Related papers: Two Combinatorial Models with identical Statics ye…
A new type of kinetic models with non-instantaneous binary collisions is considered. Collisions are described by a transport process in the joint state space of a pair of particles. The interactions are of alignment type, where the states…
We develop a novel analytical method for studying optimal paths in dynamic optimization problems under general monotonicity conditions. The method centers on a locator function -- a simple object constructed directly from the model's…
In the framework of simple spin-boson Hamiltonian we study an interplay between dynamic and spectral roots to stochastic-like behavior. The Hamiltonian describes an initial vibrational state coupled to discrete dense spectrum reservoir. The…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
We consider a multivariate non-linear Hawkes process in a multi-class setup where particles are organised within two populations of possibly different sizes, such that one of the populations acts excitatory on the system while the other…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
We discuss a general relation between the solitons and statistical mechanics and show that the partition function of the normal random matrix model can be obtained from the multi-soliton solutions of the two-dimensional Toda lattice…
We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a…
We discuss a hierarchy of broken symmetries with special emphasis on partial dynamical symmetries (PDS). The latter correspond to a situation in which a non-invariant Hamiltonian accommodates a subset of solvable eigenstates with good…
We study very simple sorting algorithms based on a probabilistic comparator model. In our model, errors in comparing two elements are due to (1) the energy or effort put in the comparison and (2) the difference between the compared…
Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact)…
Two types of population models are well known -- the continuous and the discrete types.The two have very different characteristics and methods of solutions and analysis.In this note, we point out that an iterative technique when applied to…
The classical Cahn-Hilliard (CH) equation corresponds to a gradient dynamics model that describes phase decomposition in a binary mixture. In the spinodal region, an initially homogeneous state spontaneously decomposes via a large-scale…
A cranking harmonic oscillator model, widely used for the physics of fast rotating nuclei and Bose-Einstein condensates, is re-investigated in the context of PT-symmetry. The instability points of the model are identified as exceptional…
We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties.…
In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…