Related papers: Functional-differential equations for $F_q$%-trans…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In…
In this article, after introducing a kind of q-deformation in quantum mechanics, first, q-deformed form of Dirac equation in relativistic quantum mechanics is derived. Then three important scat erring problem in physics are studied. All…
In the present work, we investigate the intrinsic relation between quantum fidelity susceptibility (QFS) and the dynamical structure factor. We give a concise proof of the QFS beyond the perturbation theory. With the QFS in the Lehmann…
In this paper, we extend the quadratic phase Fourier transform of a complex valued functions to that of the quaternion valued functions of two variables. We call it the quaternion quadratic phase Fourier transform (QQPFT). Based on the…
In this paper, we discuss the representability almost everywhere (a.e.) in the plane of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite…
Using factorization we determine the allowed domains of the ratios of form factors, $x = A_2(0)/A_1(0)$ and $y = V(0)/A_1(0)$, from the experimentally measured ratio $R_h \equiv \Gamma(D_s^+ \ra \phi \rho^+)/\Gamma(D_s^+ \ra \phi \pi^+)$…
While several instances of shifted convolution problems for GL(3) x GL(2) have been solved, the case where one factor is the classical divisor function and one factor is a GL(3) Fourier coefficient has remained open. We solve this case in…
We develop a QCD sum rule analysis of the form factor $F_{\gamma^*\gamma^*\pi^0}(q^2,Q^2)$ in the region where virtuality of one of the spacelike photons is small $q^2 \ll 1 GeV^2$ while another is large: $Q^2 \gapprox 1 GeV^2$. We…
We examine, for $-1<q<1$, $q$-Gaussian processes, i.e. families of operators (non-commutative random variables) $X_t=a_t+a_t^*$ -- where the $a_t$ fulfill the $q$-commutation relations $a_sa_t^*-qa_t^*a_s=c(s,t)\cdot \id$ for some…
Quantum Fourier Transform (QFT) plays a principal role in the development of efficient quantum algorithms. Since the number of quantum bits that can currently built is limited, while many quantum technologies are inherently three- (or more)…
Integral transformations of the QCD invariant (running) coupling and of some related objects are discussed. Special attention is paid to the Fourier transformation, that is to transition from the space-time to the energy--momentum…
Using an exact integrodifferential equation we study the properties of the gauge invariant quark Green's function, defined with a path-ordered gluon field phase factor along a straight line, in two-dimensional QCD in the large-N_c limit.…
Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker-Planck equation to account for non-classical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here we introduce a…
We have studied the kinetics of $q$-deformed bosons and fermions, within a semiclassical approach. This investigation is realized by introducing a generalized exclusion-inclusion principle, intrinsically connected with the quantum…
In this short note we partially answer a question of Fukaya and Kato by constructing a $q$-expansion with coefficients in a non-commutative Iwasawa algebra whose constant term is a non-commutative p-adic zeta function.
We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier…
Quantum signal processing (QSP) and quantum singular value transformation (QSVT) are powerful techniques for the development of quantum procedures. They allow to derive circuits preparing desired polynomial transformations. Recent research…
The transition gamma*(q_1)gamma*(q_2) -> \pi0(p) is studied within the QCD sum rule framework. As a first step, we analyze the kinematic situation when both photon virtualities are spacelike and large. We construct a QCD sum rule for…
We discuss the nonleading, ``soft" contribution to the pion form factor at intermediate momentum transfer within operator product expansion approach. We argue, that the corresponding contribution can temporarily {\bf simulate} the leading…