Related papers: Hamiltonian dynamics and spectral theory for spin-…
We consider properties of a two-dimensional electron system in a random magnetic field. It is assumed that the magnetic field not only influences orbital electron motion but also acts on the electron spin. For calculations, we suggest a new…
A general spin symmetry argument is proposed for spin currents in semiconductors. In particular, due to the symmetry with respect to spin polarization of the helicity eigenstates of the Luttinger Hamiltonian for a hole-doped semiconductor,…
The spin of an electron trapped in a quantum dot is a promising candidate implementation of a qubit for quantum information processing. We study the central spin problem of the effect of the hyperfine interaction between such an electron…
Inspired by path integral molecular dynamics, we build a spin model, in terms of spin coherent states, from which we can compute the quantum expectation values of a spin in a constant magnetic field, at finite temperature. This formulation…
We provide a theoretical set up for studying the dynamics in quantum spin chain models with inhomogeneous two-body interaction. We frame in our formalism models that can be mapped into a fermion system with a quadratic Hamiltonian. Local…
Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…
We propose an integrable model of a multicomponent spinor Bose-Einstein condensate in one dimension, which allows an exact description of the dynamics of bright solitons with spin degrees of freedom. We consider specifically an atomic…
The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…
In this work, previous results concerning the infinitely many zeros of single stochastic oscillators driven by random forces are extended to the general class of coupled stochastic oscillators. We focus on three main subjects: 1) the…
We describe the symplectic structure and Hamiltonian dynamics for a class of Grassmannian manifolds. Using the two dimensional sphere ($S^2$) and disc ($D^2$) as illustrative cases, we write their path integral representations using…
In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in [Sasamoto-Wadati], [Barraquand-Corwin] and [Povolotsky] in the context of KPZ universality…
Spin relaxation is investigated theoretically in two-dimensional systems. Various semiconductor structures of both n- and p-types are studied in detail. The most important spin relaxation mechanisms are considered. The spin relaxation times…
Spin waves are the fundamental excitations in magnetically ordered spin systems and are ubiquitously observed in magnetic materials. However, the standard understanding of spin waves as collective spin oscillations in an effective harmonic…
Helicity plays a unique role as an integral invariant of a dynamical system. In this paper, the concept of helicity in the general setting of Hamiltonian dynamics is discussed. It is shown, through examples, how the conservation of overall…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a…
In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of symplectic groupoids give rise to discrete dynamical systems,…
There is a renewed interest to study spin-polarized transport and spin dynamics in various electronic materials. The motivation to examine the spin degrees of freedom (mostly in electrons, but also in holes and nuclei) comes from various…
We analyze a new class of time-periodic nonreciprocal dynamics in interacting chaotic classical spin systems, whose equations of motion are conservative (phase-space-volume-preserving) yet possess no symplectic structure. As a result, the…
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution…