Scheme for directly measuring the Wigner characteristic function via the driven Jaynes－Cummings model

A scheme is proposed for measuring the Wigner characteristic function of a cavity field. In the scheme an atom is sent through a slightly detuned cavity and driven by a strong resonant classical field. Then the population of the atom in the ground state directly yields the Wigner characteristic function of the cavity field.     

Tunable Wigner states with dipolar atoms and molecules

We study the few-body physics of trapped atoms or molecules with electric or magnetic dipole moments aligned by an external field. Using exact numerical diagonalization appropriate for the strongly correlated regime, as well as a classical analysis, we show how Wigner localization emerges with increasing coupling strength. The Wigner states exhibit nontrivial geometries due to the anisotropy of the interaction. This leads to transitions between different Wigner states as the tilt angle of the dipoles with the confining plane is changed. Intriguingly, while the individual Wigner states are well described by a classical analysis, the transitions between different Wigner states are strongly affected by quantum statistics. This can be understood by considering the interplay between quantum-mechanical and spatial symmetry properties. Finally, we demonstrate that our results are relevant to experimentally realistic systems.     

Covariant Wigner function approach to the relativistic quantum electron gas in a strong magnetic field

This paper is concerned with a unified approach to some equilibrium properties of the relativistic quantum electron plasma embedded in a strong external magnetic field. This unified approach rests on the systematic use of a covariant Wigner function. The equilibrium Wigner function of the noninteracting gas is derived and its main properties are studied. In particular, it satisfies equations that are the complete analog of the usual Liouville equation and thus can be termed “relativistic quantum Liouville equation” whose properties are considered. The equations of state are rederived in this formalism and the results obtained earlier by Canuto and Chiu are found anew. Also, the covariant Wigner funetion of the magnetized vacuum is derived: it is needed, in this formalism, in order to obtain, e.g., the vacuum polarization tensor. Since we are also interested in the plasma modes, the fluctuations of one-particle quantities—and their spectrum—(in particular, of the four current) are calculated in view of their use in the fluctuation-dissipation theorem. We also outline a microscopic proof of this theorem, on the basis of a BBGKY hierarchy for the covariant Wigner functions, and point out the existence of an effective plasma frequency.     

Magnetic field induced Wigner transition in inversion layers

It is shown that under the influence of a strong magnetic field the electrons in an inversion layer will crystallize. The field strengths required are within experimental reach. The stability analysis of such a Wigner lattice is presented. We have also calculated the melting temperature as a function of the magnetic field.     

Covariant Wigner function approach to the relativistic charged gas in a strong magnetic field: I. Electron gas in thermal equilibrium

The relativistic quantum electron gas embedded in a strong magnetic field is studied by calculating its covariant Wigner function in thermal equilibrium. Previous results obtained earlier by Canuto and Chiu are then recovered in a unified way. The polarization tensor is calculated with the use of a covariant quantum BGK equation. Also the lifetime of the neutron in such a medium is calculated for the sake of illustration of the usefulness of the covariant Wigner function.     

Dynamical fluctuation spectra of two-dimensional classical electron liquids in magnetic fields

Dynamical fluctuation spectra of a two-dimensional classical system of electrons in a magnetic field are obtained by numerical experiments in the domain of a strongly coupled liquid. Excitations in these systems have dispersion relations similar to those in the Wigner lattice of the same number density.     

Effect of quantum fluctuations on the dipolar motion of bose-einstein condensates in optical lattices

We reexamine dipolar motion of condensate atoms in one-dimensional optical lattices and harmonic magnetic traps including quantum fluctuations within the truncated Wigner approximation. In the strong tunneling limit we reproduce the mean field results with a sharp dynamical transition at the critical displacement. When the tunneling is reduced, on the contrary, strong quantum fluctuations lead to finite damping of condensate oscillations even at infinitesimal displacement. We argue that there is a smooth crossover between the chaotic classical transition at finite displacement and the superfluid-to-insulator phase transition at zero displacement. We further analyze the time dependence of the density fluctuations and of the coherence of the condensate and find several nontrivial dynamical effects, which can be observed in the present experimental conditions.     

Thermally averaged orbital diamagnetism of a localized wigner oscillator

Summary Electron crystallization due to sufficiently strong Coulomb repulsions leads to a model of electrons oscillating about lattice sites in harmonic potentials. We have studied the orbital diamagnetism of such a localized Wigner oscillator in an applied magnetic field of arbitrary strength. The two contributions from orbital angular momentum and from Langevin-Pauli behaviour are separately calculated using Feynman's theorem. Possible relevance to the melting curve of the Wigner crystals in a magnetic field is pointed out.

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Riassunto La localizzazione di elettroni per effetto di repulsioni coulombiane sufficientemente forti porta ad un modello di elettroni che oscillano attorno a siti reticolari in potenziali armonici. Si studia il diamagnetismo orbitale di un siffatto oscillatore localizzato di Wigner in campo magnetico d'intensità arbitraria. Il contributo dovuto al momento angolare orbitale e quello di Langevin-Pauli sono calcolati separatamente mediante il teorema di Feynman. Si discute la possibile connessione dei risultati con il problema della curva di fusione del cristallo di Wigner in campo magnetico.

     

Dynamics of the wigner distribution function: conservation of positivity in time

The necessary and sufficient conditions are found under which the Wigner distribution function conserves (i) positivity, and (ii) factorization. The proof is based on the study of the continuous representation of three-dimensional linear-canonical-transformed minimum-uncertainty-states. The validity of (i) and (ii) for all initial conditions leads to quadratic Hamiltonians; when the condition is relaxed to the validity for only some initial conditions, non-quadratic systems are obtained. In all the above cases, the Wigner function is a true probability and follows the classical trajectory in phase space. The calculational advantage of the method here proposed is shown in the study of parabolic tunneling in a uniform magnetic field.     

Some dynamical properties of a two-dimensional Wigner crystal

Results for the static part of the ground state energy of the square and hexagonal two-dimensional Wigner lattices are given. The hexagonal lattice has the lower energy. Phonon dispersion curves and the vibrational zeropoint energy are calculated for the hexagonal lattice. The dielectric susceptibility tensor of a two-dimensional Wigner crystal χ_αβ(q) has been determined in the long wavelength limit in the presence of a static magnetic field perpendicular to the crystal, and explicit expressions have been obtained for the hexagonal lattice. Applying the analysis developed by Chiu and Quinn, the results for the susceptibility have been used to obtain the dispersion relation for the plasma oscillations in the electron crystal on the assumption that the crystal is embedded in a dielectric medium. The dispersion curves have been calculated for differing magnitudes of the applied magnetic field.     

Disorder induced transition into a one-dimensional wigner glass

The destruction of quasi-long-range crystalline order as a consequence of strong disorder effects is shown to accompany the strict localization of all classical plasma modes of one-dimensional Wigner crystals at T=0. We construct a phase diagram that relates the structural phase properties of Wigner crystals to a plasmon delocalization transition recently reported. Deep inside the strictly localized phase of the strong disorder regime, we observe glasslike behavior. However, well into the critical phase with a plasmon mobility edge, the system retains its crystalline composition. We predict that a transition between the two phases occurs at a critical value of the relative disorder strength. This transition has an experimental signature in the ac conductivity as a local maximum of the largest spectral amplitude as a function of the relative disorder strength.     

Fingerprints of quantal Wigner solid-like correlations in D-dimensional assemblies

After a brief summary of the mechanism of quantal Wigner electron crystallization, we emphasize experimental situations in three, two, and one dimensions in which fingerprints of Wigner solid-like correlations are in evidence. Special stress is placed on the way applied magnetic fields can aid Wigner localization, as first pointed out in relation to n-type InSb by Durkan et al. (1968). Semiconductor heterojunctions with a two-dimensional electron fluid in the presence of a transverse magnetic field are given some prominence in relation to melting of the Wigner solid and its connection with magnetic properties. It is also proposed that a Wigner “hole” solid may be induced by a magnetic field of 60 T in a specific high $T_{\mathrm{c}}$ cuprate and that the fulleride phase diagram may also contain Wigner solids.     

Synchronization,zero-resistance states and rotating Wigner crystal

We show, in a framework of a classical nonequilibrium model, that rotational angles of electrons moving in two dimensions (2D) in a perpendicular magnetic field can be synchronized by an external microwave field whose frequency is close to the Larmor frequency. The synchronization eliminates collisions between electrons and thus creates a regime with zero diffusion corresponding to the zero-resistance states observed in experiments with high mobility 2D electron gas (2DEG). For long range Coulomb interactions electrons form a rotating hexagonal Wigner crystal. Possible relevance of this effect of synchronization-induced self-assembly for planetary rings is discussed.     

Scheme for direct measurement of Wigner function in two-mode cavity QED driven by classical fields

We propose a scheme for the direct measurement of Wigner function in two-mode cavity QED.The atoms are sent to resonantly interact with two orthogonally polarized cavity modes in the presence of strong classical field.The probability of measuring the atom in the ground state directly gives the useful information of the cavity field.This method can be used for quantum non-demolition measurement of the photon number.     

Classical Model of Confinement

The confinement mechanism proposed earlier and then applied successfully to meson spectroscopy by one of the authors is interpreted in classical terms. For this aim the unique solution of the Maxwell equations, an analog of the corresponding unique solution of the SU(3)-Yang-Mills equations describing linear confinement in quantum chromodynamics, is used. Motion of a charged particle is studied in the field representing magnetic part of the mentioned solution and it is shown that one deals with the full classical confinement of the charged particle in such a field: under any initial conditions the particle motion is accomplished within a finite region of space so that the particle trajectory is near magnetic field lines while the latter are compact manifolds (circles). An asymptotical expansion for the trajectory form in the strong field limit is adduced. The possible application of the obtained results in thermonuclear plasma physics is also shortly outlined.     

The Wigner Functions for a Spin-1/2 Relativistic Particle in the Presence of Magnetic Field

This paper provides a study of Wigner functions for a spin-1/2 relativistic particle in the presence of magnetic field. Since the Dirac equation is described as a matrix equation, it is necessary to describe the Wigner function as a matrix function in phase space. What’s more, this function is then proved to satisfy the Dirac equation with ⋆-product. Finally, by solving the ⋆-product Dirac equation, the energy levels as well as the Wigner functions for a spin-1/2 relativistic particle in the presence of magnetic field are obtained.     

Anomalous resistivity resulting from MeV-electron transport in overdense plasma

Laser produced hot electron transport in an overdense plasma is studied by three-dimensional particle-in-cell simulations. Hot electron currents into the plasma generate neutralizing return currents in the cold plasma electrons, leading to a configuration which is unstable to electromagnetic Weibel and tearing instabilities. The resulting current filaments self-organize through a coalescence process finally settling into a single global current channel. The plasma return current experiences a strong anomalous resistivity due to diffusive flow of cold electrons in the magnetic perturbations. The resulting electrostatic field leads to an anomalously rapid stopping of fast MeV electrons (almost 3 orders of magnitude stronger than that through classical collisional effects).