Letters in Mathematical Physics最新文献

It is well-known that a formal deformation of a commutative algebra (mathcal {A}) leads to a Poisson bracket on (mathcal {A}) and that the classical limit of a derivation on the deformation leads to a derivation on (mathcal {A}), which is Hamiltonian with respect to the Poisson bracket. In this paper we present a generalization of it for formal deformations of an arbitrary noncommutative algebra (mathcal {A}). The deformation leads in this case to a Poisson algebra structure on (Pi (mathcal {A}){:}{=}Z(mathcal {A})times (mathcal {A}/Z(mathcal {A}))) and to the structure of a (Pi (mathcal {A}))-Poisson module on (mathcal {A}). The limiting derivations are then still derivations of (mathcal {A}), but with the Hamiltonian belong to (Pi (mathcal {A})), rather than to (mathcal {A}). We illustrate our construction with several cases of formal deformations, coming from known quantum algebras, such as the ones associated with the nonabelian Volterra chains, Kontsevich integrable map, the quantum plane and the quantized Grassmann algebra.

We study, via the eigenvalue theory of completely continuous operators, the existence and asymptotic behavior of nontrivial p-k-convex radial solutions for a p-k-Hessian equation. This is probably the first time that p-k-Hessian equations have been studied by employing this technique. Several new nonexistence conclusions are also derived in this paper.

A central task of theoretical physics is to analyse spectral properties of quantum mechanical observables. In this endeavour, Mourre’s conjugate operator method emerged as an effective tool in the spectral theory of Schrödinger operators. This paper introduces a novel class of examples from relativistic quantum field theory that are amenable to Mourre’s method. By assuming Lorentz covariance and the spectrum condition, we derive a limiting absorption principle for the energy-momentum operators and provide new proofs of the absolute continuity of the energy-momentum spectra. Moreover, under the assumption of dilation covariance, we show that the spectrum of the relativistic mass operator is purely absolutely continuous in ((0,infty )).

In constructive quantum theory, the free field is constructed based on a Gaussian measure on the space of tempered distributions. We generalize the classic results about support property of the Gaussian measure from Euclidean space-time to fractal space-time (mathbb {R}times F). More precisely, we show that the set ((I-Delta _F)^{(d_s-1)/4+alpha }(1+| x| ^2)^{(d_H+1)/4+beta }L^2(mathbb {R}times F)) is of the Gaussian measure one if (alpha >0) and (beta >0), while the set is of the Gaussian measure zero if (alpha >0) and (beta <0). Here, (Delta _F) is the Laplacian on the underlying fractal space F, (d_s) is the spectral dimension of (Delta _F), and (d_H) is the Hausdorff dimension of F.

We construct the Jucys–Murphy elements and the Jucys–Murphy basis for the q-Brauer algebra in the sense of Mathas. We also give a necessary and sufficient condition for the q-Brauer algebra being (split) semisimple over an arbitrary field.

We propose a generalization of the double affine Hecke algebra of type-(C^vee C_1) at specific parameters by introducing a “Heegaard dual” of the Hecke operators. Shown is a relationship with the skein algebra on double torus. We give automorphisms of the algebra associated with the Dehn twists on the double torus.

The aim of this note is to show the existence of a large family of Cantorvals arising in the projection description of primitive two-letter substitutions. This provides a common and naturally occurring class of Cantorvals.

We show that non-trivial two-dimensional topological insulators protected by an odd time-reversal symmetry have absolutely continuous edge spectrum. To accomplish this, we establish a time-reversal symmetric version of the Wold decomposition that singles out extended edge modes of the topological insulator.

We present a new exact solution to the defocusing modified Korteweg–de Vries equation to describe the interaction of a dark soliton and a traveling periodic wave. The solution (which we refer to as the dark breather) is obtained by using the Darboux transformation with the eigenfunctions of the Lax system expressed in terms of the Jacobi theta functions. Properties of elliptic functions including the quarter-period translations in the complex plane are applied to transform the solution to the simplest form. We explore the characteristic properties of these dark breathers and show that they propagate faster than the periodic wave (in the same direction) and attain maximal localization at a specific parameter value which is explicitly computed.