Asynchronous vibration problem of centrifugal compressor

An unstable asynchronous vibration problem in a high pressure centrifugal compressor and the remedial actions against it are described. Asynchronous vibration of the compressor took place when the discharge pressure (Pd) was increased, after the rotor was already at full speed. The typical spectral data of the shaft vibration indicate that as the pressure Pd increases, pre-unstable vibration appears and becomes larger, and large unstable asynchronous vibration occurs suddenly (Pd = 5.49MPa). A computer program was used which calculated the logarithmic decrement and the damped natural frequency of the rotor bearing systems. The analysis of the log-decrement is concluded to be effective in preventing unstable vibration in both the design stage and remedial actions

On the Generalised Pauli--Villars Regularization of the Standard Model

We show that the regularization of the Standard Model proposed by Frolov and Slavnov describes a nonlocal theory with quite simple Lagrangian.Comment: 7 pages, harvma

A Perturbative Study of a General Class of Lattice Dirac Operators

A perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer. The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. We study one-loop fermion contributions to the self-energy of the gauge field, which are related to the fermion contributions to the one-loop $\beta$ function and to the Weyl anomaly. We first explicitly demonstrate that the Ward identity is satisfied by the self-energy tensor. By performing careful analyses, we then obtain the correct self-energy tensor free of infra-red divergences, as a general consideration of the Weyl anomaly indicates. This demonstrates that our general operators give correct chiral and Weyl anomalies. In general, however, the Wilsonian effective action, which is supposed to be free of infra-red complications, is expected to be essential in the analyses of our general class of Dirac operators for dynamical gauge field.Comment: 30 pages. Some of the misprints were corrected. Phys. Rev. D (in press

CP-violating theta parameter in the domain model of the QCD vacuum

A non-zero CP-violating $\theta$ parameter is treated in the domain model which assumes a cluster-like vacuum structure whose units are characterised in particular by a topological charge which is not necessarily an integer number. In the present paper we restrict consideration to rational values of the charge. The model has previously been shown to manifest confinement, spontaneous chiral symmetry breaking and the absence of an axial U(1) Goldstone boson. We find that the specific structure of the minima of the free energy density of the domain ensemble forces a $2\pi$-periodicity of observables in $\theta$ for any number of light quarks, that vacuum doubling occurs at $\theta=\pi$ for any $N_f>1$ and any value of topological charge $q$. These features are in agreement with expectations based on anomalous Ward identities and large $N_c$ effective theories. We find also additional values of $\theta$ depending on $q$ for which vacuum doubling occurs.Comment: 10 pages, 6 figures. Final version with modification of Eq.(2), additional references, minor typographical correction

Phase Operator for the Photon Field and an Index Theorem

An index relation $dim\ ker\ a^{\dagger}a - dim\ ker\ aa^{\dagger} = 1$ is satisfied by the creation and annihilation operators $a^{\dagger}$ and $a$ of a harmonic oscillator. A hermitian phase operator, which inevitably leads to $dim\ ker\ a^{\dagger}a - dim\ ker\ aa^{\dagger} = 0$, cannot be consistently defined. If one considers an $s+1$ dimensional truncated theory, a hermitian phase operator of Pegg and Barnett which carries a vanishing index can be defined. However, for arbitrarily large $s$, we show that the vanishing index of the hermitian phase operator of Pegg and Barnett causes a substantial deviation from minimum uncertainty in a characteristically quantum domain with small average photon numbers. We also mention an interesting analogy between the present problem and the chiral anomaly in gauge theory which is related to the Atiyah-Singer index theorem. It is suggested that the phase operator problem related to the above analytic index may be regarded as a new class of quantum anomaly. From an anomaly view point ,it is not surprising that the phase operator of Susskind and Glogower, which carries a unit index, leads to an anomalous identity and an anomalous commutator.Comment: 32 pages, Late

Fluctuation-dissipation theorem and quantum tunneling with dissipation

We suggest to take the fluctuation-dissipation theorem of Callen and Welton as a basis to study quantum dissipative phenomena (such as macroscopic quantum tunneling) in a manner analogous to the Nambu-Goldstone theorem for spontaneous symmetry breakdown. It is shown that the essential physical contents of the Caldeira-Leggett model such as the suppression of quantum coherence by Ohmic dissipation are derived from general principles only, namely, the fluctuation-dissipation theorem and unitarity and causality (i.e., dispersion relations), without referring to an explicit form of the Lagrangian. An interesting connection between quantum tunneling with Ohmic dissipation and the Anderson's orthogonality theorem is also noted.Comment: To appear in Phys. Rev.

Remark on Pauli-Villars Lagrangian on the Lattice

It is interesting to superimpose the Pauli-Villars regularization on the lattice regularization. We illustrate how this scheme works by evaluating the axial anomaly in a simple lattice fermion model, the Pauli-Villars Lagrangian with a gauge non-invariant Wilson term. The gauge non-invariance of the axial anomaly, caused by the Wilson term, is remedied by a compensation among Pauli-Villars regulators in the continuum limit. A subtlety in Frolov-Slavnov's scheme for an odd number of chiral fermions in an anomaly free complex gauge representation, which requires an infinite number of regulators, is briefly mentioned.Comment: 14 pages, Phyzzx. The final version to appear in Phys. Rev.

Bosonization in d=2 from finite chiral determinants with a Gauss decomposition

We show how to bosonize two-dimensional non-abelian models using finite chiral determinants calculated from a Gauss decomposition. The calculation is quite straightforward and hardly more involved than for the abelian case. In particular, the counterterm $A\bar A$, which is normally motivated from gauge invariance and then added by hand, appears naturally in this approach.Comment: 4 pages, Revte

Topological properties of Berry's phase

By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian in the present formulation. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial for any finite time interval $T$. The topological interpretation of Berry's phase such as the topological proof of phase-change rule thus fails in the practical Born-Oppenheimer approximation, where a large but finite ratio of two time scales is involved.Comment: 9 pages. A new reference was added, and the abstract and the presentation in the body of the paper have been expanded and made more precis

Invariant Regularization of Anomaly-Free Chiral Theories

We present a generalization of the Frolov-Slavnov invariant regularization scheme for chiral fermion theories in curved spacetimes. local gauge symmetries of the theory, including local Lorentz invariance. The perturbative scheme works for arbitrary representations which satisfy the chiral gauge anomaly and the mixed Lorentz-gauge anomaly cancellation conditions. Anomalous theories on the other hand manifest themselves by having divergent fermion loops which remain unregularized by the scheme. Since the invariant scheme is promoted to also include local Lorentz invariance, spectator fields which do not couple to gravity cannot be, and are not, introduced. Furthermore, the scheme is truly chiral (Weyl) in that all fields, including the regulators, are left-handed; and only the left-handed spin connection is needed. The scheme is, therefore, well suited for the study of the interaction of matter with all four known forces in a completely chiral fashion. In contrast with the vectorlike formulation, the degeneracy between the Adler-Bell-Jackiw current and the fermion number current in the bare action is preserved by the chiral regularization scheme.Comment: 28pgs, LaTeX. Typos corrected. Further remarks on singlet current