几何相位的伽利略变换性质

对几何相位的伽利略变换性质结果表明：通常实验中所测量体系的几何相位的确是伽利略不变的.但一般量子体系的几何相位不具有伽利略不变性.还仔细考察了几何相位在伽利略boost作用下变化的物理起源.文章最后通过对假想实验的分析，进一步证明几何相位对参考系的依赖并不意味着相应物理可观测量的非伽利略协变性.     

Galilean-Covariant Clifford Algebras in the Phase-Space Representation

We apply the Galilean covariant formulation of quantum dynamics to derive the phase-space representation of the Pauli–Schrödinger equation for the density matrix of spin-1/2 particles in the presence of an electromagnetic field. The Liouville operator for the particle with spin follows from using the Wigner–Moyal transformation and a suitable Clifford algebra constructed on the phase space of a (4 + 1)-dimensional space–time with Galilean geometry. Connections with the algebraic formalism of thermofield dynamics are also investigated.     

Relativistic effects on LEED intensities from Au(111)

Comparison of relativistically and nonrelativistically calculated intensity versus energy profiles in low energy electron diffraction (LEED) from the (111) surface of Au (Z = 79) reveals that relativistic corrections are quite significant. They can however, be obtained in very good approximation by quasirelativistic calculations, in which spin-averaged relativistic phase shifts are used as input for the nonrelativistic multiple scattering formalism. Further, relativistic effects on intensities are found to be comparable to differences arising from different approximations to the exchange part of the ion core potential.     

The extended third-order nonlinear Schrödinger equation and Galilean transformation

The extended third-order nonlinear Schrödinger equation and its solutions are studied on the basis of Galilean transformation and generalized Galilean invariance.Received: 15 September 2003, Published online: 12 July 2004PACS: 42.65.Tg Optical solitons; nonlinear guided waves - 52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)     

Spinless Duffin-Kemmer-Petiau Oscillator in a Galilean Non-commutative Phase Space

We examine Galilei-invariant linear wave equations in a non-commutative phase space. Specifically, we establish and solve the Galilean covariant Duffin-Kemmer-Petiau equation for spin-0 fields in a harmonic oscillator potential. We obtain these wave equations with a Galilean covariant approach, based on a (4+1)-dimensional manifold with light-cone coordinates followed by a reduction to a (3+1)-dimensional spacetime. We find the exact wave functions and their energy levels, and we examine the effects of non-commutativity.     

Nonperturbative canonical formulation and Ward-Takahashi relations for quantum many-body systems at finite temperatures

A nonperturbative canonical field-theoretic approach to Matsubara's finite temperature quantum many-body theory is presented. The finite temperature Ward-Takahashi relations for the phase transformation, the Galilean transformation and general time-independent continuous transformations are derived for both fermions and bosons with interactions. The finite temperature Ward-Takahashi relations for nonconserved currents and the finite temperature Goldstone's theorem are also discussed.     

Unitary cocycle representations of the Galilean line group: Quantum mechanical principle of equivalence

We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these representations determine the structure of quantum mechanics in non-inertial reference frames. Our representations of the Galilean line group contain the usual unitary projective representations of the Galilei group, but have a more intricate cocycle structure. The transformation formula for the Hamiltonian under the Galilean line group shows that in a non-inertial reference frame it acquires a fictitious potential energy term that is proportional to the inertial mass, suggesting the equivalence of inertial mass and gravitational mass in quantum mechanics.     

Ion track etching revisited: II. Electronic properties of aged tracks in polymers

We compile here electronic ion track etching effects, such as capacitive-type currents, current spike emission, phase shift, rectification and background currents that eventually emerge upon application of sinusoidal alternating voltages across thin, aged swift heavy ion-irradiated polymer foils during etching. Both capacitive-type currents and current spike emission occur as long as obstacles still prevent a smooth continuous charge carrier passage across the foils. In the case of sufficiently high applied electric fields, these obstacles are overcome by spike emission. These effects vanish upon etchant breakthrough. Subsequent transmitted currents are usually of Ohmic type, but shortly after breakthrough (during the track’ core etching) often still exhibit deviations such as strong positive phase shifts. They stem from very slow charge carrier mobility across the etched ion tracks due to retarding trapping/detrapping processes. Upon etching the track’s penumbra, one occasionally observes a split-up into two transmitted current components, one with positive and another one with negative phase shifts. Usually, these phase shifts vanish when bulk etching starts. Current rectification upon track etching is a very frequent phenomenon. Rectification uses to inverse when core etching ends and penumbra etching begins. When the latter ends, rectification largely vanishes. Occasionally, some residual rectification remains which we attribute to the aged polymeric bulk itself. Last not least, we still consider background currents which often emerge transiently during track etching. We could assign them clearly to differences in the electrochemical potential of the liquids on both sides of the etched polymer foils. Transient relaxation effects during the track etching cause their eventually chaotic behaviour.     

Conformally covariant vector–spinor field in de Sitter space

Unlike the Lorentz transformation which replaces the Galilean transformation among inertial frames at high relative velocities, there seems to be no such a consensus in the case of coordinate transformation between inertial frames and uniformly rotating ones. There have been some attempts to generalize the Galilean rotational transformation to high rotational velocities. Here we introduce a modified version of one of these transformations proposed by Philip Franklin in 1922. The modified version is shown to resolve some of the drawbacks of the Franklin transformation, specially with respect to the corresponding spacetime metric in the rotating frame. This new transformation introduces non-inertial eccentric observers on a uniformly rotating disk and the corresponding metric in the rotating frame is shown to be consistent with the one obtained through Galilean rotational transformation for points close to the rotation axis. Employing the threading formulation of spacetime decomposition, spatial distances and time intervals in the spacetime metric of a rotating observer’s frame are also discussed.     

用伽利略变换审视牛顿力学

用伽利略变换审视了牛顿力学的规律,发现有的规律遵从相对性原理,有的规律不遵从相对性原理.     

Singularities and spectral changes of Gaussian beams focused by a lens with spherical aberration

We address the effect of the truncation parameter and spherical aberration (SA) on the singularity transformation and spectral behavior of the polychromatic Gaussian beams focused by an aperture lens with SA in detail. The numerical simulation results, based on the derived equations of the intensity and the spectral density, are given. It is found that the axial singularities vanished with the change of the truncated parameter. The intensity and drastic spectral change fade away with an annihilation process of the phase singularities, and the drastic spectral change does not disappear immediately at the moment the phase singularity annihilates. The singularities in the focal region will redistribute with the increment of SA coefficient, some singularities will vanish, some will spilt into two new singularities, and other off-axial singularities will appear and split into two new singularities as well. When SA coefficient changed, we can find that the axial singularities disappear as well with the decreasing value of truncation parameter. These new splitted singularities due to the change of SA coefficient will converge into one singularity again and disappear gradually.     

Hidden symmetry breaking and the Haldane phase inS=1 quantum spin chains

We study the phase diagram ofS=1 antiferromagnetic chains with particular emphasis on the Haldane phase. The hidden symmetry breaking measured by the string order parameter of den Nijs and Rommelse can be transformed into an explicit breaking of aZ ₂×Z ₂ symmetry by a nonlocal unitary transformation of the chain. For a particular class of Hamiltonians which includes the usual Heisenberg Hamiltonian, we prove that the usual Néel order parameter is always less than or equal to the string order parameter. We give a general treatment of rigorous perturbation theory for the ground state of quantum spin systems which are small perturbations of diagonal Hamiltonians. We then extend this rigorous perturbation theory to a class of diagonally dominant Hamiltonians. Using this theory we prove the existence of the Haldane phase in an open subset of the parameter space of a particular class of Hamiltonians by showing that the string order parameter does not vanish and the hiddenZ ₂×Z ₂ symmetry is completely broken. While this open subset does not include the usual Heisenberg Hamiltonian, it does include models other than VBS models.     

On the concepts of mass and linear momentum in Galilean thermodynamics

The paper presents a systematic treatment of the consequences of the first law of thermodynamics and of the Galilean principle of relativity for continuous bodies. It is shown that these two principles, when combined, imply not only the existence of energy, but also the existence of linear momentum. Both these quantities are represented by extensive state functions satisfying the equations of balance of energy and linear momentum, respectively. The linear momentum doesnot generally have the usual classical Newtonian form (mass times velocity). If, additionally, an assumption is made that the linear momentum is a function of velocity only, then the classical expression is recovered. The general equation of balance of linear momentum reduces then to Cauchy's equations of motion of continuum mechanics. But even without this additional assumption the concept of mass emerges as a derived concept in the theory: it figures in the transformation law for linear momentum under Galilean transformations.     

Nonuniform growth of embedded silicon nanocrystals in an amorphous matrix

The phase transformation of a metastable system occurs when islands of a second stable phase form and grow. The growth velocity of the islands controls the kinetics of the phase transformation. In this work we consider the amorphous-to-crystalline transformation in silicon as the prototype of a solid-to-solid transformation. The results of atomistic simulations are fit using an analytic model for the growth of [100]-oriented nanosized crystalline fibers embedded into an amorphous matrix. We demonstrate that the radius of the island does not grow, in general, at constant velocity. On the contrary, we identify a decelerated motion that is due to anisotropic effects of the crystal grain. Such a nonuniform growth should be taken into account in the modeling of solid-to-solid crystallization.     

The Schrödinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

We investigate the non-relativistic Schrödinger and Pauli-Dirac oscillators in noncommutative phase space using the five-dimensional Galilean covariant framework. The Schrödinger oscillator presented the correct energy spectrum whose non isotropy is caused by the noncommutativity with an expected similarity between this system and the particle in a magnetic field. A general Hamiltonian for the 3-dimensional Galilean covariant Pauli-Dirac oscillator was obtained and it presents the usual terms that appears in commutative space, like Zeeman effect and spin-orbit terms. We find that the Hamiltonian also possesses terms involving the noncommutative parameters that are related to a type of magnetic moment and an electric dipole moment.     

Perturbations of unitary representations of the Galilei group: Mass operators with continuous spectra

We present a systematic procedure for constructing mass operators with continuous spectra for a system of particles in a manner consistent with Galilean relativity. These mass operators can be used to construct what may be called point-form Galilean dynamics. As in the relativistic case introduced by Dirac, the point-form dynamics for the Galilean case is characterized by both the Hamiltonian and momenta being altered by interactions. An interesting property of such perturbative terms to the Hamiltonian and momentum operators is that, while having well-defined transformation properties under the Galilei group, they also satisfy Maxwell’s equations. This result is an alternative to the well-known Feynman-Dyson derivation of Maxwell’s equations from non-relativistic quantum physics.     

Investigation of Galilean invariance of multi-phase lattice Boltzmann methods

We examine the Galilean invariance of standard lattice Boltzmann methods for two-phase fluids. We show that the known Galilean invariant term that is cubic in the velocities, and is usually neglected, is a major source of Galilean invariance violations. We show that incorporating a correction term can improve the Galilean invariance of the method by up to two orders of magnitude for large velocities. We found that this is true in particular for methods in which the interactions are incorporated through a forcing term. Methods in which interactions are incorporated through a non-ideal pressure tensor only benefit for large velocities.     

A quantum mechanical twin paradox

When a quantummechanical wavepacket undergoes a series of Galilean boosts, the Schrödinger theory predicts the occurrence of a geometrical phase effect that is an example of Berry's phase (Sagnac's phase). In the present paper the conceptual consequences of this phenomenon are considered, in particular for the status of Galilean invariance in nonrelativistic quantum mechanics, and for the relation between that theory and classical physics.     

Polarimetry of the Galilean satellites and Jupiter near opposition

We present new polarimetric observations of the Galilean satellites Io, Europa, Ganymede, and Callisto as well as the North and South polar regions of Jupiter in the V filter within the range of phase angles ?0.13?0.62°. The differences between our results and observations of other authors are discussed. It is shown that there is no second inversion point near the phase angle 0.5°. New observations fully confirmed the presence of the polarization opposition effect for the Galilean satellites Io, Europa, and Ganymede in the region of phase angles smaller than 2°. Observations of Jupiter verified a sharp turn of the angle between the observed polarization plane and the plane perpendicular to the scattering plane by 90°.