1,398 research outputs found
Entanglement in fermionic chains with finite range coupling and broken symmetries
We obtain a formula for the determinant of a block Toeplitz matrix associated
with a quadratic fermionic chain with complex coupling. Such couplings break
reflection symmetry and/or charge conjugation symmetry. We then apply this
formula to compute the Renyi entropy of a partial observation to a subsystem
consisting of contiguous sites in the limit of large . The present work
generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A
striking new feature of our formula for the entanglement entropy is the
appearance of a term scaling with the logarithm of the size of . This
logarithmic behaviour originates from certain discontinuities in the symbol of
the block Toeplitz matrix. Equipped with this formula we analyse the
entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev
fermionic chain with long range pairing.Comment: 27 pages, 5 figure
On the M\"obius transformation in the entanglement entropy of fermionic chains
There is an intimate relation between entanglement entropy and Riemann
surfaces. This fact is explicitly noticed for the case of quadratic fermionic
Hamiltonians with finite range couplings. After recollecting this fact, we make
a comprehensive analysis of the action of the M\"obius transformations on the
Riemann surface. We are then able to uncover the origin of some symmetries and
dualities of the entanglement entropy already noticed recently in the
literature. These results give further support for the use of entanglement
entropy to analyse phase transition.Comment: 29 pages, 5 figures. Final version published in JSTAT. Two new
figures. Some comments and references added. Typos correcte
Million frames per second infrared imaging system
An infrared imaging system has been developed for measuring the temperature increase during the dynamic deformation of materials. The system consists of an 8Ă—8 HgCdTe focal plane array, each with its own preamplifier. Outputs from the 64 detector/preamplifiers are digitized using a row-parallel scheme. In this approach, all 64 signals are simultaneously acquired and held using a bank of track and hold amplifiers. An array of eight 8:1 multiplexers then routes the signals to eight 10 MHz digitizers, acquiring data from each row of detectors in parallel. The maximum rate is one million frames per second. A fully reflective lens system was developed, consisting of two Schwarszchild objectives operating at infinite conjugation ratio. The ratio of the focal lengths of the objectives determines the lens magnification. The system has been used to image the distribution of temperature rise near the tip of a notch in a high strength steel sample (C-300) subjected to impact loading by a drop weight testing machine. The results show temperature rises at the crack tip up to around 70 K. Localization of temperature, and hence, of deformation into "U" shaped zones emanating from the notch tip is clearly seen, as is the onset of crack propagation
Super-roughening as a disorder-dominated flat phase
We study the phenomenon of super-roughening found on surfaces growing on
disordered substrates. We consider a one-dimensional version of the problem for
which the pure, ordered model exhibits a roughening phase transition. Extensive
numerical simulations combined with analytical approximations indicate that
super-roughening is a regime of asymptotically flat surfaces with non-trivial,
rough short-scale features arising from the competition between surface tension
and disorder. Based on this evidence and on previous simulations of the
two-dimensional Random sine-Gordon model [Sanchez et al., Phys. Rev. E 62, 3219
(2000)], we argue that this scenario is general and explains equally well the
hitherto poorly understood two-dimensional case.Comment: 7 pages, 4 figures. Accepted for publication in Europhysics Letter
CECM: A continuous empirical cubature method with application to the dimensional hyperreduction of parameterized finite element models
We present the Continuous Empirical Cubature Method (CECM), a novel algorithm
for empirically devising efficient integration rules. The CECM aims to improve
existing cubature methods by producing rules that are close to the optimal,
featuring far less points than the number of functions to integrate.
The CECM consists on a two-stage strategy. First, a point selection strategy
is applied for obtaining an initial approximation to the cubature rule,
featuring as many points as functions to integrate. The second stage consists
in a sparsification strategy in which, alongside the indexes and corresponding
weights, the spatial coordinates of the points are also considered as design
variables. The positions of the initially selected points are changed to render
their associated weights to zero, and in this way, the minimum number of points
is achieved.
Although originally conceived within the framework of hyper-reduced order
models (HROMs), we present the method's formulation in terms of generic
vector-valued functions, thereby accentuating its versatility across various
problem domains. To demonstrate the extensive applicability of the method, we
conduct numerical validations using univariate and multivariate Lagrange
polynomials. In these cases, we show the method's capacity to retrieve the
optimal Gaussian rule. We also asses the method for an arbitrary
exponential-sinusoidal function in a 3D domain, and finally consider an example
of the application of the method to the hyperreduction of a multiscale finite
element model, showcasing notable computational performance gains.
A secondary contribution of the current paper is the Sequential Randomized
SVD (SRSVD) approach for computing the Singular Value Decomposition (SVD) in a
column-partitioned format. The SRSVD is particularly advantageous when matrix
sizes approach memory limitations
Second order equation of motion for electromagnetic radiation back-reaction
We take the viewpoint that the physically acceptable solutions of the
Lorentz--Dirac equation for radiation back-reaction are actually determined by
a second order equation of motion, the self-force being given as a function of
spacetime location and velocity. We propose three different methods to obtain
this self-force function. For two example systems, we determine the second
order equation of motion exactly in the nonrelativistic regime via each of
these three methods, the three methods leading to the same result. We reveal
that, for both systems considered, back-reaction induces a damping proportional
to velocity and, in addition, it decreases the effect of the external force.Comment: 13 page
Experimental behaviour of a three-stage metal hydride hydrogen compressor
A three-stage metal hydride hydrogen compressor (MHHC) system based in
AB2-type alloys has been set-up. Every stage can be considered as a
Sieverts-type apparatus. The MHHC system can work in the pressure and
temperature ranges comprised from vacuum to 250 bar and from RT to 200C,
respectively. An efficient thermal management system was set up for the
operational ranges of temperature designed. It dumps temperature shifts due to
hydrogen expansion during stage coupling and hydrogen absorption/desorption in
the alloys. Each reactor consists of a single and thin stainless-steel tube to
maximize heat transfer. They are filled with similar amount of AB2 alloy. The
MHHC system was able to produce a compression ratio (CR) as high as of 84.7 for
inlet and outlet hydrogen pressures of 1.44 and 122 bar for a temperature span
of 23 to 120C
Hyper-reduction for Petrov-Galerkin reduced order models
Projection-based Reduced Order Models minimize the discrete residual of a
"full order model" (FOM) while constraining the unknowns to a reduced dimension
space. For problems with symmetric positive definite (SPD) Jacobians, this is
optimally achieved by projecting the full order residual onto the approximation
basis (Galerkin Projection). This is sub-optimal for non-SPD Jacobians as it
only minimizes the projection of the residual, not the residual itself. An
alternative is to directly minimize the 2-norm of the residual, achievable
using QR factorization or the method of the normal equations (LSPG). The first
approach involves constructing and factorizing a large matrix, while LSPG
avoids this but requires constructing a product element by element,
necessitating a complementary mesh and adding complexity to the hyper-reduction
process. This work proposes an alternative based on Petrov-Galerkin
minimization. We choose a left basis for a least-squares minimization on a
reduced problem, ensuring the discrete full order residual is minimized. This
is applicable to both SPD and non-SPD Jacobians, allowing element-by-element
assembly, avoiding the use of a complementary mesh, and simplifying finite
element implementation. The technique is suitable for hyper-reduction using the
Empirical Cubature Method and is applicable in nonlinear reduction procedures
Entanglement entropy in the Long-Range Kitaev chain
In this paper we complete the study on the asymptotic behaviour of the
entanglement entropy for Kitaev chains with long range pairing. We discover
that when the couplings decay with the distance with a critical exponent new
properties for the asymptotic growth of the entropy appear. The coefficient of
the leading term is not universal any more and the connection with conformal
field theories is lost. We perform a numerical and analytical approach to the
problem showing a perfect agreement. In order to carry out the analytical
study, a new technique for computing the asymptotic behaviour of block Toeplitz
determinants with discontinuous symbols has been developed.Comment: 20 pages, 5 figure
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