Authors: Sara Dal Cengio, Pedro E. Harunari, Vivien Lecomte, Matteo Polettini
Link: http://arxiv.org/abs/2502.04298v1
Summary:
C currents are fundamental entities that describe the flows of energy, particles, individuals, chemical species, information, or other quantities. They apply to systems described by agents transitioning between vertices along the edges of a network (at some rate in each direction) It has recently been shown that, at stationarity, a hidden linearity exists between currents that flow along edges. In this paper, we extend this result to the situation where one controls the currents of several edges, and prove that other currents are in linear-affine relation with the input ones.
Authors: Nicolas Crampe, Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov
Link: http://arxiv.org/abs/2502.04275v1
Summary:
The properties of the Wilson rational functions with three different normalizations are described. The so-called Wilson rational algebra is introduced, which encodes algebraically the spectral properties of these special functions. For one of these, the spectral algebra simplifies to yield the meta
Authors: Xing M. Wang, Tony C. Scott
Link: http://arxiv.org/abs/2502.04257v1
Summary:
The Bracket Notation (PBN) is based on the Dirac Notation in Quantum Mechanics. Using the PBN, many formulae, such as normalizations and expectations in systems of one or more random variables, can now be written in abstract basis-independent expressions. The time evolution of homogeneous Markov processes can also be formatted in such a way. Potential applications show the usefulness of PBN beyond the constrained domain and range of Hermitian operators on Hilbert Spaces in QM all the way to IT.
Authors: Abhay Ashtekar
Link: http://arxiv.org/abs/2502.04252v1
Summary:
The conference marked the 50th anniversary of Hawking's seminal paper on black hole radiance. It was clear already from Hawking's analysis that a proper quantum gravity theory would be essential for a more complete understanding of the evaporation process. This task was undertaken in Loop Quantum Gravity (LQG) two decades ago and by now the literature on the subject is quite rich. The goal of this contribution is to summarize a mainstream perspective that has emerged. The intended audience is the broader gravitational physics community, rather than quantum gravity experts.
Authors: Parveen Kumar, Yuval Gefen, Kyrylo Snizhko
Link: http://arxiv.org/abs/2502.04214v1
Summary:
Non-Hermitian systems are widespread in both classical and quantum physics. The dynamics of such systems has recently become a focal point of research. Yet the current literature features a number of apparently irreconcilable results. Here we develop a general theory for slow evolution of non-Hermitsian systems. It provides efficient tools to predict the outcome of the system's evolution, avoiding the need to follow costly time-evolution simulations, say the authors. The approach may be useful for designing devices based on non- hermitian physics.
5. Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes
Authors: Vijay Kumar, Tomaž Prosen, Dibyendu Roy
Link: http://arxiv.org/abs/2502.04152v1
Summary:
We show the emergence of random matrix theory (RMT) spectral correlations in the chaotic phase of generic periodically kicked interacting quantum many-body systems. spectral form factor (SFF),
Authors: April Lynne D. Say-awen, Sam Coates
Link: http://arxiv.org/abs/2502.04133v1
Summary:
We introduce a family of octagonal tilings which are composed of three prototiles. We define our tilings with respect to two non-negative integers,
Authors: Moritz Dober, Alexander Glazman, Sébastien Ott
Link: http://arxiv.org/abs/2502.04129v1
Summary:
The planar q-state Potts model undergoes a discontinuous phase transition when q > 4 and there are exactly q + 1 extremal Gibbs measures at the transition point. We show emergence of a free layer of width between the two ordered phases (wetting) and establish convergence of its boundaries to two Brownian bridges conditioned not to intersect. In a companion work, we provide a detailed study of the Pottsmodel under order-order Dobrushin conditions. The coupling relates the interface in FK-percolation to a long subcritical cluster in the ATRC model.
Authors: Sébastien Ott
Link: http://arxiv.org/abs/2502.04117v1
Summary:
weak mixing in lattice models is informally the property that information does not propagate inside a system. In dimension two, the boundary of reasonable systems is one dimensional, so information should not be able to propagate there. This led to the conjecture that in 2D, weak mixing implies strong mixing. The present work gives a new proof of these results, extends the family of models for which the implication holds, and, most interestingly, provides a ``percolative picture'' of the information propagation.
Authors: Karol K. Kozlowski, Alex Simon
Link: http://arxiv.org/abs/2502.03894v1
Summary:
This work provides a closed, explicit and rigorous expression for the appropriately truncated
Authors: Kacper Taźbierski, Marcin Magdziarz
Link: http://arxiv.org/abs/2502.03889v1
Summary:
We analyze the equivalents of the celebrated arcsine laws for Brownian motion undergoing Poissonian resetting. We obtain closed-form formulae for the probability density functions of the corresponding random variables in the cases of the first and second arcsine law. Furthermore, we obtain numerical results for the third law. We conclude that the laws are equivalent to the first, second, and third arcsine Laws of Brownian Motion. The results of the study are published in the Journal of Applied Mathematics.
Authors: Vladislav A. Yastrebov, Camille Noûs
Link: http://arxiv.org/abs/2502.03886v1
Summary:
Adaptive Cross Approximation (ACA) method is widely used to approximate admissible blocks of hierarchical matrices. ACA constructs a low-rank approximation by evaluating only a few rows and columns of the original operator. This paper proposes combining the classical, purely algebraic ACA method with a geometrical pivot selection based on the central subsets and extreme property subsets. The method is named ACA-GP, GP stands for Geometrical Pivots. The superiority of the ACA- GP compared to the classical ACA is demonstrated using a classical Green operator for two clouds of interacting points.
Authors: Tatsuaki Wada, Sousuke Noda
Link: http://arxiv.org/abs/2502.03866v1
Summary:
The gradient-flow equations are derived from the proposed action which is invariant under the Weyl's gauge transformations. In Weyl integrable geometry, we have related Amari's
Authors: Yves Colin de Verdière
Link: http://arxiv.org/abs/2502.03838v1
Summary:
We study spectral theory of sign-changing Laplace operators using semi-classical Dirichlet-to-Neumann maps. We prove the existence of modesconcentrated on the interface and describe an effective semi- classical equation for them. We also show that modes can be focused on a single point on the surface of the Laplace operator. The results are published in the open-access issue of the Journal of Applied Mathematics, published by the University of California, Los Angeles.
Authors: A. V. Tsiganov
Link: http://arxiv.org/abs/2502.03786v1
Summary:
Multi-symplectic integrators are typically regarded as a discretization of the Hamiltonian partial differential equations. This is due to the fact that, for generic finite-dimensional Hamiltonian systems, there exists only one independent symplectic structure. In this note, the second invariant symplectic form is presented for the nonintegrable Henon-Heiles system, Kepler problem, integrable and non-integrably Toda type systems. This approach facilitates the construction of a multi-syMPlectic integrator, which effectively preserves both symplectic forms for these benchmark problems.
15. Quantum integrable model for the quantum cohomology/quantum K-theory of flag varieties and the double $β$ -Grothendieck polynomials
Authors: Jirui Guo
Link: http://arxiv.org/abs/2502.03768v1
Summary:
A GL$(n)$ quantum integrable system generalizing the asymmetric five vertices spin chain is shown to encode the ring relations of the equivariant quantum cohomology and quantum K-theory ring of flag varieties. We also show that the Bethe ansatz states of this system generate the double
Authors: Mulyanto, Ardian N. Atmaja, Fiki T. Akbar, Bobby E. Gunara
Link: http://arxiv.org/abs/2502.03733v1
Summary:
In this paper, we show the global existence and uniqueness of classical solutions of the Maxwell-Chern-Simmons-Higgs system. Our methods rely only on classical existence theorems, including energy estimates, the Sobolev inequality, and the choice of the Coulomb gauge condition. The equations are well-posed for finite initial data and the solution preserves any additional