General Wigner Rotations in D Dimensions

We construct general Wigner rotations for both massive and massless particles in D-dimensional spacetime.We work out the explicit expressions of these Wigner rotations for arbitrary Lorentz transformations. We study the relation between the electromagnetic gauge invariance and the non-uniqueness of Wigner rotation.     

Polarization catastrophe in the polaronic Wigner crystal

We consider a three dimensional Wigner crystal of electrons lying in a host ionic dielectric. Owing to their interaction with the lattice polarization, each localized electron forms a polaron. We study the collective excitations of such a polaronic Wigner crystal at zero temperature, taking into account the quantum fluctuations of the polarization within the Feynman harmonic approximation. We show that, contrary to the ordinary electron crystal, the system undergoes a polarization catastrophe when the density is increased. An optical signature of this instability is derived, whose trend agrees with the experiments carried out in Nd-based cuprates. Received 4 July 2002 Published online 17 September 2002     

Thomas Rotation and Thomas Precession

Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. A straightforward derivation of the Fermi–Walker equation is also given. Besides the simplicity of calculations the absolute treatment of spacetime allows us to make a clear conceptual distinction between the phenomena of Thomas rotation and Thomas precession.Supported by Hungarian research fund OTKA-T048489.Supported by Hungarian research funds OTKA-T047276, F049457, T049301.     

Moving Wigner glasses and smectics: dynamics of disordered Wigner crystals

We examine the dynamics of driven classical Wigner solids interacting with quenched disorder from charged impurities. For strong disorder, the initial motion is plastic, in the form of crossing winding channels. For increasing drive, there is a reordering into a moving Wigner smectic with the electrons moving in separate 1D channels. These different dynamic phases can be related to the conduction noise and I(V) curves. For strong disorder, we show criticality in the voltage onset just above depinning. We obtain the dynamic phase diagram for driven Wigner solids and demonstrate a finite threshold of force for transverse sliding, recently observed experimentally.     

Thomas Precession and the Bargmann-Michel-Telegdi Equation

A direct method showing the Thomas precession for an evolution of any vector quantity (a spatial part of a four-vector) is proposed. A useful application of this method is a possibility to trace correctly the presence of the Thomas precession in the Bargmann-Michel-Telegdi equation. It is pointed out that the Thomas precession is not incorporated in the kinematical term of the Bargmann-Michel-Telegdi equation, as it is commonly believed. When the Bargmann-Michel-Telegdi equation is interpreted in curved spacetimes, this term is shown to be equivalent to the affine connection term in the covariant derivative of the spin four-vector evolving in a gravitational field. It then contributes to the geodetic precession. The described problem is an interesting and unexpected example showing that approximate methods used in special relativity, in this case to identify the Thomas precession, can distort the true meaning of physical laws.     

Precession of classical spin and spin-orbit splitting

We present solutions of a fermion-boson model based on the supersymmetric (Susy) extension of theU(N) σ-models with the Wess-Zumino-Witten (WZW) term. We study some properties of these solutions. We point out that the obtained solutions are related to the components of the energy-momentum tensor of the purely bosonicU(N)σ-model and that some classes of these solutions are traceless.     

Precession of the Orbit of Mercury

Doklady Physics - The influence of the planets of the Solar System on the precession of the orbit of Mercury is investigated in the framework of classical mechanics. The influence of each planet on...     

Noise at the crossover from Wigner liquid to Wigner glass

Using a simple classical model for interacting electrons in two dimensions with random disorder, we show that a crossover from a Wigner liquid to a Wigner glass occurs as a function of charge density. The noise power increases strongly at the crossover and the characteristics of the 1/f(alpha) noise change. When the temperature is increased, the noise power decreases. We compare these results with recent noise measurements in systems with two-dimensional metal-insulator transitions.     

Wigner rotations and little groups

Wigner’s little groups are the subgroups of the Poincaré group whose transformations leave the four-momentum of a given particle invariant. For a relativistic particle in motion the little group is a boosted rotation. On the other hand, the kinematical effect of two non-colinear Lorentz boosts is another boost preceded or follwed by a rotation, which is called the Wigner rotation. It is shown that there is always a Wigner rotation for a given little group rotation. The differences between those two rotations are clearly demonstrated and some interesting physical applications are presented.     

Wigner function and normal ordering

The Wigner function is calculated for a relativistic system of interacting scalar particles and anti-particles in thermal equilibrium. It is pointed out that the prerequisite for obtaining the correct result is normal ordering, as opposed to the customary process of symmetrization of the field operators, whether combined with a vacuum subtraction or not.     

Precession of an electron-magnetohydrodynamic field-reversed configuration

A field-reversed configuration is generated in a large laboratory plasma in the parameter regime of electron magnetohydrodynamics. During its free relaxation, the magnetic moment is observed to precess when tilted from its original axis. The precession velocity is the electron drift velocity in the toroidal current layer. The precession is a manifestation of frozen-in field lines in a moving electron fluid.     

Conductivity of Wigner liquid

The conductivity of two-dimensional electron systems with low carrier concentration is considered on the basis of the previously suggested model (Fermi liquid with a soft mode) under the assumption that the equilibrium in each of the (fermion and boson) subsystems is established faster than the impurity relaxation and the relaxation between the subsystems (hydrodynamic approximation). The conductivity of the system depends on three characteristic times: τ₁(τ₂) is determined by the fermion (boson) impurity scattering and τ₁₂ is determined by the friction between the subsystems; the respective temperature dependences are obtained. The conductivity is related to the relaxation time τ in the usual way, and τ obeys the relationship τ^?1=τ ₁ ^?1 +(τ₂+τ₁₂)^?1. It follows from the results obtained that the resistivity of pure samples should increase with temperature and tend towards saturation.     

General Wigner Transforms Studied by Virtue of Weyl Ordering of the Wigner Operator

By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for deriving miscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can also be easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transforms and the squeezing transforms in quantum optics is investigated.     

General Wigner Transforms Studied by Virtue of Weyl Ordering of the Wigner Operator

By virtue of the property that Weyl ordering is invariant under similar transformations we show that the Weyl ordered form of the Wigner operator, a Dirac δ-operator function, brings much convenience for derivingmiscellaneous Wigner transforms. The operators which engender various transforms of the Wigner operator, can alsobe easily deduced by virtue of the Weyl ordering technique. The correspondence between the optical Wigner transformsand the squeezing transforms in quantum optics is investigated.     

Moving-Reference-Frame Imaging under Steady-State Free Precession

Steady-state free precession (SSFP) has a sharply defined, symmetrical response to motion which acts as a bandpass filter for magnetization over a narrow range of velocities, typically less than a few millimeters per second wide. A radiofrequency-pulse-generated moving reference frame (MORF) has been developed, which may be used within an SSFP imaging sequence. The magnetization of material moving in the MORF is suppressed by up to a factor of 10 relative to that moving at the MORF velocity. This new technique is demonstrated without slice selection for flow in a Hele-Shaw cell.