Related papers: Diffusive wavelets on the Spin group
A variety of physical phenomena, such as amplification, absorption, and radiation, can be effectively described using non-Hermitian operators. However, the introduction of non-uniform non-Hermiticity can lead to the formation of exceptional…
We characterize lower bounds for the Bakry-Emery Ricci tensor of nonsymmetric diffusion operators by convexity of entropy on the $L^2$-Wasserstein space, and define a curvature-dimension condition for general metric measure spaces together…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…
Both algebras, Clifford and Grassmann, offer "basis vectors" for describing the internal degrees of freedom of fermions. The oddness of the "basis vectors", transferred to the creation operators, which are tensor products of the finite…
We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained…
In this paper we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as…
This paper constructs translation invariant operators on L2(R^d), which are Lipschitz continuous to the action of diffeomorphisms. A scattering propagator is a path ordered product of non-linear and non-commuting operators, each of which…
We introduce qubit substitutions in $\mathbb{Z}^m$, which have non-rectangular domains based on an endomorphism $Q$ of $\mathbb{Z}^m$ and a set $\mathcal{D}$ of coset representatives of $\mathbb{Z}^m/Q\mathbb{Z}^m$. We then focus on a…
The aim of this work is to study the electron transport in graphene with impurities by introducing a generalization of linear response theory for linear dispersion relations and spinor wave functions. Current response and density response…
The propagation and scattering of electromagnetic waves in magnetized plasmas in a state where a global mode has been established or is in turbulence, are of theoretical and experimental interest in thermonuclear fusion research.…
Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of…
We describe an on-shell, amplitudes-based approach to incorporating radiation absorption effects in the post-Minkowskian scattering of generic, compact, spinning bodies. Classical spinning observables are recovered by extrapolating to large…
This paper is meant to be an informative introduction to spinor representations of Clifford algebras. In this paper we will have a look at Clifford algebras and the octonion algebra. We begin the paper looking at the quaternion algebra…
A set of two-parameter bi-orthogonal eigen-spinors has been constructed from a deformed pseudo- Hermitian extension of Pauli Hamiltonian and its Hermitian conjugate. The Hamiltonians thus obtained are iso-spectral to the original Pauli…
This work was intended as an attempt to extend the results on localization of Fourier-Laplace series to the spectral expansions of distributions on the unit sphere. It is shown that the spectral expansions of the distribution on the unit…
We present the idea of intertwining of two diffusions by Feynman-Kac operators. We present some variations and implications of the method and give examples of its applications. Among others, it turns out to be a very useful tool for finding…
Rarita-Schwinger fields are solutions to the relativistic field equation of spin-$3/2$ fermions in four dimensional flat spacetime, which are important in supergravity and superstring theories. Bure\v s et al. generalized it to arbitrary…
The aim of this paper is to find new estimates for the norms of functions of the (minus) Laplace operator $\cal L$ on the `$ax+b$' groups. The central part is devoted to spectrally localized wave propagators, that is, functions of the type…
In this paper, using the recently discovered notion of the $S$-spectrum, we prove the spectral theorem for a bounded or unbounded normal operator on a Clifford module (i.e., a two-sided Hilbert module over a Clifford algebra based on units…
We address recent spin transport experiments in ultracold unitary Fermi gases. We provide a theoretical understanding for how the measured temperature dependence of the spin diffusivity at low $T$ can disagree with the expected behavior of…