Search results for "Mathematica"
showing 10 items of 7971 documents
p-harmonic coordinates for Hölder metrics and applications
2017
We show that on any Riemannian manifold with H¨older continuous metric tensor, there exists a p-harmonic coordinate system near any point. When p = n this leads to a useful gauge condition for regularity results in conformal geometry. As applications, we show that any conformal mapping between manifolds having C α metric tensors is C 1+α regular, and that a manifold with W1,n ∩ C α metric tensor and with vanishing Weyl tensor is locally conformally flat if n ≥ 4. The results extend the works [LS14, LS15] from the case of C 1+α metrics to the H¨older continuous case. In an appendix, we also develop some regularity results for overdetermined elliptic systems in divergence form. peerReviewed
A form factor approach to the asymptotic behavior of correlation functions in critical models
2011
We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states to one over the particle/hole excitations lying on the Fermi surface in the thermodynamic limit. We compute these sums, over the so-called critical form factors, exactly. Thus we obtain the leading large distance behavior of each oscillating harmonic of the correlation function asymptotic expansion, including the corresponding amplitudes. Our method is applicable to a wide variety of integrable models and yields precisely the results stemming from the Lutt…
Form factor approach to dynamical correlation functions in critical models
2012
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time asymptotic behavior of various two-point functions of this model. We also compute edge exponents and amplitudes characterizing the power-law behavior of dynamical response functions on the particle/hole excitation thresholds. These last results confirm predictions based on the non-linear Luttinger liquid method. Our results rely on a first principles derivation, based on the microscopic analysis of the model, without invoking, at any stage, some correspon…
Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
2013
We derive expressions for the form factors of the quantum transfer matrix of the spin-1/2 XXZ chain which are suitable for taking the infinite Trotter number limit. These form factors determine the finitely many amplitudes in the leading asymptotics of the finite-temperature correlation functions of the model. We consider form-factor expansions of the longitudinal and transversal two-point functions. Remarkably, the formulae for the amplitudes are in both cases of the same form. We also explain how to adapt our formulae to the description of ground state correlation functions of the finite chain. The usefulness of our novel formulae is demonstrated by working out explicit results in the hig…
Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
2010
We study the thermodynamic limit of the particle-hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly computed power-law in the system-size. Moreover, the corresponding amplitudes can be obtained as a product of a "smooth" and a "discrete" part: the former depends continuously on the rapidities of the particles and holes, whereas the latter has an additional explicit dependence on the set of integer numbers that label each excited state in the associated logarithmic Bethe equations. We also show that special form factors corresponding to zero-energy excitations lying on the Fermi surface decrease as a …
Asymptotics of correlation functions of the Heisenberg-Ising chain in the easy-axis regime
2016
We analyze the long-time large-distance asymptotics of the longitudinal correlation functions of the Heisenberg-Ising chain in the easy-axis regime. We show that in this regime the leading asymptotics of the dynamical two-point functions is entirely determined by the two-spinon contribution to their form factor expansion. Its explicit form is obtained from a saddle-point analysis of the corresponding double integral. It describes the propagation of a wave front with velocity $v_{c_1}$ which is found to be the maximal possible group velocity. Like in wave propagation in dispersive media the wave front is preceded by a precursor running ahead with velocity $v_{c_2}$. As a special case we obta…
Partition function of the trigonometric SOS model with reflecting end
2010
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.
Immune networks: multitasking capabilities near saturation
2013
Pattern-diluted associative networks were introduced recently as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T- and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with $N_T$ T-lymphocytes can manage a number $N_B!=!\order(N_T^\delta)$ of B-lymphocytes simultaneously, with $\delta!<!1$. Here we study this model in the extensive load regime $N_B!=!\alpha N_T$, with also a high degree of pattern dilution, in agreement with immunological findings. We use graph theory and statistical mechanical analysis based on replica methods to show that in the finite-connectivit…
Corrigendum: Partial inner product spaces, metric operators and generalized hermiticity
2013
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Updating input–output matrices: assessing alternatives through simulation
2009
A problem that frequently arises in economics, demography, statistics, transportation planning and stochastic modelling is how to adjust the entries of a matrix to fulfil row and column aggregation constraints. Biproportional methods in general and the so-called RAS algorithm in particular, have been used for decades to find solutions to this type of problem. Although alternatives exist, the RAS algorithm and its extensions are still the most popular. Apart from some interesting empirical and theoretical properties, tradition, simplicity and very low computational costs are among the reasons behind the great success of RAS. Nowadays computer hardware and software have made alternative proce…