Letters in Mathematical Physics最新文献

We construct combinatorial analogs of 2d higher topological quantum field theories. We consider triangulations as vertices of a certain CW complex (Xi ). In the “flip theory,” cells of (Xi _textrm{flip}) correspond to polygonal decompositions obtained by erasing the edges in a triangulation. These theories assign to a cobordism (Sigma ) a cochain Z on (Xi _textrm{flip}) constructed as a contraction of structure tensors of a cyclic (A_infty ) algebra V assigned to polygons. The cyclic (A_infty ) equations imply the closedness equation ((delta +Q)Z=0). In this context, we define combinatorial BV operators and give examples with coefficients in (mathbb {Z}_2). In the “secondary polytope theory,” (Xi _textrm{sp}) is the secondary polytope (due to Gelfand–Kapranov–Zelevinsky) and the cyclic (A_infty ) algebra has to be replaced by an appropriate refinement that we call an (widehat{A}_infty ) algebra. We conjecture the existence of a good Pachner CW complex (Xi ) for any cobordism, whose local combinatorics is described by secondary polytopes and the homotopy type is that of Zwiebach’s moduli space of complex structures. Depending on this conjecture, one has an “ideal model” of combinatorial 2d HTQFT determined by a local (widehat{A}_infty ) algebra.

Joyce structures were introduced by T. Bridgeland in the context of the space of stability conditions of a three-dimensional Calabi–Yau category and its associated Donaldson–Thomas invariants. In subsequent work, T. Bridgeland and I. Strachan showed that Joyce structures satisfying a certain non-degeneracy condition encode a complex hyperkähler structure on the tangent bundle of the base of the Joyce structure. In this work we give a definition of an analogous structure over an affine special Kähler (ASK) manifold, which we call a special Joyce structure. Furthermore, we show that it encodes a real hyperkähler (HK) structure on the tangent bundle of the ASK manifold, possibly of indefinite signature. Particular examples include the semi-flat HK metric associated to an ASK manifold (also known as the rigid c-map metric) and the HK metrics associated to certain uncoupled variations of BPS structures over the ASK manifold. Finally, we relate the HK metrics coming from special Joyce structures to HK metrics on the total space of algebraic integrable systems.

We study 3d (mathcal {N}=2) U(1) Chern–Simons-Matter QFT on a cylinder (Ctimes mathbb {R}). The topology of C gives rise to BPS sectors of low-energy solitons known as kinky vortices, which interpolate between (possibly) different vacua at the ends of the cylinder and at the same time carry magnetic flux. We compute the spectrum of BPS vortices on the cylinder in an isolated Higgs vacuum, through the framework of warped exponential networks, which we introduce. We then conjecture a relation between these and standard vortices on (mathbb {R}^2), which are related to genus-zero open Gromov–Witten invariants of toric branes. More specifically, we show that in the limit of large Fayet–Iliopoulos coupling, the spectrum of kinky vortices on C undergoes an infinite sequence of wall-crossing transitions and eventually stabilizes. We then propose an exact relation between a generating series of stabilized CFIV indices and the Gromov–Witten disk potential and discuss its consequences for the structure of moduli spaces of vortices.

We show that the wave operators for Schrödinger scattering in (mathbb {R}^4) have a particular form which depends on the existence of resonances. As a consequence of this form, we determine the contribution of resonances to the index of the wave operator.

We analyse the ergodic properties of quantum channels that are covariant with respect to diagonal orthogonal transformations. We prove that the ergodic behaviour of a channel in this class is essentially governed by a classical stochastic matrix. This allows us to exploit tools from classical ergodic theory to study quantum ergodicity of such channels. As an application of our analysis, we study dual unitary brickwork circuits which have recently been proposed as minimal models of quantum chaos in many-body systems. Upon imposing a local diagonal orthogonal invariance symmetry on these circuits, the long-term behaviour of spatio-temporal correlations between local observables in such circuits is completely determined by the ergodic properties of a channel that is covariant under diagonal orthogonal transformations. We utilize this fact to show that such symmetric dual unitary circuits exhibit a rich variety of ergodic behaviours, thus emphasizing their importance.

According to Zuo and an unpublished work of Bertola, there is a two-index series of Dubrovin–Frobenius manifold structures associated to a B-type Coxeter group. We study the relations between these structures for the different values of these indices. We show that part of the data of such Dubrovin–Frobenius manifold indexed by (k, l) can be recovered by the ((k+r,l+r)) Dubrovin–Frobenius manifold.Continuing the program of Basalaev et al. (J Phys A: Math Theor 54:115201, 2021) we associate an infinite system of commuting PDEs to these Dubrovin–Frobenius manifolds and show that these PDEs extend the dispersionless BKP hierarchy.

In Gérard et al. (Ann Sci Ecole Norm Sup 56:127–196, 2023), the Unruh state for massless fermions on a Kerr spacetime was constructed and the authors showed its Hadmard property in the case of very slowly rotating black holes ({left| a right| }ll M). In this note, we extend this result to the full non extreme case ({left| a right| }<M).

In this paper, we develop the radial transfer matrix formalism for unitary one-channel operators. This generalizes previous formalisms for CMV matrices and scattering zippers. We establish an analog of Carmona’s formula and deduce criteria for absolutely continuous spectrum which we apply to random Hilbert Schmidt perturbations of periodic scattering zippers.

In this paper, we construct Young wall models for the level 1 highest weight and Fock space crystals of quantum affine algebras in types (E_6^{(2)}) and (F_4^{(1)}). Our starting point in each case is a combinatorial realization for a certain level 1 perfect crystal in terms of Young columns. Then, using energy functions and affine energy functions we define the notions of reduced and proper Young walls, which model the highest weight and Fock space crystals, respectively.

We provide an analytic method for estimating the entanglement of the non-Gaussian energy eigenstates of disordered harmonic oscillator systems. We invoke the explicit formulas of the eigenstates of the oscillator systems to establish bounds for their (epsilon )-Rényi entanglement entropy (epsilon in (0,1)). Our methods result in a logarithmically corrected area law for the entanglement of eigenstates, corresponding to one excitation, of the disordered harmonic oscillator systems.