1,435 research outputs found
Approach to ground state and time-independent photon bound for massless spin-boson models
It is widely believed that an atom interacting with the electromagnetic field
(with total initial energy well-below the ionization threshold) relaxes to its
ground state while its excess energy is emitted as radiation. Hence, for large
times, the state of the atom+field system should consist of the atom in its
ground state, and a few free photons that travel off to spatial infinity.
Mathematically, this picture is captured by the notion of asymptotic
completeness. Despite some recent progress on the spectral theory of such
systems, a proof of relaxation to the ground state and asymptotic completeness
was/is still missing, except in some special cases (massive photons, small
perturbations of harmonic potentials). In this paper, we partially fill this
gap by proving relaxation to an invariant state in the case where the atom is
modelled by a finite-level system. If the coupling to the field is sufficiently
infrared-regular so that the coupled system admits a ground state, then this
invariant state necessarily corresponds to the ground state. Assuming slightly
more infrared regularity, we show that the number of emitted photons remains
bounded in time. We hope that these results bring a proof of asymptotic
completeness within reach.Comment: 45 pages, published in Annales Henri Poincare. This archived version
differs from the journal version because we corrected an inconsequential
mistake in Section 3.5.1: to do this, a new paragraph was added after Lemma
3.
Non-equilibrium work relations
This is a brief review of recently derived relations describing the behaviour
of systems far from equilibrium. They include the Fluctuation Theorem,
Jarzynski's and Crooks' equalities, and an extended form of the Second
Principle for general steady states. They are very general and their proofs
are, in most cases, disconcertingly simple.Comment: Brief Summer School Lecture Note
'Return to equilibrium' for weakly coupled quantum systems: a simple polymer expansion
Recently, several authors studied small quantum systems weakly coupled to
free boson or fermion fields at positive temperature. All the approaches we are
aware of employ complex deformations of Liouvillians or Mourre theory (the
infinitesimal version of the former). We present an approach based on polymer
expansions of statistical mechanics. Despite the fact that our approach is
elementary, our results are slightly sharper than those contained in the
literature up to now. We show that, whenever the small quantum system is known
to admit a Markov approximation (Pauli master equation \emph{aka} Lindblad
equation) in the weak coupling limit, and the Markov approximation is
exponentially mixing, then the weakly coupled system approaches a unique
invariant state that is perturbatively close to its Markov approximation.Comment: 23 pages, v2-->v3: Revised version: The explanatory section 1.7 has
changed and Section 3.2 has been made more explici
Fluctuation theorems for stochastic dynamics
Fluctuation theorems make use of time reversal to make predictions about
entropy production in many-body systems far from thermal equilibrium. Here we
review the wide variety of distinct, but interconnected, relations that have
been derived and investigated theoretically and experimentally. Significantly,
we demonstrate, in the context of Markovian stochastic dynamics, how these
different fluctuation theorems arise from a simple fundamental time-reversal
symmetry of a certain class of observables. Appealing to the notion of Gibbs
entropy allows for a microscopic definition of entropy production in terms of
these observables. We work with the master equation approach, which leads to a
mathematically straightforward proof and provides direct insight into the
probabilistic meaning of the quantities involved. Finally, we point to some
experiments that elucidate the practical significance of fluctuation relations.Comment: 48 pages, 2 figures. v2: minor changes for consistency with published
versio
Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
The fluctuations in nonequilibrium systems are under intense theoretical and
experimental investigation. Topical ``fluctuation relations'' describe
symmetries of the statistical properties of certain observables, in a variety
of models and phenomena. They have been derived in deterministic and, later, in
stochastic frameworks. Other results first obtained for stochastic processes,
and later considered in deterministic dynamics, describe the temporal evolution
of fluctuations. The field has grown beyond expectation: research works and
different perspectives are proposed at an ever faster pace. Indeed,
understanding fluctuations is important for the emerging theory of
nonequilibrium phenomena, as well as for applications, such as those of
nanotechnological and biophysical interest. However, the links among the
different approaches and the limitations of these approaches are not fully
understood. We focus on these issues, providing: a) analysis of the theoretical
models; b) discussion of the rigorous mathematical results; c) identification
of the physical mechanisms underlying the validity of the theoretical
predictions, for a wide range of phenomena.Comment: 44 pages, 2 figures. To appear in Nonlinearity (2007
Relating the thermodynamic arrow of time to the causal arrow
Consider a Hamiltonian system that consists of a slow subsystem S and a fast
subsystem F. The autonomous dynamics of S is driven by an effective
Hamiltonian, but its thermodynamics is unexpected. We show that a well-defined
thermodynamic arrow of time (second law) emerges for S whenever there is a
well-defined causal arrow from S to F and the back-action is negligible. This
is because the back-action of F on S is described by a non-globally Hamiltonian
Born-Oppenheimer term that violates the Liouville theorem, and makes the second
law inapplicable to S. If S and F are mixing, under the causal arrow condition
they are described by microcanonic distributions P(S) and P(S|F). Their
structure supports a causal inference principle proposed recently in machine
learning.Comment: 10 page
Search for the standard model Higgs boson in the H to ZZ to 2l 2nu channel in pp collisions at sqrt(s) = 7 TeV
A search for the standard model Higgs boson in the H to ZZ to 2l 2nu decay
channel, where l = e or mu, in pp collisions at a center-of-mass energy of 7
TeV is presented. The data were collected at the LHC, with the CMS detector,
and correspond to an integrated luminosity of 4.6 inverse femtobarns. No
significant excess is observed above the background expectation, and upper
limits are set on the Higgs boson production cross section. The presence of the
standard model Higgs boson with a mass in the 270-440 GeV range is excluded at
95% confidence level.Comment: Submitted to JHE
Search for New Physics with Jets and Missing Transverse Momentum in pp collisions at sqrt(s) = 7 TeV
A search for new physics is presented based on an event signature of at least
three jets accompanied by large missing transverse momentum, using a data
sample corresponding to an integrated luminosity of 36 inverse picobarns
collected in proton--proton collisions at sqrt(s)=7 TeV with the CMS detector
at the LHC. No excess of events is observed above the expected standard model
backgrounds, which are all estimated from the data. Exclusion limits are
presented for the constrained minimal supersymmetric extension of the standard
model. Cross section limits are also presented using simplified models with new
particles decaying to an undetected particle and one or two jets
Search for anomalous t t-bar production in the highly-boosted all-hadronic final state
A search is presented for a massive particle, generically referred to as a
Z', decaying into a t t-bar pair. The search focuses on Z' resonances that are
sufficiently massive to produce highly Lorentz-boosted top quarks, which yield
collimated decay products that are partially or fully merged into single jets.
The analysis uses new methods to analyze jet substructure, providing
suppression of the non-top multijet backgrounds. The analysis is based on a
data sample of proton-proton collisions at a center-of-mass energy of 7 TeV,
corresponding to an integrated luminosity of 5 inverse femtobarns. Upper limits
in the range of 1 pb are set on the product of the production cross section and
branching fraction for a topcolor Z' modeled for several widths, as well as for
a Randall--Sundrum Kaluza--Klein gluon. In addition, the results constrain any
enhancement in t t-bar production beyond expectations of the standard model for
t t-bar invariant masses larger than 1 TeV.Comment: Submitted to the Journal of High Energy Physics; this version
includes a minor typo correction that will be submitted as an erratu
Combined search for the quarks of a sequential fourth generation
Results are presented from a search for a fourth generation of quarks
produced singly or in pairs in a data set corresponding to an integrated
luminosity of 5 inverse femtobarns recorded by the CMS experiment at the LHC in
2011. A novel strategy has been developed for a combined search for quarks of
the up and down type in decay channels with at least one isolated muon or
electron. Limits on the mass of the fourth-generation quarks and the relevant
Cabibbo-Kobayashi-Maskawa matrix elements are derived in the context of a
simple extension of the standard model with a sequential fourth generation of
fermions. The existence of mass-degenerate fourth-generation quarks with masses
below 685 GeV is excluded at 95% confidence level for minimal off-diagonal
mixing between the third- and the fourth-generation quarks. With a mass
difference of 25 GeV between the quark masses, the obtained limit on the masses
of the fourth-generation quarks shifts by about +/- 20 GeV. These results
significantly reduce the allowed parameter space for a fourth generation of
fermions.Comment: Replaced with published version. Added journal reference and DO
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