Letters in Mathematical Physics最新文献

The mathematical classification of topological phases of matter is a crucial step toward comprehending and characterizing the properties of quantum materials. In this study, our focus is on investigating phases of matter in one-dimensional open quantum systems. Our goal is to elucidate the emerging phase diagram of one-dimensional tensor network mixed states that act as renormalization fixed points. These operators hold special significance since, as we prove, they manifest as boundary states of two-dimensional topologically ordered states, encompassing all known two-dimensional topological phases. To achieve their classification we begin by constructing families of such states from C*-weak Hopf algebras, which are algebras with fusion categories as their representations, and we present explicit local fine-graining and coarse-graining quantum channels defining the renormalization procedure. Lastly, we prove that a subset of these states, originating from C*-Hopf algebras, are in the trivial phase.

In our earlier work, we studied the ({hat{Z}})-invariant(or homological blocks) for SO(3) gauge group and we found it to be same as ({hat{Z}}^{SU(2)}). This motivated us to study the ({hat{Z}})-invariant for quotient groups (SU(N)/{mathbb {Z}}_m), where m is some divisor of N. Interestingly, we find that ({hat{Z}})-invariant is independent of m.

We show that the (tau )-functions of the regular KP solitons from the totally nonnegative Grassmannians can be expressed by the Riemann theta functions on singular curves. We explicitly write the parameters in the Riemann theta function in terms of those of the KP soliton. We give a short remark on the Prym theta function on a double covering of singular curves. We also discuss the KP soliton on quasi-periodic background, which is obtained by applying the vertex operators to the Riemann theta function.

We construct a Wick-type deformation quantization of contact metric manifolds. The construction is fully canonical and involves no arbitrary choice. Unlike the case of symplectic or Poisson manifolds, not every classical observable on a general contact metric manifold can be promoted to a quantum one due to possible obstructions to quantization. We prove, however, that all these obstructions disappear for Sasakian manifolds.

The semi-classical limit of ground states of large systems of fermions was studied by Fournais et al. (Calc Var Partial Differ Equ 57:105, 2018). In particular, the authors prove weak convergence toward classical states associated with the minimizers of the Thomas–Fermi functional. In this paper, we revisit this limit and show that under additional assumptions—and, using simple arguments—it is possible to prove that strong convergence holds in relevant normed spaces.

It is a well-known fact that the Schwarzschild spacetime admits a maximal spacetime extension in null coordinates which extends the exterior Schwarzschild region past the Killing horizon, called the Kruskal–Szekeres extension. This method of extending the Schwarzschild spacetime was later generalized by Brill–Hayward to a class of spacetimes of “profile h” across non-degenerate Killing horizons. Circumventing analytical subtleties in their approach, we reconfirm this fact by reformulating the problem as an ODE, and showing that the ODE admits a solution if and only if the naturally arising Killing horizon is non-degenerate. Notably, this approach lends itself to discussing regularity across the horizon for non-smooth metrics. We will discuss applications to the study of photon surfaces, extending results by Cederbaum–Galloway and Cederbaum–Jahns–Vičánek-Martínez beyond the Killing horizon. In particular, our analysis asserts that photon surfaces approaching the Killing horizon must necessarily cross it.

We introduce the topologically twisted index for four-dimensional ({mathcal {N}}=1) gauge theories quantized on ({textrm{AdS}_2}times S^1). We compute the index by applying supersymmetric localization to partition functions of vector and chiral multiplets on ({textrm{AdS}_2}times T^2), with and without a boundary: in both instances we classify normalizability and boundary conditions for gauge, matter and ghost fields. The index is twisted as the dynamical fields are coupled to a R-symmetry background 1-form with non-trivial exterior derivative and proportional to the spin connection. After regularization, the index is written in terms of elliptic gamma functions, reminiscent of four-dimensional holomorphic blocks, and crucially depends on the R-charge.

We construct and compare two alternative quantizations, as a time-orderable prefactorization algebra and as an algebraic quantum field theory valued in cochain complexes, of a natural collection of free BV theories on the category of m-dimensional globally hyperbolic Lorentzian manifolds. Our comparison is realized as an explicit isomorphism of time-orderable prefactorization algebras. The key ingredients of our approach are the retarded and advanced Green’s homotopies associated with free BV theories, which generalize retarded and advanced Green’s operators to cochain complexes of linear differential operators.

In this work, we investigate the geometry and topology of compact Einstein-type manifolds with nonempty boundary. First, we prove a sharp boundary estimate and as consequence we obtain, under certain hypotheses, that the Hawking mass is bounded from below in terms of area. Then we give a topological classification for its boundary. Finally, we deduce some classification results for compact Einstein-type manifolds with positive constant scalar curvature and assuming a pointwise inequality for the traceless Ricci tensor.

Lagrangian multiforms provide a variational framework to describe integrable hierarchies. The case of Lagrangian 1-forms covers finite-dimensional integrable systems. We use the theory of Lie dialgebras introduced by Semenov-Tian-Shansky to construct a Lagrangian 1-form. Given a Lie dialgebra associated with a Lie algebra (mathfrak {g}) and a collection (H_k), (k=1,dots ,N), of invariant functions on (mathfrak {g}^*), we give a formula for a Lagrangian multiform describing the commuting flows for (H_k) on a coadjoint orbit in (mathfrak {g}^*). We show that the Euler–Lagrange equations for our multiform produce the set of compatible equations in Lax form associated with the underlying r-matrix of the Lie dialgebra. We establish a structural result which relates the closure relation for our multiform to the Poisson involutivity of the Hamiltonians (H_k) and the so-called double zero on the Euler–Lagrange equations. The construction is extended to a general coadjoint orbit by using reduction from the free motion of the cotangent bundle of a Lie group. We illustrate the dialgebra construction of a Lagrangian multiform with the open Toda chain and the rational Gaudin model. The open Toda chain is built using two different Lie dialgebra structures on (mathfrak {sl}(N+1)). The first one possesses a non-skew-symmetric r-matrix and falls within the Adler–Kostant–Symes scheme. The second one possesses a skew-symmetric r-matrix. In both cases, the connection with the well-known descriptions of the chain in Flaschka and canonical coordinates is provided.