相关论文: How Wigner Functions Transform Under Symplectic Ma…

A large class of variational equations for geometric objects is studied. The results imply conformal monotonicity and Liouville theorems for steady, polytropic, ideal flow, and the regularity of weak solutions to generalized Yang-Mills and…

Metaplectic Wigner distributions are joint time-frequency representations that are parametrized by a symplectic matrix and generalize the short-time Fourier transform and the Wigner distribution. We investigate the question which…

Low-order nonlinear phase gates allow the construction of versatile higher-order nonlinearities for bosonic systems and grant access to continuous variable quantum simulations of many unexplored aspects of nonlinear quantum dynamics. The…

We consider the quantum mechanical equivalence of the Seiberg-Witten map in the context of the Weyl-Wigner-Groenewold-Moyal phase-space formalism in order to construct a quantum mechanics over noncommutative Heisenberg algebras. The…

We develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. The main result of this paper is that each symplectic foliation has an attached $L_\infty$-algebra controlling its…

We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a…

We analyze different families of discrete maps\ in the N-qubit systems in the context of the permutation invariance. We prove that the tomographic condition imposed on the self-dual (Wigner) map is incompatible with the requirement of the…

A nonlinear modification of a parabolic Cauchy problem for entire functions of a single complex variable is considered. The modification means that the time half-line is divided onto the intervals of equal length and on each such interval…

Sturm-Liouville problem with generalized derivative of self-similar Cantor type function as a weight is considered. Under Neumann and mixed boundary conditions the oscillating properties of the eigenfunctions are studied. The spectral…

For an elliptic, semilinear differential operator of the form $S(u) = A : D^2 u + b(x, u , Du)$, consider the functional $E_\infty(u) = \mathop{\mathrm{ess \, sup}}_\Omega |S(u)|$. We study minimisers of $E_\infty$ for prescribed boundary…

In the context of a noncommutative differential calculus on the algebra of real valued functions of an $n$-dimensional manifold $M$, a commutative and associative product of 1-forms is naturally defined. Ordinary differential calculus…

Symplectic maps can provide a straightforward and accurate way to visualize and quantify the dynamics of conservative systems with two degrees of freedom. These maps can be easily iterated from the simplest computers to obtain trajectories…

We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or…

By a Liouville structure on a symplectic manifold $(M, \omega)$ we mean a choice of symplectic potential: that is, a choice of one-form $\theta$ on $M$ such that ${\rm d} \theta = \omega$. We determine precisely all the automorphisms of a…

Whittaker functions are special functions that arise in $p$-adic number theory and representation theory. They may be defined on representations of reductive groups as well as their metaplectic covering groups: fascinatingly, many of their…

We make some comments on the renormalization of Wilson operators (not just vacuum -expectation values of Wilson operators), and the features which arise in Minkowski space. If the Wilson loop contains a straight light-like segment, charge…

The generalized Weinberg sum rules containing the difference of isovector vector and axial-vector spectral functions saturated by both finite and infinite number of narrow resonances are considered. We summarize the status of these sum…

Recently a paper on the construction of consistent Wigner functions for cylindrical phase spaces S^1 x R, i.e. for the canonical pair angle and angular momentum, was presented (arXiv:1601.02520), main properties of those functions derived,…

We consider a broad class of systems of nonlinear integro-differential equations posed on the real line that arise as Euler-Lagrange equations to energies involving nonlinear nonlocal interactions. Although these equations are not readily…

Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…