatures T*(L)
and of magnetic fields B*(L) are identified, for which the probability density
function is similar to that for the 2D-XY model in the spin wave
approximation.The characteristics of the fluctuations along these points are
largely independent of universality class. We show that the largest range of
fluctuations relative to the variance of the distribution occurs along these
loci of points, rather than at the critical temperature itself and we discuss
this observation in terms of intermittency. Our motivation is the
identification of a generic form for fluctuations in correlated systems in
accordance with recent experimental and numerical observations. We conclude
that a universality class dependent form for the fluctuations is a
particularity of critical phenomena related to the change in symmetry at a
phase transition.Comment: to appear in Phys. Rev.
Quelques aspects de physique statistique des systèmes corrélés
This thesis deals with different aspects of statistical physics of correlated systems. The first partis related to the fluctuations of global quantities in correlated systems. Various studies clam that suchfluctuations are well described by the BHP distribution. We use the 2D Ising model to test and quantifythis proposition. Using observations from Monte Carlo simulations, we build a theoretical analysis, showingthat the apparent universality of the BHP distribution is related to the Gaussian model obtained fromperturbation expansion. Deviations from BHP, due to a non-linear term are expected. In the second partwe consider a new model for a 1/f classical intermittent noise and study its effects on the dephasing of atwo-level system.Within this model, the evolution of the relative phase between the two states is described asa continuous time random walk. Using renewal theory, we find exact expressions for the dephasing factor andidentify the physically relevant various regimes in terms of the coupling to the noise. In particular, we pointout the consequences of the non-stationarity and pronounced non-Gaussian features of this noise, includingsome new anomalous and aging dephasing scenarios. In the last part we present an alternative method toobtain some exact results for the 2D Ising model with a boundary magnetic field, for a finite size system.This method is a generalisation of ideas from Plechko presented for the 2D Ising model in zero field, basedon the representation of the Ising model using a Grassmann algebra. A Gaussian 1D action is obtained for ageneral configuration of the boundary magnetic field. When the magnetic field is homogeneous, our resultsare in agreement with McCoy and Wu's previous work. This 1D action is used to compute in an efficientway the free energy in a special case of inhomogeneous boundary magnetic field. This allows us to computethe phase diagram of a wetting transition induced by a boundary defect.Les travaux regroupés dans cette th`ese traitent de différents aspects de la physique statistique dessystèmes corrélés. Dans la première partie de cette thèse on s'intéresse aux fluctuations de grandeurs globalesdans les systèmes corrélés, dont de nombreux travaux sur des systèmes variés proposent qu'elles soientbien d´ecrites par la distribution BHP issue du modèle XY 2d. Le modèle d'Ising 2d est utilisé pour tester cette proposition et laquantifier. En utilisant des observations issues de simulations Monte Carlo, une étude analytique montre quel'apparente universalité de BHP est reliée au modèle gaussien obtenu par perturbation. et que des écarts àBHP d'importance variable existe, provenant de la contribution d'un terme non-gaussien. Dans la secondepartie, on s'intéresse à l'étude de la décohérence d'un système quantique à deux niveaux, induite par unbruit intermittent présentant un spectre en 1/f et du vieillissement. Un tel bruit peut schématiser l'effet d'unenvironnement corrélé sur un Qbit. En utilisant des résultats de probabilité, on peut calculer le facteur dedécohérence dans de nombreux régimes. On obtient alors des scénarios de décohérence anormaux, présentantune décroissance en loi de puissance aux temps longs, ainsi que de la non-stationnarité. Enfin la dernièrepartie est dédiée `a l'étude des solutions exactes du modèle d'Ising 2d classique, avec un champ magnétiquesur un bord. En généralisant une méthode due à Plechko, on obtient la fonction de partition de ce systèmeau moyen d'une action gaussienne fermionique unidimensionnelle. Dans le cas d'un champ homogène, onretrouve les résultats précédents de McCoy et Wu. On peut aller au-delà en considérant le cas où le champmagnétique change de direction une fois au bord. Cette méthode permet alors de décrire une transition detype mouillage, induite par ce défaut d'orientation. Il est en particulier possible d'obtenir analytiquement lediagramme de phase de ce système
Temperature can enhance coherent oscillations at a Landau-Zener transition
We consider sweeping a system through a Landau-Zener avoided-crossing, when
that system is also coupled to an environment or noise. Unsurprisingly, we find
that decoherence suppresses the coherent oscillations of quantum superpositions
of system states, as superpositions decohere into mixed states. However, we
also find an effect we call "Lamb-assisted coherent oscillations", in which a
Lamb shift exponentially enhances the coherent oscillation amplitude. This
dominates for high-frequency environments such as super-Ohmic environments,
where the coherent oscillations can grow exponentially as either the
environment coupling or temperature are increased. The effect could be used as
an experimental probe for high-frequency environments in such systems as
molecular magnets, solid-state qubits, spin-polarized gases (neutrons or He3)
or Bose-condensates.Comment: 4 Pages & 4 Figs - New version: introduction extended & citations
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Generalised extreme value statistics and sum of correlated variables
We show that generalised extreme value statistics -the statistics of the k-th
largest value among a large set of random variables- can be mapped onto a
problem of random sums. This allows us to identify classes of non-identical and
(generally) correlated random variables with a sum distributed according to one
of the three (k-dependent) asymptotic distributions of extreme value
statistics, namely the Gumbel, Frechet and Weibull distributions. These
classes, as well as the limit distributions, are naturally extended to real
values of k, thus providing a clear interpretation to the onset of Gumbel
distributions with non-integer index k in the statistics of global observables.
This is one of the very few known generalisations of the central limit theorem
to non-independent random variables. Finally, in the context of a simple
physical model, we relate the index k to the ratio of the correlation length to
the system size, which remains finite in strongly correlated systems.Comment: To appear in J.Phys.