اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMother wavelet functions generalized through q-exponentials
42
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We generalize some widely used mother wavelets by means of the q-exponential function $e_q^x equiv [1+(1-q)x]^{1/(1-q)}$ ($q in {mathbb R}$, $e_1^x=e^x$) that emerges from nonextensive statistical mechanics. Particularly, we define extend
قيم البحث
اقرأ أيضاً
We study a symmetric generalization $mathfrak{p}^{(N)}_k(eta, alpha)$ of the binomial distribution recently introduced by Bergeron et al, where $eta in [0,1]$ denotes the win probability, and $alpha$ is a positive parameter. This generalization is ba
sed on $q$-exponential generating functions ($e_{q^{gen}}^z equiv [1+(1-q^{gen})z]^{1/(1-q^{gen})};,e_{1}^z=e^z)$ where $q^{gen}=1+1/alpha$. The numerical calculation of the probability distribution function of the number of wins $k$, related to the number of realizations $N$, strongly approaches a discrete $q^{disc}$-Gaussian distribution, for win-loss equiprobability (i.e., $eta=1/2$) and all values of $alpha$. Asymptotic $Nto infty$ distribution is in fact a $q^{att}$-Gaussian $e_{q^{att}}^{-beta z^2}$, where $q^{att}=1-2/(alpha-2)$ and $beta=(2alpha-4)$. The behavior of the scaled quantity $k/N^gamma$ is discussed as well. For $gamma<1$, a large-deviation-like property showing a $q^{ldl}$-exponential decay is found, where $q^{ldl}=1+1/(etaalpha)$. For $eta=1/2$, $q^{ldl}$ and $q^{att}$ are related through $1/(q^{ldl}-1)+1/(q^{att}-1)=1$, $forall alpha$. For $gamma=1$, the law of large numbers is violated, and we consistently study the large-deviations with respect to the probability of the $Ntoinfty$ limit distribution, yielding a power law, although not exactly a $q^{LD}$-exponential decay. All $q$-statistical parameters which emerge are univocally defined by $(eta, alpha)$. Finally we discuss the analytical connection with the P{o}lya urn problem.
The various types of generalized Cattaneo, called also telegraphers equation, are studied. We find conditions under which solutions of the equations considered so far can be recognized as probability distributions, textit{i.e.} are normalizable and n
on-negative on their domains. Analysis of the relevant mean squared displacements enables us to classify diffusion processes described by such obtained solutions and to identify them with either ordinary or anomalous super- or subdiffusion. To complete our study we analyse derivations of just considered examples the generalized Cattaneo equations using the continuous time random walk and the persistent random walk approaches.
We introduce a class of generalized Lipkin-Meshkov-Glick (gLMG) models with su$(m)$ interactions of Haldane-Shastry type. We have computed the partition function of these models in closed form by exactly evaluating the partition function of the restr
iction of a spin chain Hamiltonian of Haldane-Shastry type to subspaces with well-defined magnon numbers. As a byproduct of our analysis, we have obtained strong numerical evidence of the Gaussian character of the level density of the latter restricted Hamiltonians, and studied the distribution of the spacings of consecutive unfolded levels. We have also discussed the thermodynamic behavior of a large family of su(2) and su(3) gLMG models, showing that it is qualitatively similar to that of a two-level system.
We study matrix product unitary operators (MPUs) for fermionic one-dimensional (1D) chains. In stark contrast with the case of 1D qudit systems, we show that (i) fermionic MPUs do not necessarily feature a strict causal cone and (ii) not all fermioni
c Quantum Cellular Automata (QCA) can be represented as fermionic MPUs. We then introduce a natural generalization of the latter, obtained by allowing for an additional operator acting on their auxiliary space. We characterize a family of such generalized MPUs that are locality-preserving, and show that, up to appending inert ancillary fermionic degrees of freedom, any representative of this family is a fermionic QCA and viceversa. Finally, we prove an index theorem for generalized MPUs, recovering the recently derived classification of fermionic QCA in one dimension. As a technical tool for our analysis, we also introduce a graded canonical form for fermionic matrix product states, proving its uniqueness up to similarity transformations.
We present a new approach to the static finite temperature correlation functions of the Heisenberg chain based on functional equations. An inhomogeneous generalization of the n-site density operator is considered. The lattice path integral formulatio
n with a finite but arbitrary Trotter number allows to derive a set of discrete functional equations with respect to the spectral parameters. We show that these equations yield a unique characterization of the density operator. Our functional equations are a discrete version of the reduced q-Knizhnik-Zamolodchikov equations which played a central role in the study of the zero temperature case. As a natural result, and independent of the arguments given by Jimbo, Miwa, and Smirnov (2009) we prove that the inhomogeneous finite temperature correlation functions have the same remarkable structure as for zero temperature: they are a sum of products of nearest-neighbor correlators.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
