8,526 research outputs found
Glauber dynamics for the quantum Ising model in a transverse field on a regular tree
Motivated by a recent use of Glauber dynamics for Monte-Carlo simulations of
path integral representation of quantum spin models [Krzakala, Rosso,
Semerjian, and Zamponi, Phys. Rev. B (2008)], we analyse a natural Glauber
dynamics for the quantum Ising model with a transverse field on a finite graph
. We establish strict monotonicity properties of the equilibrium
distribution and we extend (and improve) the censoring inequality of Peres and
Winkler to the quantum setting. Then we consider the case when is a regular
-ary tree and prove the same fast mixing results established in [Martinelli,
Sinclair, and Weitz, Comm. Math. Phys. (2004)] for the classical Ising model.
Our main tool is an inductive relation between conditional marginals (known as
the "cavity equation") together with sharp bounds on the operator norm of the
derivative at the stable fixed point. It is here that the main difference
between the quantum and the classical case appear, as the cavity equation is
formulated here in an infinite dimensional vector space, whereas in the
classical case marginals belong to a one-dimensional space
A probabilistic approach to evaluate the risk due to a fire in unidirectional road tunnels ventilated by jet fans
The risk produced by a fire is one of the most important aspects to be analysed for the safety of a road tunnel. In one-way ventilated tunnels with jet-fans it may happen that during a fire the fumes move in the opposite direction to that of the fresh air entering the tunnel. This phenomenon (back-layering) can involve people fleeing towards the mouth of the mountain with dramatic consequences. Since many parameters that characterize the phenomenon are known only with a certain approximation, it is necessary to adopt a probabilistic approach. In this work this approach is illustrated, applying it to a road tunnel in Northern Italy. The probability that the fumes of the fire can reach people fleeing has been plotted as a function of the total number of jet-fans in the tunnel, so that the definition of the ventilation system can be carried out in the design phase in relation to safety during the emergency phase
Lacunary generating functions of Hermite polynomials and symbolic methods
We employ an umbral formalism to reformulate the theory of Hermite polynomials and the derivation of the associated lacunary generating functions
Low-Metallicity Gas Clouds in a Galaxy Proto-Cluster at Redshift 2.38
We present high resolution spectroscopy of a QSO whose sight-line passes
through the halo of a pair of elliptical galaxies at redshift 2.38. This pair
of galaxies probably lies at the center of a galaxy proto-cluster, and is
embedded in a luminous extended Ly-alpha nebula.
The QSO sight-line intersects two small gas clouds within this halo. These
clouds have properties similar to those of high velocity clouds (HVCs) seen in
the halo of the Milky Way. The gas is in a cool (< 2 x 10^4 K) and at least 20%
neutral phase, with metallicities in the range -3.0 < [Fe/H] < -1.1 and neutral
hydrogen column densities of ~10^19.5 /cm^2.
The origin of these clouds is unclear. The presence of low metallicity gas
within this possible proto-cluster implies either that the intra-cluster medium
has not been enriched with metals at this redshift, or the clouds are embedded
within a hot, ionized, metal-rich gas phase.Comment: Accepted to appear in ApJ Letter
Cutoff for the Ising model on the lattice
Introduced in 1963, Glauber dynamics is one of the most practiced and
extensively studied methods for sampling the Ising model on lattices. It is
well known that at high temperatures, the time it takes this chain to mix in
on a system of size is . Whether in this regime there is
cutoff, i.e. a sharp transition in the -convergence to equilibrium, is a
fundamental open problem: If so, as conjectured by Peres, it would imply that
mixing occurs abruptly at for some fixed , thus providing
a rigorous stopping rule for this MCMC sampler. However, obtaining the precise
asymptotics of the mixing and proving cutoff can be extremely challenging even
for fairly simple Markov chains. Already for the one-dimensional Ising model,
showing cutoff is a longstanding open problem.
We settle the above by establishing cutoff and its location at the high
temperature regime of the Ising model on the lattice with periodic boundary
conditions. Our results hold for any dimension and at any temperature where
there is strong spatial mixing: For this carries all the way to the
critical temperature. Specifically, for fixed , the continuous-time
Glauber dynamics for the Ising model on with periodic boundary
conditions has cutoff at , where is
the spectral gap of the dynamics on the infinite-volume lattice. To our
knowledge, this is the first time where cutoff is shown for a Markov chain
where even understanding its stationary distribution is limited.
The proof hinges on a new technique for translating to mixing
which enables the application of log-Sobolev inequalities. The technique is
general and carries to other monotone and anti-monotone spin-systems.Comment: 34 pages, 3 figure
Cutoff for the East process
The East process is a 1D kinetically constrained interacting particle system,
introduced in the physics literature in the early 90's to model liquid-glass
transitions. Spectral gap estimates of Aldous and Diaconis in 2002 imply that
its mixing time on sites has order . We complement that result and show
cutoff with an -window.
The main ingredient is an analysis of the front of the process (its rightmost
zero in the setup where zeros facilitate updates to their right). One expects
the front to advance as a biased random walk, whose normal fluctuations would
imply cutoff with an -window. The law of the process behind the
front plays a crucial role: Blondel showed that it converges to an invariant
measure , on which very little is known. Here we obtain quantitative
bounds on the speed of convergence to , finding that it is exponentially
fast. We then derive that the increments of the front behave as a stationary
mixing sequence of random variables, and a Stein-method based argument of
Bolthausen ('82) implies a CLT for the location of the front, yielding the
cutoff result.
Finally, we supplement these results by a study of analogous kinetically
constrained models on trees, again establishing cutoff, yet this time with an
-window.Comment: 33 pages, 2 figure
Application of the tying force method in the design of alternative load paths in post-and-beam timber structures: A case building
This work aims to present an application of the tying force method recently proposed in the literature to a mid-rise post-and-beam timber building. Internal and edge column loss scenarios are analysed. A steel-to-timber connection is proposed and extensively evaluated as a potential solution to ensure the robustness of the structure, thereby satisfying the requirements imposed by the tying force method and effectively minimizing the risk of progressive collapse of the structure. Finally, a parametric analysis evaluating the variation of the tying force as a function of the chord rotation and different beam span lengths is carried out. The results obtained show that the tying force method represents a promising and rapid strategy for designing robust post-and-beam timber buildings falling in low and medium consequence classes
Light hadron spectroscopy on the lattice with the non-perturbatively improved Wilson action
We present results for the light meson masses and decay constants as obtained
from calculations with the non-perturbatively improved (`Alpha') action and
operators on a 24^3 \times 64 lattice at beta = 6.2, in the quenched
approximation. The analysis was performed in a way consistent with O(a)
improvement. We obtained: reasonable agreement with experiment for the
hyperfine splitting; f_K=156(17) MeV, f_pi =139(22) MeV, f_K/f_pi = 1.13(4) ;
f_{K*}=219(7) MeV, f_rho =199(15) MeV, f_phi =235(4) MeV; f_{K*}^{T}(2 GeV) =
178(10) MeV, f_rho^{T}(2 GeV) =165(11) MeV, where f_V^{T} is the coupling of
the tensor current to the vector mesons; the chiral condensate
^\bar{MS} (2 GeV)= - (253 +/- 25 MeV)^3. Our results are compared to
those obtained with the unimproved Wilson action. We also verified that the
free-boson lattice dispersion relation describes our results very accurately
for a large range of momenta.Comment: 29 pages (LaTeX), 14 Postscript figure
Robust polarization-based quantum key distribution over collective-noise channel
We present two polarization-based protocols for quantum key distribution. The
protocols encode key bits in noiseless subspaces or subsystems, and so can
function over a quantum channel subjected to an arbitrary degree of collective
noise, as occurs, for instance, due to rotation of polarizations in an optical
fiber. These protocols can be implemented using only entangled photon-pair
sources, single-photon rotations, and single-photon detectors. Thus, our
proposals offer practical and realistic alternatives to existing schemes for
quantum key distribution over optical fibers without resorting to
interferometry or two-way quantum communication, thereby circumventing,
respectively, the need for high precision timing and the threat of Trojan horse
attacks.Comment: Minor changes, added reference
Axially open nonradiative structures: an example of single-mode resonator based on the sample holder
The concept of nonradiative dielectric resonator is generalized in order to
include axially open configurations having rotational invariance. The resulting
additional nonradiative conditions are established for the different resonance
modes on the basis of their azimuthal modal index. An approximate chart of the
allowed dielectric and geometrical parameters for the TE011 mode is given. A
practical realization of the proposed device based on commercial fused quartz
tubes is demonstrated at millimeter wavelengths, together with simple
excitation and tuning mechanisms. The observed resonances are characterized in
their basic parameters, as well as in the field distribution by means of a
finite element method. The predictions of the theoretical analysis are well
confirmed, both in the general behaviour and in the expected quality factors.
The resulting device, in which the sample holder acts itself as single-mode
resonating element, combines an extreme ease of realization with
state-of-the-art performances. The general benefits of the proposed open
single-mode resonators are finally discussed.Comment: 18 pages, 10 figure
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