Letters in Mathematical Physics最新文献

We consider a system of three particles with identical mass interacting via short-range potentials, such that two of the particles are on parallel lines in a plane and the third one is on a line perpendicular to this plane. In this geometry, we prove that the corresponding Schrödinger operator only has a finite number of eigenvalues under physically reasonable assumptions on the decay of the interaction potentials. Our result disproves a recent prediction made in physics literature.

We construct a non-perturbative action of the higher spin symmetry algebra on the asymptotic Yang–Mills phase space. We introduce a symmetry algebroid which admits a realization on the asymptotic phase space generated by a Noether charge defined non-perturbatively for all spins. This Noether charge is naturally conserved in the absence of radiation. Furthermore, the algebroid can be restricted to the covariant wedge symmetry algebra,integrates to 0 for fields in the Schwartz which we analyze for non-radiative cuts. The key ingredient in this construction is to consider field and time dependent symmetry parameters constrained to evolve according to equations of motion dual to (a truncation of) the asymptotic Yang–Mills equations of motion. This result then guarantees that the underlying symmetry algebra is represented canonically as well.

In Lett. Math. Phys. 114, 54 (2024) and 115, 70 (2025), the author introduces what is presented as a novel method for determining whether a sequence of orthogonal polynomials is “classical”, based solely on its initial recurrence coefficients. This note demonstrates that all the results contained in those works are already encompassed by two general theorems previously established in J. Math. Anal. Appl. 515 (2022), Article 126390. A symbolic algorithm, implemented in Mathematica, is also provided to enable automated verification of the classical character of orthogonal polynomial sequences on quadratic lattices. As an application, it is shown that the so-called para-Krawtchouk polynomials on bi-lattices, discussed in Lett. Math. Phys. 115, 70 (2025), constitute a particular instance of a classical orthogonal family on a linear lattice. Consequently, their algebraic properties follow as a specific case of one of the main theorems established in J. Math. Anal. Appl. 515 (2022), Article 126390.

We show that the structure of an almost-commutative spectral triple emerges in a semi-classical limit from a geometric construction on a configuration space of gauge connections. The geometric construction resembles that of a spectral triple with a Dirac operator on the configuration space that interacts with the so-called (textbf{HD})-algebra, which is an algebra of operator-valued functions on the configuration space, and which is generated by parallel transports along flows of vector fields on the underlying manifold. In a semi-classical limit, the (textbf{HD})-algebra produces an almost-commutative algebra where the finite factor depends on the representation of the (textbf{HD})-algebra and on the point in the configuration space over which the semi-classical state is localized. Interestingly, we find that the Hilbert space, in which the almost-commutative algebra acts, comes with a double fermionic structure that resembles the fermionic doubling found in the noncommutative formulation of the standard model. Finally, the emerging almost-commutative algebra interacts with a spatial Dirac operator that emerges in the semi-classical limit. This interaction involves both factors of the almost-commutative algebra.

In this study, we undertake a rigorous examination of the three-state Chui–Weeks model on a third-order Cayley tree, marking its first application in this context. The Chui–Weeks model, initially introduced by S. T. Chui and J. D. Weeks in Phys. Rev. B 14, 4978–4982 (1976), is characterized by an infinitely dimensional transfer matrix, posing significant analytical challenges. Prior investigations, such as those presented in Cuesta and Sanchez, J. Stat. Phys. (2004), have predominantly focused on the study of phase transition phenomena within one-dimensional systems. However, to date, the structural and statistical mechanical properties of the Chui–Weeks model on a Cayley tree remain unexplored. In this work, we systematically characterize and classify all translation-invariant and two-periodic ground states associated with this model on a third-order Cayley tree. Furthermore, we establish the existence of Gibbs measures corresponding to the constructed ground states by applying the contour method and Peierls-type arguments, and then, we develop the boundary law approach, deriving recursive relations that characterize Gibbs measures, and compare these solutions with those obtained by the contour method. By extending the theoretical framework of the Chui–Weeks model to hierarchical lattice structures, we aim to contribute novel insights into its equilibrium properties and phase behavior. The findings of this study provide a foundational basis for further investigations into critical phenomena and phase transitions in complex hierarchical systems.

The Marsden–Weinstein–Meyer symplectic reduction has an analogous version for cosymplectic manifolds. In this paper, we extend this cosymplectic reduction to the context of groupoids. Moreover, we prove how in the case of an algebroid associated to a cosymplectic groupoid, the integration commutes with the reduction (analogously to what happens in Poisson geometry). On the other hand, we show how the cosymplectic reduction of a groupoid induces a symplectic reduction on a canonical symplectic subgroupoid. Finally, we study what happens to the multiplicative Chern class associated with the (S^1)-central extensions of the reduced groupoid.

We present a closed inhomogeneous quantum XX spin chain on the periodic integer lattice (mathbb {Z}_m) which is diagonalized by means of Slater determinants built from Rogers’ q-ultraspherical polynomials with (q^m=1). The hermiticity of our periodic quantum spin Hamiltonian encodes a discrete orthogonality relation for these q-ultraspherical polynomials that is of a type studied previously by Spiridonov and Zhedanov.

We prove a multiplicative ergodic theorem for bistochastic completely positive (bcp) linear cocycles acting on finite-dimensional matrix algebras, giving an invariant splitting described explicitly in terms of the multiplicative domains of the underlying bcp maps. As an application of our theorem, we classify when compositions of random bcp maps are asymptotically entanglement breaking, and use this classification to show that occasionally positive partial transpose bcp maps are asymptotically entanglement breaking. We conclude by demonstrating a certain class of bcp linear cocycles are almost surely entanglement breaking in finite time.

In this paper, we investigate a class of one-dimensional bounded Jacobi operators under a uniform electric field. We rigorously demonstrate that their eigenstates exhibit uniform exponential localization and satisfy strong dynamical localization. As an application, we further employ the strong dynamical localization properties of these operators to derive the Stark dynamical localization for a class of quantum chains under a linearly increasing transverse magnetic field.

We demonstrate that interesting examples of Lagrangian multiforms appear naturally in the theory of multidimensional dispersionless integrable systems as (a) higher-order conservation laws of linearly degenerate PDEs in 3D, and (b) in the context of Gibbons–Tsarev equations governing hydrodynamic reductions of heavenly type equations in 4D.