A simple model of the classicalZitterbewegung: Photon wave function

We propose a simple classical model of the zitterbewegung. In this model spin is proportional to the velocity of the particle, the component parallel top is constant and the orthogonal components are oscillating with2p frequency. The quantization of the system gives wave equations for spin,0, 1/2, 1, 3/2,…, etc. respectively. These equations are convenient for massless particles. The wave equation of the spin-1, massless free particle is equivalent to the Maxwell equations and the state functions have a probability interpretation and exhibit conserved current densities. The ground state has zero energy.     

Relativistic kinetic theory of quantum systems: I. Wigner functions for a relativistic spin-12 system

For a dilute and nondegenerate relativistic spin-$\text{1}\text{2}$ system two kinds of Wigner functions are defined: one has sixteen spinor components and the other four spin components. Their relationship is established. Statistical expressions for the current density, the energy-momentum density and the spin density are obtained in terms of both kinds of Wigner functions. The transformation properties of the latter under Lorentz transformations are discussed.     

Probability Representation of Quantum States

The review of new formulation of conventional quantum mechanics where the quantum states are identified with probability distributions is presented. The invertible map of density operators and wave functions onto the probability distributions describing the quantum states in quantum mechanics is constructed both for systems with continuous variables and systems with discrete variables by using the Born’s rule and recently suggested method of dequantizer–quantizer operators. Examples of discussed probability representations of qubits (spin-1/2, two-level atoms), harmonic oscillator and free particle are studied in detail. Schrödinger and von Neumann equations, as well as equations for the evolution of open systems, are written in the form of linear classical–like equations for the probability distributions determining the quantum system states. Relations to phase–space representation of quantum states (Wigner functions) with quantum tomography and classical mechanics are elucidated.     

Stabilization of a steady state in oscillators coupled by a digital delayed connection

We propose the mapping of polynomial of degree 2S constructed as a linear combination of powers of spin-S (for simplicity, we called as spin-S polynomial) onto spin-crossover state. The spin-S polynomial in general can be projected onto non-symmetric degenerated spin up (high-spin) and spin down (low-spin) momenta. The total number of mapping for each general spin-S is given by 2(2^2S ? 1). As an application of this mapping, we consider a general non-bilinear spin-S Ising model which can be transformed onto spin-crossover described by Wajnflasz model. Using a further transformation we obtain the partition function of the effective spin-1/2 Ising model, making a suitable mapping the non-symmetric contribution leads us to a spin-1/2 Ising model with a fixed external magnetic field, which in general cannot be solved exactly. However, for a particular case of non-bilinear spin-S Ising model could become equivalent to an exactly solvable Ising model. The transformed Ising model exhibits a residual entropy, then it should be understood also as a frustrated spin model, due to competing parameters coupling of the non-bilinear spin-S Ising model.     

On the simultaneous measurement of spin components using spin-1/2 meters: Naimark embedding and projections

Measurements involving spin-1/2 meters which result in the simultaneous measurement of spin components are described. The spin analoge of the Arthur-Kelly experiment is contrasted with a simultaneous measurement which interacts with the system. Naimark extensions are constructed and Bloch state projection properties are discussed for each case. The theory is extended to squeezed angular momentum measurement.     

Spin squeezing and quantum correlations

We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.     

Exponential Mixing and Time Scales¶in Quantized Hyperbolic Maps on the Torus

We study the behaviour, in the simultaneous limits , of the Husimi and Wigner distributions of initial coherent states and position eigenstates, evolved under the quantized hyperbolic toral automorphisms and the quantized baker map. We show how the exponential mixing of the underlying dynamics manifests itself in those quantities on time scales logarithmic in . The phase space distributions of the coherent states, evolved under either of those dynamics, are shown to equidistribute on the torus in the limit , for times t between and , where γ is the Lyapounov exponent of the classical system. For times shorter than , they remain concentrated on the classical trajectory of the center of the coherent state. The behaviour of the phase space distributions of evolved position eigenstates, on the other hand, is not the same for the quantized automorphisms as for the baker map. In the first case, they equidistribute provided t→∞ as , and as long as t is shorter than . In the second case, they remain localized on the evolved initial position at all such times. Received: 1 October 1999/Accepted: 4 January 2000     

Quantum Correlations of Two Relativistic Spin-12 Particles Under Noisy Channels

We study the quantum correlation dynamics of bipartite spin-\(\frac {1}{2}\) density matrices for two particles under Wigner rotations induced by Lorentz transformations which is transmitted through noisy channels. We compare quantum entanglement, geometric discord(GD), and quantum discord (QD) for bipartite relativistic spin-\(\frac {1}{2}\) states under noisy channels. We find out QD and GD tend to death asymptotically but a sudden change in the decay rate of the entanglement occurs under noisy channels. Also, bipartite relativistic spin density matrices are considered as a quantum channel for teleportation one-qubit state under the influence of depolarizing noise and compare fidelity for various velocities of observers.     

The anisotropic multichannel spin-$\mathsf{S}$ Kondo model: Calculation of scales from a novel exact solution

A novel exact solution of the multichannel spin-S Kondo model is presented, based on a lattice path integral approach of the single channel spin-1/2 case. The spin exchange between the localized moment and the host is of XXZ-type, including the isotropic XXX limit. The free energy is given by a finite set of non-linear integral equations, which allow for an accurate determination of high- and low-temperature scales.Received: 9 June 2004, Published online: 3 August 2004PACS: 72.15.Qm Scattering mechanisms and Kondo effect - 04.20.Jb Exact solutions - 75.20.Hr Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions - 75.10.Lp Band and itinerant models     

Informational incompleteness of the observablesS x,S y,S z for spin-1 systems

By a counter-example, we show that the set of the three spin components S_x, S_y, S_z of spin-1 systems is not informationally complete.     

Electron spin polarization in the photoemission of NEA GaAs1−x P x

Negative electron affinity GaAs_1–x P _x -photocathodes emit spin-polarized electrons if irradiated with circularly polarized light. The spectra of spin polarization of photoelectrons emitted from crystals with different phosphorus contentx resemble each other in shape but shift to shorter wavelengths with increasingx. Polarization values up to 40% are observed for electrons from crystals withx=0 andx=0.38. Cathodes with higher phosphorus contents increasing fromx=0.65 tox=0.87 and tox = 1.0 deliver photoelectrons with decreasing degrees of spin polarization of 17%, 15%, and 9%, respectively, at maximum.     

Quantum Moment Hydrodynamics and the Entropy Principle

This paper presents how a non-commutative version of the entropy extremalization principle allows to construct new quantum hydrodynamic models. Our starting point is the moment method, which consists in integrating the quantum Liouville equation with respect to momentum p against a given vector of monomials of p. Like in the classical case, the so-obtained moment system is not closed. Inspired from Levermore's procedure in the classical case,⁽²⁶⁾ we propose to close the moment system by a quantum (Wigner) distribution function which minimizes the entropy subject to the constraint that its moments are given. In contrast to the classical case, the quantum entropy is defined globally (and not locally) as the trace of an operator. Therefore, the relation between the moments and the Lagrange multipliers of the constrained entropy minimization problem becomes nonlocal and the resulting moment system involves nonlocal operators (instead of purely local ones in the classical case). In the present paper, we discuss some practical aspects and consequences of this nonlocal feature.     

Crossover scaling function for the free energy

A cubic field, coupling tos|s|², inn-component spin models induces a bicritical crossover fromn-isotropic to Ising like (m=1) critical behaviour for 1<n<, but to classical behaviour in the limitn. By following the analysis of Nelson and Domany, the bicritical scaling function for the free energy ind dimensions is obtained correct to order =4–d and for general (m,n). The mechanism responsible for the breakdown of hyperscaling in the classical behaviour is discussed.     

A set of exactly solvable Ising models with half-odd-integer spin

We present a set of exactly solvable Ising models, with half-odd-integer spin-S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin-(S,1/2) and only nearest-neighbor interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin-S lattice. By imposing the condition that the mixed half-odd-integer spin-(S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the free fermion condition of the eight vertex model. The number of solutions for a general half-odd-integer spin-S is given by S+1/2. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number.     

Nuclear spin conversion of methyl groups

A theory is presented for nuclear spin conversion of methyl groups, where the total spin of the three protons changes fromI=1/2 toI=3/2. The transition may be mediated by the magnetic dipolar interaction of the protons among themselves or with a nearby unpaired electron. In general the excess energy, i.e. the tunnelling energy , is transferred from the spin system to the lattice via the rotor-phonon coupling; for the case of an almost free rotor in the magnetic field of an unpaired electron spin, the direct coupling of the electron-proton interaction to the lattice motion may be the more efficient mechanism. AtT=0 the rate is found to be finite, at high temperatures it shows an Arrhenius behaviour. In the intermediate range, two different power laws may govern the temperature dependence, namely 1/T or 1/T ⁷; the latter is due to two-phonon scattering.     

Quantum domain walls in the one-dimensional Ising model in a transverse field

Within the exactly soluble spin-$\text{1}\text{2}$ Ising chain in a transverse field, wavefunctions are identified which correspond to the domain wall-type solutions in the related classical model. For these wavefunctions the energy expectation values and longitudinal spin correlations are evaluated exactly. The results are used to comment on the relation between the quantum and classical domain walls.     

Exact results for the dynamics of the classical one dimensional easy plane ferromagnet at low temperatures

The in-plane and out-of-plane dynamical correlation functions for the classical one dimensional easy plane ferromagnet are calculated asymptotically exactly at low temperatures. The results are restricted to temperatures much below the crossover temperature at which spins begin aligning in the plane. The long wavelength behavior of the in-plane fluctuations is consistent with dynamical scaling, in contrast to the isotropic case, and agrees with the results of Villain and of Nelson and Fisher. The linewidths for the in-plane fluctuations at short wavelengths are calculated exactly, and approach those of the isotropic model for small anisotropy. The theory of Villain, the theory of Cieplak and Sjolander, and the simulations of Loveluck, Jauslin, Schneider and Stoll all give incorrect results for these linewidths. The out of plane linewidths show an anomalous temperature dependence due to a singularity in the three spin wave density of states that is characteristic of one dimensional systems. The linewidth is proportional toT ² lnT except at the wavevector for which the second derivative of the spin wave frequency with respect to wavevector vanishes (/2 for CsNiF₃) where the linewidth is proportional toT ^5/3. The linewidth has a strong discontinuity as the wavevector increases as a result of a catastrophe occurring in the calculation of the three spin wave density of states. The position and strength of the discontinuity are temperature dependent. The diffusion coefficient is logarithmically dependent on the anisotropy, and diverges as (T ² lnD)^–1, which is consistent with the (lnT)^–1 behavior predicted for the isotropic ferromagnet in earlier work. The results are derived for the case of single ion anisotropy, using a spin wave theory for static correlations and the spin current damping function, and can be readily extended to the case of anisotropic exchange.     

Decomposition of Ising spin of spin-S Ising model

We propose a general method by which an Ising spin of a spin-S Ising model is decomposed into Ising spins less than S. Some exactly solvable spin-S Ising models with S greater than 1/2 are obtained without using Horiguchi's condition or its extended conditions. These systems are reduced to the Ising model of spin ± 1 or an Ashkin-Teller model.     

A direct proof of dimerization in a family of <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">n</Emphasis>)-invariant quantum spin chains

We study the family of spin-S quantum spin chains with a nearest neighbor interaction given by the negative of the singlet projection operator. Using a random loop representation of the partition function in the limit of zero temperature and standard techniques of classical statistical mechanics, we prove dimerization for all sufficiently large values of S.