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We studied quantum phase transitions in the antiferromagnetic dimerized spin-1/2 XY chain andvtwo-leg ladders. From analysis of several spin models we present our main result: the framework to deal with topological orders and hidden…
We study the closure problem for continuum balance equations that model mesoscale dynamics of large ODE systems. The underlying microscale model consists of classical Newton equations of particle dynamics. As a mesoscale model we use the…
Naz and Chaudhry [3] established multiple closed-form solutions for the basic Lucas-Uzawa model. According to Boucekkine and Ruiz-Tamarit [1] and Chilarescu [2] unique closed-form solutions exist for the basic Lucas-Uzawa model. We equate…
We derive heuristically an integro-differential equation, as well as a shell model, governing the dynamics of the Lowest Landau Level equation in a high frequency regime.
We develop a rigorous analytical framework for metastable stochastic transitions in Landau-type gradient systems inspired by QCD phenomenology. The functional $F(\sigma;u)=\int_\Omega [\frac{\kappa}{2}|\nabla\sigma|^2+V(\sigma;u)]\,dx$,…
The Landau collision integral is an accurate model for the small-angle dominated Coulomb collisions in fusion plasmas. We investigate a high order accurate, fully conservative, finite element discretization of the nonlinear multi-species…
We propose a collision-oriented particle system to approximate a class of Landau-type equations. This particle system is formally derived from a particle system with random collisions in the grazing regime, and happens to be a special…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
In this paper, the coupled fractional Ginzburg-Landau equations are first time investigated numerically. A linearized implicit finite difference scheme is proposed. The scheme involves three time levels, is unconditionally stable and…
A new integration scheme, combining the stability and the precision of usual pseudo-spectral codes with the locality of finite differences methods, is introduced. It turns out to be particularly suitable for the study of front and…
We discuss solvable multistate Landau-Zener (MLZ) models whose Hamiltonians have commuting partner operators with $\sim 1/\tau$-time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive the…
In this paper, we study a class of bilevel optimization problems where the lower-level problem is a convex composite optimization model, which arises in various applications, including bilevel hyperparameter selection for regularized…
Continuous linear dynamical systems are used extensively in mathematics, computer science, physics, and engineering to model the evolution of a system over time. A central technique for certifying safety properties of such systems is by…
We propose a simple ansatz that allows to generate new exactly solvable multi-state Landau-Zener models. It is based on a system of two decoupled two-level atoms whose levels vary with time and cross at some moments. Then we consider…
We consider a set of non-stationary quantum models. We show that their dynamics can be studied using links to Knizhnik-Zamolodchikov (KZ) equations for correlation functions in conformal field theories. We specifically consider the boundary…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
Laplace transforms for integrals of stochastic processes have been known in analytically closed form for just a handful of Markov processes: namely, the Ornstein-Uhlenbeck, the Cox-Ingerssol-Ross (CIR) process and the exponential of…
This paper introduces a new method for the efficient computation of oscillatory multidimensional lattice sums in geometries with boundaries. Such sums are ubiquitous in both pure and applied mathematics, and have immediate applications in…
The Landau-Zener problem, where a minimum energy separation is passed with constant rate in a two-state quantum-mechanical system, is an excellent model quantum system for a computational project. It requires a low-level computational…
Coarse graining techniques offer a promising alternative to large-scale simulations of complex dynamical systems, as long as the coarse-grained system is truly representative of the initial one. Here, we investigate how the dynamical…