Related papers: Asymptotic observables in gapped quantum spin syst…
An asymptotic low-temperature expansion is performed for an integrable bosonic lattice model and for the critical spin-1/2 Heisenberg chain in a magnetic field. The results apply to the integrable Bose gas as well. We also comment on a…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
This paper proposes parametric and non-parametric hypothesis testing algorithms for detecting anisotropy -- rotational variance of the covariance function in random fields. Both algorithms are based on resampling mechanisms, which enable…
We present the asymptotic distribution theory for a class of increment-based estimators of the fractal dimension of a random field of the form g{X(t)}, where g:R\to R is an unknown smooth function and X(t) is a real-valued stationary…
We analyze asymptotic symmetry algebras in (2+1)-dimensional non-AdS higher-spin gravity with a focus on AdS$_2\times\mathbb{R}$ and $\mathbb{H}_2\times\mathbb{R}$. We find a consistent set of boundary conditions for spin-3 gravity in the…
A frequentist asymptotic expansion method for error estimation is employed for a network of gravitational wave detectors to assess the amount of information that can be extracted from gravitational wave observations. Mathematically we…
Ising model with quenched random magnetic fields is examined for single Gaussian, bimodal and double Gaussian random field distributions by introducing an effective field approximation that takes into account the correlations between…
We review quantum phase transitions of spin systems in transverse magnetic fields taking the examples of the spin-1/2 Ising and XY models in a transverse field. Beginning with an overview of quantum phase transitions, we introduce a number…
In this article we propose an alternate model for the so called {\it protective measurements}, more appropriately {\it adiabatic measurements} of a spin 1/2 system where the {\it apparatus} is also a quantum system with a {\em finite…
We study the classical limit of the ELPR/FK spin foam models by analyzing the large-distance asymptotics of the corresponding graviton propagators. This is done by examining the large-spin asymptotics of the Hartle-Hawking wavefunction…
Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in…
We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic…
We study the anisotropic Heisenberg (XYZ) spin-1/2 chain placed in a magnetic field pointing along the x-axis. We use bosonization and a renormalization group analysis to show that the model has a non-trivial fixed point at a certain value…
The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The asymptotic expression for the corresponding state overlap function,…
We provide a rigorous derivation of an asymptotic formula for perturbations in the resonance values caused by the presence of finite number of anisotropic imperfections of small shapes with constitutive parameters different from the…
This paper develops an asymptotic likelihood theory for triangular arrays of stationary Gaussian time series depending on a multidimensional unknown parameter. We give sufficient conditions for the associated sequence of statistical models…
In this paper, we study the effect of dependence on detecting a class of signals in Ising models, where the signals are present in a structured way. Examples include Ising Models on lattices, and Mean-Field type Ising Models…
It is shown that the full unknown state of a spin-1/2 system, S, which, within Born's statistical interpretation, is meant as the state of an ensamble of identically prepared systems, can be determined with a simultaneous measurement with…
Methods of continuation of holomorphic functions of several complex variables are investigated within the axiomatic framework of Araki, Haag, and Kastler in local quantum field theory. The motivation comes from the analysis of a mass gap in…
The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…