Letters in Mathematical Physics最新文献

This paper continues the study of explicit asymptotic formulas for standing coastal trapped waves, focusing on the spectral properties of the operator (langle nabla , D(x)nabla rangle ), which is the spatial component of the wave operator with a degenerating wave propagation velocity. We aim to construct spectral series—pairs of asymptotic eigenvalues and formal asymptotic eigenfunctions—corresponding to the high-frequency regime, where the eigenvalue is (varvec{omega }rightarrow infty ). Extending earlier results, this study addresses the nearly integrable case, providing a more detailed asymptotic behavior of eigenfunctions. Depending on their domain of localization, these eigenfunctions can be expressed in terms of Airy functions and their derivatives or Bessel functions. In addition, we introduce a canonical operator with violated (imprecisely satisfied) quantization conditions.

Motivated by the simplest case of tt*-Toda equations, we study the large and small x asymptotics for ( x>0 ) of real solutions of the sinh-Godron Painlevé III((D_6)) equation. These solutions are parametrized through the monodromy data of the corresponding Riemann–Hilbert problem. This unified approach provides connection formulae between the behavior at the origin and infinity of the considered solutions.

We use the Hamiltonian reduction method to construct the Ruijsenaars dual systems to generalized Toda chains associated with the classical Lie algebras of types (B, C, D). The dual systems turn out to be the B, C and D analogues of the rational goldfish model, which is, as in the type A case, the strong coupling limit of rational Ruijsenaars systems. We explain how both types of systems emerge in the reduction of the cotangent bundle of a Lie group and provide the formulae for dual Hamiltonians. We compute explicitly the higher Hamiltonians of goldfish models using the Cauchy–Binet theorem.

The Stone–von Neumann theorem is a fundamental result which unified the competing quantum-mechanical models of matrix mechanics and wave mechanics. In this article, we continue the broad generalization set out by Huang and Ismert and by Hall, Huang, and Quigg, analyzing representations of locally compact quantum-dynamical systems defined on Hilbert modules, of which the classical result is a special case. We introduce a pair of modular representations which subsume numerous models available in the literature and, using the classical strategy of Rieffel, prove a Stone–von Neumann-type theorem for maximal actions of regular locally compact quantum groups on elementary C*-algebras. In particular, we generalize the Mackey–Stone–von Neumann theorem to regular locally compact quantum groups whose trivial actions on (mathbb {C}) are maximal and recover the multiplicity results of Hall, Huang, and Quigg. With this characterization in hand, we prove our main result showing that if a dynamical system ((mathbb {G},A,alpha )) satisfies the multiplicity assumption of the generalized Stone–von Neumann theorem, and if the coefficient algebra A admits a faithful state, then the spectrum of the iterated crossed product (widehat{mathbb {G}}^textrm{op}ltimes (mathbb {G}ltimes A)) consists of a single point. In the case of a separable coefficient algebra or a regular acting quantum group, we further characterize features of this system, and thus obtain a partial converse to the Stone–von Neumann theorem in the quantum group setting. As a corollary, we show that a regular locally compact quantum group satisfies the generalized Stone–von Neumann theorem if and only if it is strongly regular.

There exist several good reasons why one may wish to add a total derivative to an interaction in quantum field theory, e.g., in order to improve the perturbative construction. Unlike in classical field theory, adding derivatives in general changes the theory. The analysis whether and how this can be prevented is presently limited to perturbative orders (g^n), (nle 3). We drastically simplify it by an all-orders formula, which also allows to answer some salient structural questions. The method is part of a larger program to (re)derive interactions of particles by quantum consistency conditions, rather than a classical principle of gauge invariance.

In this paper, we mainly investigate Lax structure and tau function for the large BKP hierarchy, which is also known as Toda hierarchy of B type. Firstly, the large BKP hierarchy can be derived from fermionic BKP hierarchy by using a special bosonization, which is presented in the form of bilinear equation. Then from bilinear equation, the corresponding Lax equation is given, where in particular the relation of flow generator with Lax operator is obtained. Also starting from Lax equation, the corresponding bilinear equation and existence of tau function are discussed. After that, large BKP hierarchy is viewed as sub-hierarchy of modified Toda (mToda) hierarchy, also called two-component first modified KP hierarchy. Finally by using two basic Miura transformations from mToda to Toda, we understand two typical relations between large BKP tau function (tau _n(textbf{t})) and Toda tau function (tau _n^textrm{Toda}(textbf{t},-textbf{t})), that is, (tau _n^{textrm{Toda}}(textbf{t},-{textbf{t}})=tau _n(textbf{t})tau _{n-1}(textbf{t})) and (tau _n^{textrm{Toda}}(textbf{t},-{textbf{t}})=tau _n^2(textbf{t})). Further, we find (big (tau _n(textbf{t})tau _{n-1}(textbf{t}),tau _n^2(textbf{t})big )) satisfies bilinear equation of mToda hierarchy.

We prove two results which are relevant for constructing marginally outer trapped tubes (MOTTs) in de Sitter spacetime. The first one (Theorem 1) holds more generally, namely for spacetimes satisfying the null convergence condition and containing a timelike conformal Killing vector with a “temporal function”. We show that all marginally outer trapped surfaces (MOTSs) in such a spacetime are unstable. This prevents application of standard results on the propagation of stable MOTSs to MOTTs. On the other hand, it was shown recently, Charlton et al. (minimal surfaces and alternating multiple zetas, arXiv:2407.07130), that for every sufficiently high genus, there exists a smooth, complete family of CMC surfaces embedded in the round 3-sphere (mathbb {S}^3). This family connects a Lawson minimal surface with a doubly covered geodesic 2-sphere. We show (Theorem 2) by a simple scaling argument that this result translates to an existence proof for complete MOTTs with CMC sections in de Sitter spacetime. Moreover, the area of these sections increases strictly monotonically. We compare this result with an area law obtained before for holographic screens.

We extend a theorem, originally formulated by Blattner–Cohen–Montgomery for crossed products arising from Hopf algebras weakly acting on noncommutative algebras, to the realm of left Hopf algebroids. Our main motivation is an application to universal enveloping algebras of projective Lie–Rinehart algebras: for any given curved (resp. flat) connection, that is, a linear (resp. Lie–Rinehart) splitting of a Lie–Rinehart algebra extension, we provide a crossed (resp. smash) product decomposition of the associated universal enveloping algebra, and vice versa. As a geometric example, we describe the associative algebra generated by the invariant vector fields on the total space of a principal bundle as a crossed product of the algebra generated by the vertical ones and the algebra of differential operators on the base.

We study moduli of suitably framed (mathcal {N}=2) elliptic curves. We introduce the notion of tameness for a family of super-spaces and show that the non-tameness of the resulting universal family is essentially controlled by the Appell–Lerch sum (kappa ), familiar from the theory of mock modular forms. In this optic, (kappa ) arises when considering purely Fermionic deformations of (mathcal {N}=2) elliptic curves.