Authors: Alexis Drouot, Jacob Shapiro, Xiaowen Zhu
Link: http://arxiv.org/abs/2501.13096v1
Summary:
Fermionic time-reversal-invariant insulators in two dimensions -- class AII in the Kitaev table -- come in two different topological phases. We prove that if two such insulators with different indices occupy regions containing arbitrarily large balls, then the spectrum of the resulting operator fills the bulk spectral gap. Our argument follows a proof by contradiction developed in an earlier work by two of the authors for quantum Hall systems. It boils down to showing that the
Authors: Michał Studziński, Tomasz Młynik, Marek Mozrzymas, Michał Horodecki
Link: http://arxiv.org/abs/2501.13067v1
Summary:
This paper investigates the representation theory of the algebra of partially transposed permutation operators. We demonstrate that the given irreducible matrix units are, in fact, eigenoperators for the considered class. The obtained results are applied to a special class of operators motivated by the mathematical formalism appearing in all variants of the port-based teleportation protocols through the mixed Schur-Weyl duality. The framework is general and applies to systems with arbitrary numbers of components and local dimensions.
2. Efficient simulation of parametrized quantum circuits under non-unital noise through Pauli backpropagation
Authors: Victor Martinez, Armando Angrisani, Ekaterina Pankovets, Omar Fawzi, Daniel Stilck França
Link: http://arxiv.org/abs/2501.13050v1
Summary:
quantum devices continue to grow in size but remain affected by noise. It is crucial to determine when and how they can outperform classical computers on practical tasks. A central piece in this effort is to develop the most efficient classical simulation algorithms possible. Among the most promising approaches are Pauli backpropagation algorithms. They have already demonstrated their ability to efficiently simulate certain classes of parameterized quantum circuits. But their efficiency was not previously established for more realistic non-unital noise models, such as amplitude damping.
Authors: Jacob J. Richardson, Mats Vermeeren
Link: http://arxiv.org/abs/2501.13012v1
Summary:
Discrete Lagrangian multiform theory is a perspective on lattice equations that are integrable in the sense of multidimensional consistency. The ABS equations formed the start of this theory. We present alternative Lagrangians that have Euler-Lagrange equations equivalent to the ABS equations. We recover integer-valued fields, related to possible the branch choices, in the action sums. We give counterexamples for both these properties, but we recover them by including integer-value fields related to the branch choice.
4. Complex hidden symmetries in real spacetime and their algebraic structures
Authors: R. Vilela Mendes
Link: http://arxiv.org/abs/2501.12960v1
Summary:
Real spacetime is a Lorentzian fiber in a complex manifold. There is a mismatch of the elementary linear representations of their symmetry groups. No spinors are allowed as linear irreducible representations for the complex case. When a spin$^{h}$ structure is implemented on the associated principal bundles, one is naturally led to an algebraic structure similar to the one of the standard model. This last (dynamical) structure might therefore be inherited from the kinematical symmetries of a larger space.
5. Euler--Poincaré reduction and the Kelvin--Noether theorem for discrete mechanical systems with advected parameters and additional dynamics
Authors: Yusuke Ono, Simone Fiori, Linyu Peng
Link: http://arxiv.org/abs/2501.12940v1
Summary:
The Euler--Poincar'e equations arise from the application of Lagrangian mechanics to systems on Lie groups that exhibit symmetries. These equations have been extended to various settings, such as semidirect products, advected parameters, and field theory. In this paper, we show both continuous and discrete Euler -- Poincar 'e formulations about the dynamics of underwater vehicles. Numerical results illustrate the scheme's ability to preserve geometric properties over extended time intervals.
Authors: L. V. Bogdanov
Link: http://arxiv.org/abs/2501.12858v1
Summary:
The dispersionless integrable system we consider here was introduced to the literature rather recently. It is connected with the general local form of self-dual conformal structure (SDCS) for the signature (2,2) In integrability framework this system possesses a rich structure of reductions, including differential reductions. We will discuss several characteristic reductions for this system, using the Lax pair, hierarchy structure and the dressing scheme. We use reductions to construct solutions for the SDCS equations.
7. Perturbations of embedded eigenvalues of asymptotically periodic magnetic Schrödinger operators on a cylinder
Authors: Jonas Jansen, Sara Maad Sasane, Wilhelm Treschow
Link: http://arxiv.org/abs/2501.12817v1
Summary:
We investigate the persistence of embedded eigenvalues for a class of magnetic Laplacians on an infinite cylindrical domain. The proof employs tools from Floquet theory, exponential dichotomies, and Lyapunov--Schmidt reduction. We give an example of a potential which satisfies the assumptions of our main theorem. We show that the set of nearby potentials for which the embedded eigenevalue persists forms a smooth manifold of finite and even codimension. We conclude that the proof of the main theorem is correct.
Authors: Luc Vinet, Alexei Zhedanov
Link: http://arxiv.org/abs/2501.12806v1
Summary:
The sieved Jacobi polynomials (either on the unit circle or on the real line) are bispectral. Eigenvalue equations for the sieved ultraspherical polynmials of the first and second kind are obtained as special cases. It is shown that the CMV Laurent poynomials associated to the sieving Jacobipolynomial on theUnit circle satisfy an eigenvalue equation with respect to a first order differential operator of Dunkl type.
Authors: David Fajman, Maximilian Ofner, Todd Oliynyk, Zoe Wyatt
Link: http://arxiv.org/abs/2501.12798v1
Summary:
We prove the nonlinear stability of homogeneous barotropic perfect fluid solutions in fixed cosmological spacetimes undergoing decelerated expansion. The results hold provided a specific inequality between the speed of sound of the fluid and the expansion rate of spacetime is valid. Our proof relies on an energy functional which is universal in the sense that it also applies to the case of linear expansion and enables a significantly simplified proof of bounds for fluids on linearly expanding spacetime. Finally, we consider the special cases of dust and radiation fluids in the de slowed regime and prove shock formation for arbitrarily small perturbations of homogenous solutions.
Authors: Ignacio Acevedo, Claudio Muñoz
Link: http://arxiv.org/abs/2501.12790v1
Summary:
The Yang-Mills field in an extremal Reissner-Nordstr"om black hole is considered. The kink is a fundamental, strongly unstable stationary solution in a non-perturbative, variable coefficients model. In this paper, we introduce and extend several virial techniques, adapt them to the inhomogeneous medium setting, and construct a finite codimensional manifold of the energy space. We handle the emergence of a weak threshold resonance in the description of the stable manifold.
11. Achronal localization and representation of the causal logic from conserved current, application to massive scalar boson
Authors: Domenico P. L. Castrigiano, Carmine De Rosa, Valter Moretti
Link: http://arxiv.org/abs/2501.12699v1
Summary:
Covariant achronal localizations are gained out of Covariant conserved currents computing their flux passing through a chronal surfaces. This general method applies to the probability density currents with causal kernel regarding the massive scalar boson. Due to the one-to-one correspondence between (covariants) localizations and representations of the causal logic thus, apparently for the first time, a covariant representation for an elementary quantum mechanical system has been achieved. While reaching this result the divergence theorem is proven for open sets with almost Lipschitz boundary.
12. The multiplicative constant in asymptotics of higher-order analogues of the Tracy-Widom distribution
Authors: Dan Dai, Wen-Gao Long, Shuai-Xia Xu, Lu-Ming Yao, Lun Zhang
Link: http://arxiv.org/abs/2501.12679v1
Summary:
In this paper, we are concerned with higher-order analogues of the Tracy-Widom distribution. We present a novel approach to establish the multiplicative constant in the large gap asymptotics of the distribution. An important new feature of the expression is the involvement of an integral of the Hamiltonian associated with a special, real, pole-free solution for $k. Our approach can also be adapted to calculate similar critical constants in other problems arising from mathematical physics, we say.
Authors: Théo Ballu, Cédric Boutillier, Sevak Mkrtchyan, Kilian Raschel
Link: http://arxiv.org/abs/2501.12664v1
Summary:
In this paper we study a triple generalization of the Leaky Abelian Sandpile Model. Each site can hold several different stacks of sand, one for each of a certain number of different layers or colors. When a stack of one color at a site topples, it can send sand not only to its nearest neighbors in equal amounts, but to all possible locations and colors. Stacks of different colors can topple according to different distributions and different leakiness parameters, however the toppling rule should be site-independent.
14. The BCS-Bogoliubov gap equation with external magnetic field and the first-order phase transition
Authors: Shuji Watanabe
Link: http://arxiv.org/abs/2501.12609v1
Summary:
We deal with a type I superconductor in a constant external magnetic field. We show that the transition from the normal state to the superconducting state is of the first order. We obtain the explicit expression for the entropy gap. We also show that there is a unique magnetic field (the critical magnetic field) given by a smooth function of the temperature and the gap function. We conclude that there are two solutions to the BCS-Bogoliubov gap equation and the implicit function theorem.
Authors: John Chae
Link: http://arxiv.org/abs/2501.12566v1
Summary:
We provide the first computations of colored unknots and Hopf link in the toric Calabi-Yau manifold. We conjecture that they are Poincare series of an infinite dimensional link homology theory. We compare our results with that of the