Related papers: Dynamical and spectral Dirac systems: response fun…
A simple relation between the Maxwell system and the Dirac equation based on their quaternionic reformulation is discussed. We establish a close connection between solutions of both systems as well as a relation between the wave parameters…
Dynamical systems can autonomously adapt their organization so that the required target dynamics is reproduced. In the previous Rapid Communication [Phys. Rev. E 90,030901(R) (2014)], it was shown how such systems can be designed using…
A forward problem for the Dirac system is to find $u=\begin{pmatrix}u_1(x,t)\\u_2(x,t)\end{pmatrix}$ obeying $iu_t+\begin{pmatrix}0&1\\-1&0\end{pmatrix}u_x+\begin{pmatrix}p&q\\q&-p\end{pmatrix}u=0$ for…
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…
The Airy process is characterized by its finite-dimensional distribution functions. We show that each finite-dimensional distribution function is expressible in terms of a solution to a system of differential equations.
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…
We present a result relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller. The result is supported by numerical computation of the resonances of the system of n…
In this paper we investigate the existence of singular solutions to the conformal Dirac-Einstein system. Because of its conformal invariance, there are many similarities with the classical construction of singular solutions for the Yamabe…
We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass representation of surfaces in three-manifolds.…
The chiral kinetic theory is derived from exact spinor mean field equations without symmetry-breaking terms for large classes of SU(2) systems with spin-orbit coupling. The influence of the Wigner function's off-diagonal elements is worked…
We analyze a variety of Weyl invariant dynamical problems in three dimensions.
It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as…
An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation which can be solved by iterative procedure to find the wave functions is…
From flocks of birds to biomolecular assemblies, systems in which many individual components independently consume energy to perform mechanical work exhibit a wide array of striking behaviors. Methods to quantify the dynamics of these so…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
We extend the formula for correlation functions of free scalar field theories and Dirac field theories in terms of quantum $A_{\infty}$ algebras presented in arXiv:2305.11634 to general scalar-Dirac systems. We obtain the result that the…
We derive a general relation between correlators of density of states fluctuations and density response functions. It applies equally to quantum chaotic systems of pure symmetry (unitary, orthogonal, and symplectic) as well as to the…
The generalized Dirac oscillator as one of the exact solvable model in quantum mechanics was introduced in 2+1-dimensional world in this paper. What is more, the general expressions of the exact solutions for these models with the inverse…
We consider Dirac fermions interacting with a disordered non-Abelian vector potential. The exact solution is obtained through a special type of conformal field theory including logarithmic correlators, without resorting to the replica or…
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…