Classical spin and quantum propagation

We consider a classical Brownian motion model of diffusion in two spatial dimensions, where the Brownian particle moves on spiral paths. The classical spin does not change the propagator for the probability density for the position of the particle. However, the subdominant eigenvalues of the classical kernel are simply related to the dominant eigenvalues of the Feynman kernel for an analogous quantum system. The Feynman kernel can be extracted from the classical kernel by coupling to a spin angular momentum of the particle.     

Classical physics and electron spin

In the framework of classical physics, the formation of the intrinsic angular momentum of an electron is described and the correct value of the gyromagnetic ratio is obtained. The Maslov-Leray quasi-classical quantization rules result in the exact values of Landau levels obtained from the Pauli equation.     

Classical spin in a potential field

We consider an ensemble of restricted discrete random walks in 2+1 dimensions. The restriction on the walks is such as to given particles an intrinsic angular momentum. The walks are embedded in a field which affects the mean free path of the walks. We show that the dynamics of the walks is such that second-order effects are described by a discrete form of Schrödinger's equation for particles in a potential field. This provides a classical context of the equation which is independent of its quantum context.     

Classical models of elementary particles with spin

Classical models of elementary particles, regarded as the ultimate constituents of the known particles, are considered in the framework of general relativity. The work is based on that of López, using the Kerr-Newman solution of the Einstein field equations.     

Classical spin dynamics of anisotropic Heisenberg dimmers

In the present work we study the deterministic spin dynamics of two interacting anisotropic magnetic particles in the presence of an external magnetic field using the Landau-Lifshitz equation. The interaction between particles is through the exchange energy. We study both conservative and dissipative cases. In the first one, we characterize the dynamical behavior of the system by monitoring the Lyapunov exponents and bifurcation diagrams. In particular, we explore the dependence of the largest Lyapunov exponent respect to the magnitude of applied magnetic field and exchange constant. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated topology of intricately intermingled chaotic and regular regions. In the dissipative case, we calculate the final saturation states as a function of the magnitude of the applied magnetic field, exchange constant as well as the anisotropy constants.     

Classical spin models and the quantum-stabilizer formalism

We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as inner products between certain quantum-stabilizer states and product states. This connection allows us to use powerful techniques developed in quantum-information theory, such as the stabilizer formalism and classical simulation techniques, to gain general insights into these models in a unified way. We recover and generalize several symmetries and high-low temperature dualities, and we provide an efficient classical evaluation of partition functions for all interaction graphs with a bounded tree-width.     

Classical theory of laser noise

The classical theory of laser noise treats light in a classical manner, yet agrees with quantum theory for large particle numbers. The basic concept is that laser noise is caused by atomic jumps between lower and upper levels, and that atoms subjected to classically-prescribed optical fields are independent. The treatment of amplitude noise of single-mode cavities containing resonant three-level atoms is applicable to semiconductor lasers at moderate power. At high power one must account for the dependence of the gain on optical power and for state-occupancy fluctuations. The phasor theory that attributes noise to the beat between the oscillating field and the field spontaneously emitted in the mode by excited-state atoms cannot be understood consistently in semiclassical terms.     

Classical theory of wave beams

The Helmholtz and Maxwell equations describing fields of the beam type are solved. The energy streamlines in a vector beam coincide with the generatrices of an unparted hyper-boloid of revolution and are twisted. The angular momentum of a monochromatic electromagnetic field in coordinate space naturally splits into orbital and spin parts. The orbital angular momentum is perpendicular to the Poynting vector, and the spin part is parallel to it. Each beam m is characterized by a definite projection of the angular momentum on the z axis and is localized near a corresponding hyperboloid _m.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 1, pp. 101–105, January, 1971.     

Classical approach to quantum theory

A formulation of nonrelativistic, spinless, quantum mechanics is presented which is based on four postulates. Three of the postulates are very analogous to relations that hold in an operator formulation of classical mechanics, and the fourth is that the wave function evolves linearly in time. The conventional statistical assertions of quantum theory as well as the Schrödinger equation are recovered.     

Classical field theory with fermions

Classical field theory simulations have been essential for our understanding of non-equilibrium phenomena in particle physics. In this talk we discuss the possible extension of the bosonic classical field theory simulations to include fermions. In principle we use the inhomogeneous mean field approximation as introduced by Aarts and Smit. But in practice we turn from their deterministic technique to a stochastic approach. We represent the fermion field as an ensemble of pairs of spinor fields, dubbed male and female. These c-number fields solve the classical Dirac equation. Our improved algorithm enables the extension of the originally 1+1 dimensional analyses and is suitable for large-scale inhomogeneous settings, like defect networks.     

Classical theory of laser linewidth

The classical theory of light fluctuations rests on the intuitive concept that jumps between atomic states occur at independent times when the optical field has a prescribed value. The statistical properties of phase-noise sources are obtained in the present paper by applying this principle to detuned atoms. Formulae for amplitude and phase fluctuations coincide with quantum-theory results even when non-classical states of light are generated. Theories employing semiclassical or quantum concepts are reviewed. We consider particularly the linewidth of laser oscillators operating below and above threshold when the atomic polarization cannot be adiabatically eliminated. Quantum-theory results by Lax (1966) are recovered from classical theory in a straightforward manner. More general results are given for dispersive loads, applicable to external-cavity lasers and relevant to gain guidance. It is emphasized that the K-factor as calculated by Petermann is applicable only below threshold. When more than one emitting element is present, population rate equations need to be considered and the linewidth decreases when the pump fluctuations are suppressed. The role of gain compression relating to semiconductor lasers is discussed. It is shown that at low and moderate powers gain compression reduces the effective phase-amplitude coupling factor, . But at high power a number of mechanisms contribute to linewidth rebroadening. One of them is the statistical (quasi-thermal equilibrium) fluctuation of the refractive index. General concepts applicable to broadband light are outlined in an appendix.     

Classical and thermodynamic limits for generalised quantum spin systems

We prove that the rescaled upper and lower symbols for arbitrary generalised quantum spin systems converge in the classical limit. For a large class of models this enables us to derive the asyptotics of quantum free energies in the classical and in the thermodynamic limit.Research supported by a European Science Exchange Fellowship of the Royal Society, London     

Diagonalization-free implementation of spin relaxation theory for large spin systems

The Liouville space spin relaxation theory equations are reformulated in such a way as to avoid the computationally expensive Hamiltonian diagonalization step, replacing it by numerical evaluation of the integrals in the generalized cumulant expansion. The resulting algorithm is particularly useful in the cases where the static part of the Hamiltonian is dominated by interactions other than Zeeman (e.g. in quadrupolar resonance, low-field EPR and Spin Chemistry). When used together with state space restriction tools, the algorithm reported is capable of computing full relaxation superoperators for NMR systems with more than 15 spins.     

Classical scattering theory in one dimension

We discuss various scattering properties of the classical system ofn repelling particles on the real line. In the integrable case, i.e. if the asymptotic velocities are preserved under the scattering map, the asymptotic phases behave as if the particles collided pairwise.     

Classical scaling theory of quantum resonances

The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a related system. A scaling law which characterizes the structure of the resonant peaks is derived and numerically demonstrated.