Newsfeeds
Journal of Physics A: Mathematical and Theoretical - latest papers
Latest articles for Journal of Physics A: Mathematical and Theoretical
-
More on the operator space entanglement (OSE): Rényi OSE, revivals, and integrability breaking *
We investigate the dynamics of the Rényi Operator Space Entanglement (OSE) entropies Sn across several one-dimensional integrable and chaotic models. As a paradigmatic integrable system, we first consider the so-called rule 54 chain. Our numerical results reveal that the Rényi OSE entropies of diagonal operators with nonzero trace saturate at long times, in contrast with the behavior of von Neumann entropy. Oppositely, the Rényi entropies of traceless operators exhibit logarithmic growth with time, with the prefactor of this growth depending in a nontrivial manner on n. Notably, at long times, the complete operator entanglement spectrum of an operator can be reconstructed from the spectrum of its traceless part. We observe a similar pattern in the XXZ chain, suggesting Universal behavior. Additionally, we consider dynamics in nonintegrable deformations of the XXZ chain. Finite-time corrections do not allow to access the long-time behavior of the von Neumann entropy. On the other hand, for n > 1 the growth of the entropies is milder, and it is compatible with a sublinear growth, at least for operators associated with global conserved quantities. Finally, we show that in finite-size integrable systems, Sn exhibit strong revivals, which are washed out when integrability is broken.
-
Statistical inference in classification of high-dimensional Gaussian mixture
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a broad class of regularized convex classifiers in the limit where both the sample size n and the dimension p approach infinity while their ratio remains fixed. This approach contrasts with traditional large-sample theory in statistics, which examines asymptotic behavior as with p fixed. A key advantage of this asymptotic regime is that it provides precise quantitative guidelines for designing machine learning systems when both p and n are large but finite. Our focus is on the generalization error and variable selection properties of the estimators. Specifically, based on the distributional limit of the classifier, we construct a de-biased estimator to perform variable selection through an appropriate hypothesis testing procedure. Using L1-regularized logistic regression as an example, we conduct extensive computational experiments to verify that our analytical findings align with numerical simulations in finite-sized systems. Additionally, we explore the influence of the covariance structure on the performance of the de-biased estimator.
-
The dynamics of the breather, degenerate solutions and dark peakon solutions for the focusing and defocusing complex short pulse equations
This paper proposes a uniform N-fold Darboux transformation (DT) for both the focusing and defocusing complex short pulse equations, which is expressed in determinant and compact form. Through the application of uniform DT, we systematically constructed the breather under vanishing boundary condition (VBC) in the focusing case and classified its dynamics. Additionally, the degenerate uniform DT and degenerate breather (i.e. breather-positon) under VBC are also obtained by performing Taylor asymptotic expansion. The generation of breather under VBC is related to the ‘gravitation-repulsion effect’, ‘partial annihilation effect’ and ‘resonance effect’ between solitons. We further analyzed the interaction between breather, soliton and degenerate solutions, and proved that degenerate solutions are transparent when colliding with soliton and breather. Consequently, degenerate solutions are also referred to as super-reflectionless potentials. For the defocusing case, we derive multi-dark smooth soliton and dark peakon solutions under the non-VBC from the compact form of the uniform DT, utilizing a specific limit. Furthermore, a single dark soliton’s dynamic classification and asymptotic behavior were studied using the zeros analysis method and asymptotic analysis respectively. Finally, by investigating the interactions between two- and three-dark soliton solutions, we find that dark solitons exhibit greater stability.
-
Quantum circuits with free fermions in disguise
Recently multiple families of spin chain models were found, which have a free fermionic spectrum, even though they are not solvable by a Jordan–Wigner transformation. Instead, the free fermions emerge as a result of a rather intricate construction. In this work we consider the quantum circuit formulation of the problem. We construct circuits using local unitary gates built from the terms in the local Hamiltonians of the respective models, and ask the question: which circuit geometries (sequence of gates) lead to a free fermionic spectrum? Our main example is the 4-fermion model of Fendley, where we construct free fermionic circuits with various geometries. In certain cases we prove the free fermionic nature, while for other geometries we confirm it numerically. Surprisingly, we find that many standard brickwork circuits are not free fermionic, but we identify certain symmetric constructions which are. We also consider a recent generalization of the 4-fermion model and obtain the factorization of its transfer matrix, and subsequently derive a free-fermionic circuit for this case as well.
-
A geometric description of some thermodynamical systems
In this paper we show how almost cosymplectic structures are a natural framework to study thermodynamical systems. Indeed, we are able to obtain the same evolution equations obtained previously by Gay-Balmaz and Yoshimura (2019 Entropy21 39) using variational arguments. The proposed geometric description allows us to apply geometrical tools to discuss reduction by symmetries, the Hamilton–Jacobi equation or discretization of these systems.