相关论文: Nonlinear Filtering of Classical and Quantum Spin …

Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…

Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…

A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…

We investigate the existence and multiplicity of weak solutions for a nonlinear Kirchhoff type quasilinear elliptic system on the whole space $\mathbb{R}^N$. We assume that the nonlinear term satisfies the locally super-$(m_1,m_2)$…

We consider non-linear wave type solutions with mass scale parameter and vahished canonical spin density operator in a pure SU(2) quantum chtomodynamics (QCD). A new stationary solution which can be treated as a system of static Wu-Yang…

We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…

In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir…

I study the quantum mechanics of a spin interacting with an ``apparatus''. Although the evolution of the whole system is unitary, the spin evolution is not. The system is chosen so that the spin exhibits loss of quantum coherence, or…

In this paper, we investigate the existence of multiple periodic solutions for two classes of nonlinear difference systems involving $(\phi_1,\phi_2)$-Laplacian. First, by using an important critical point theorem due to B. Ricceri, we…

This paper investigates two classes of quasilinear and essentially nonlinear integral equations with a sum-difference kernel on the half-line. Such equations arise in various areas of physics, including the theory of radiative transfer in…

Quantum spin liquids are long-range entangled phases whose magnetic correlations are determined by strong quantum fluctuations. While an overarching principle specifying the precise microscopic coupling scenarios for which quantum…

The traditional Standard Quantum Mechanics is unable to solve the Spin-Statistics problem, i.e. to justify the utterly important Pauli Exclusion Principle. We show that this is due to the non completeness of the standard theory due to an…

We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This…

Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…

Classical integrable Hamiltonian systems generated by elements of the Poisson commuting ring of spectral invariants on rational coadjoint orbits of the loop algebra $\wt{\gr{gl}}^{+*}(2,{\bf R})$ are integrated by separation of variables in…

This paper introduces filtered finite difference methods for numerically solving a dispersive evolution equation with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled nonlinear Schr\"odinger…

The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…

Continuous observation of a quantum system yields a measurement record that faithfully reproduces the classically predicted trajectory provided that the measurement is sufficiently strong to localize the state in phase space but weak enough…

We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum…

In a previous paper [1] we proposed a purely mathematical way to quantum mechanics based on Cartan's simple spinors in their most elementary form of 2 component spinors. Here we proceed along that path proposing, this time, a symmetric…