Exploring the entanglement of free spin-(1/2), spin-1 and spin-2 fields

In this study, we explore the entanglement of free spin-(1/2), spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transformation and express the vacuum state with a particle pair state in the configuration space, which is used to calculate the entropy. This clearly demonstrates that the entanglement entropy originates from the particles across the boundary.Finally, we generalize this method to free spin-1 and spin-2 fields. These higher free massless spin fields have wellknown complications owing to gauge redundancy. We deal with the redundancy by gauge-fixing in the light-cone gauge. We show that this gauge provides a natural tensor product structure in the Hilbert space, while surrendering explicit Lorentz invariance. We also use the Bogoliubov transformation to calculate the entropy. The area law emerges naturally by this method.     

Noncommutative spin-1/2 representations

In this letter we apply the methods of our previous paper, hep-th/0108045, to noncommutative fermions. We show that the fermions form a spin-1/2 representation of the Lorentz algebra. The covariant splitting of the conformal transformations into a field-dependent part and a -part implies the Seiberg-Witten differential equations for the fermions. Received: 5 December 2001 / Published online: 22 May 2002     

Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model

We present a study, within a mean-field approach, of the kinetics of a mixed ferrimagnetic model on a square lattice in which two interpenetrating square sublattices have spins that can take two values, , alternated with spins that can take the four values, . We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the reduced temperature and interaction parameter planes, namely in the (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in the (d, T) plane for low values of h. The dynamic multicritical point or dynamic critical end point exist in the (d, T) plane for low values of h. Moreover, phase diagrams contain paramagnetic (p), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+p) and (i+p), that strongly depend on interaction parameters.     

Some characteristic behavior of mixed spin-1/2 and spin-1 Ising nano-tube

The magnetization of a cylindrical Ising nano-tube is investigated by the use of the effective field theory with correlations. The effects of the crystal field couplings at the surface shell to the order parameters, susceptibility, internal energy, specific heat and free energy are investigated. Some characteristic phenomena are examined in the thermal variations, depending on crystal field term. Moreover, tricritical and critical points are found on the (D/J,kT/J) plane, where D/J and kT/J are reduced crystal-field and temperature, respectively.     

Geometric phase for degenerate states of spin-1 and spin-1/2 pair

The geometric phase of a bi-particle model is discussed. One can drive the system to evolve by applying an external magnetic field, thereby controlling the geometric phase. The model has degenerate lowest-energy eigenvectors. The initial state is assumed to be the linear superposition or mixture of the eigenvectors. The relationship between the geometric phase and the structures of the initial state is considered, and the results are extended to a more general model.      

Simplified parent-child formalism for spin-0 and spin-1/2 parents

We develop further the parent-child relation, that is the calculation of the cross-sections and correlations of observed particles, typically charged leptons, arising from the decay of long-lived primarily produced “parent” particles. In the high-momentum regime, when the momenta of parent and child are closely aligned, we show how, for spinless parents, the relation can be simplified by the introduction of “fragmentation” functions derived from the invariant inclusive decay distributions. We extend the formalism to the case of spin-1/2 parents and advocate its application to charm production and decay at the quark level.     

Magnetic properties of a mixed spin-1/2 and spin-3/2 transverse Ising model

A theoretical study of a mixed spin-1/2 and spin-3/2 Ising system with independent transverse fields is presented using an effective field method within the framework of a single-site cluster theory. In this approach the effective field equations are derived using a probability distribution method based on the use of generalized van der Waerden identities accounting exactly for the single-site kinematic relations. The effect of the transverse fields on the critical behaviour is studied. The thermal dependence of the longitudinal and transverse components of the magnetization and its higher moments is also studied.     

Dynamics of spin-1/2 quantum plasmas

The fully nonlinear governing equations for spin-1/2 quantum plasmas are presented. Starting from the Pauli equation, the relevant plasma equations are derived, and it is shown that nontrivial quantum spin couplings arise, enabling studies of the combined collective and spin dynamics. The linear response of the quantum plasma in an electron-ion system is obtained and analyzed. Applications of the theory to solid state and astrophysical systems as well as dusty plasmas are pointed out.     

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments （MMs） in terms of Chiral Perturbation Theory （ChPT）.In particular,we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well.We also make predictions for the decuplet MMs at the same chiral order.Among them,the MMs of the Δ＋＋ and Δ ＋ are found to agree well with data within the experimental uncertainties.     

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments (MMs) in terms of Chiral Perturbation Theory (ChPT).In particular,we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well.We also make predictions for the decuplet MMs at the same chiral order.Among them,the MMs of the Δ++ and Δ + are found to agree well with data within the experimental uncertainties.     

The classical spin-1/2 tachyon field

We present the classical theory of a set of two spinor fields patterned closely after the Dirac theory in two-component form, but each field obeys a modified Klein-Gordon equation, in which the sign ofm ² has been changed. The solution contains parts with real and imaginary frequencies, that contribute differently to conserved quantities such as the charge and the energy-momentum vector. We also show how the minimal interaction with the electromagnetic field is obtained.     

Vacuum induced spin-1/2 Berry's phase

We calculate the Berry phase of a spin-1/2 particle in a magnetic field considering the quantum nature of the field. The phase reduces to the standard Berry phase in the semiclassical limit and the eigenstate of the particle acquires a phase in the vacuum. We also show how to generate a vacuum induced Berry phase considering two quantized modes of the field which has an interesting physical interpretation.     

Quasi-probability distribution for spin-1/2 particles

Quantum distribution functions for spin-1/2 systems are derived for various characteristic functions corresponding to different operator orderings.O. Scully wishes to express his personal thanks to Professor Henry Margenau for sage advice which he offered to his students, namely: Don't spend too much time and effort on the philosophical aspects of quantum mehanics until you have applied quantum mechanics to several laboratory problems and have thereby mastered the subject. This is certainly the approach Professor Margenau has followed, and he provides an excellent role model in matters combining physics and philosophy.     

Phase-space Lagrangian dynamics of incompressible thermofluids

Phase-space Lagrangian dynamics in ideal fluids (i.e., continua) is usually related to the so-called ideal tracer particles. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves. An unsolved theoretical problem is the correct definition of their dynamics in ideal fluids. The issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system, underlying a prescribed fluid system, which uniquely generates its time-evolution.The goal of this paper is to show that the tracer-particle dynamics can be exactly established for an arbitrary incompressible fluid uniquely based on the construction of an inverse kinetic theory (IKT) [M. Tessarotto, M. Ellero, Bull. Am. Phys. Soc. 45 (9) (2000) 40; M. Tessarotto, M. Ellero, AIP Conf. Proc. 762 (2005) 108. RGD24, Italy, July 10-16, 2004; M. Ellero, M. Tessarotto, Physica A 355 (2005) 233; M. Tessarotto, M. Ellero, Physica A 373 (2007) 142, arXiv: physics/0602140; M. Tessarotto, M. Ellero, in: M.S. Ivanov, A.K. Rebrov (Eds.), Proc. 25th RGD, International Symposium on Rarefied gas Dynamics, St. Petersburg, Russia, July 21-28, 2006, Novosibirsk Publ. House of the Siberian Branch of the Russian Academy of Sciences, 2007, p. 1001, arXiv:physics/0611113; M. Tessarotto, C. Cremaschini, Strong solutions of the incompressible Navier-Stokes equations in external domains: Local existence and uniqueness, arXiv:0809.5164v1 [math-ph], 2008]. As an example, the case of an incompressible Newtonian thermofluid is considered here.     

Tensor formulation of spin-1 and spin-2 fields

Spin projection operators which constitute a resolution of the identity in the space of second rank tensor wave functions are constructed. These projectors are then used to establish Lagrangian quantum field theories for free massive particles with spin-1 (two equivalent formulations) and spin-2.     

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest in the role of Berry phase in spintronics, we studied the adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We show, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics is conveniently described by a set of equations of motion (EOM) for a semiclassical particle coupled to a non-Abelian gauge field associated with a geometric Berry phase.

Our EOM can be viewed as a generalization of the standard Ehrenfest's theorem, and their derivation was asymptotically exact in the framework of linear response theory. Our analysis is entirely based on the concept of local Bloch bands, a good starting point for describing the adiabatic motion of a wave packet. One of the advantages of our approach is that the various types of gauge fields were classified into two categories by their different physical origin: (i) projection onto specific bands, (ii) time-dependent local Bloch basis. Using those gauge fields, we write our EOM in a covariant form, whereas the gauge-invariant field strength stems from the noncommutativity of covariant derivatives along different axes of the reciprocal parameter space. On the other hand, the degeneracy of Bloch bands makes the gauge fields non-Abelian.

For the purpose of applying our wave-packet dynamics to the analyses on transport phenomena in the context of Berry phase engineering, we focused on the Hall-type and polarization currents. Our formulation turned out to be useful for investigating and classifying various types of topological current on the same footing. We highlighted their symmetries, in particular, their behavior under time reversal (T) and space inversion (I). The result of these analyses was summarized as a set of cancellation rules. We also introduced the concept of parity polarization current, which may embody the physics of orbital current. Together with charge/spin Hall/polarization currents, this type of orbital current is expected to be a potential probe for detecting and controlling Berry phase.