Some properties of the resonant state in quantum mechanics and its computation

The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take account of the outgoing momentum flux; the number of particles would decay exponentially in a fixed volume of integration. Moreover, we introduce new numerical methods of treating the resonant state with the use of the effective potential. We first give a numerical method of finding a resonance pole in the complex energy plane. The method seeks an energy eigenvalue iteratively. We found that our method leads to a super-convergence, the convergence exponential with respect to the iteration step. The present method is completely independent of commonly used complex scaling. We also give a numerical trick for computing the time evolution of the resonant state in a limited spatial area. Since the wave function of the resonant state is diverging away from the scattering potential, it has been previously difficult to follow its time evolution numerically in a finite area.Comment: 20 pages, 12 figures embedde

Effects of thermal- and spin- fluctuations on the band structure of purple bronze Li2_2Mo12_{12}O34_{34}

The band structures of ordered and thermally disordered Li$_2$Mo$_{12}$O$_{34}$ are calculated by use of ab-initio DFT-LMTO method. The unusual, very 1-dimensional band dispersion obtained in previous band calculations is confirmed for the ordered structure, and the overall band structure agrees reasonably with existing photoemission data. Dispersion and bandstructure perpendicular to the main dispersive direction is obtained. A temperature dependent band broadening is calculated from configurations with thermal disorder of the atomic positions within the unit cell. This leads a band broadening of the two bands at the Fermi energy which can become comparable to their energy separation. The bands are particularly sensitive to in-plane movements of Mo sites far from the Li-sites, where the density-of-states is highest. The latter fact makes the effect of Li vacancies on the two bands relatively small. Spin-polarized band results for the ordered structure show a surprisingly large exchange enhancement on the high DOS Mo sites. Consequences for spin fluctuations associated with a cell doubling along the conducting direction are discussed

Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons

Electron and phonon correlations in systems of one-dimensional electrons coupled to phonons are studied at low temperatures by emphasizing on the effect of electron-phonon backward scattering. It is found that the $2k_F$-wave components of the electron density and phonon displacement field share the same correlations. Both correlations are quasi-long-ranged for a single conducting chain coupled to one-dimensional or three-dimensional phonons, and they are long-ranged for repulsive electron-electron interactions for a three-dimensional array of parallel one-dimensional conducting chains coupled to three-dimensional phonons

Alternative derivation of the Feigel effect and call for its experimental verification

A recent theory by Feigel [Phys. Rev. Lett. {\bf 92}, 020404 (2004)] predicts the finite transfer of momentum from the quantum vacuum to a fluid placed in strong perpendicular electric and magnetic fields. The momentum transfer arises because of the optically anisotropic magnetoelectric response induced in the fluid by the fields. After summarising Feigel's original assumptions and derivation (corrected of trivial mistakes), we rederive the same result by a simpler route, validating Feigel's semi-classical approach. We then derive the stress exerted by the vacuum on the fluid which, if the Feigel hypothesis is correct, should induce a Poiseuille flow in a tube with maximum speed $\approx 100\mu$m/s (2000 times larger than Feigel's original prediction). An experiment is suggested to test this prediction for an organometallic fluid in a tube passing through the bore of a high strength magnet. The predicted flow can be measured directly by tracking microscopy or indirectly by measuring the flow rate ($\approx 1$ml/min) corresponding to the Poiseuille flow. A second experiment is also proposed whereby a `vacuum radiometer' is used to test a recent prediction that the net force on a magnetoelectric slab in the vacuum should be zero.Comment: 20 pages, 1 figures. revised and improved versio

Langevin dynamics in crossed magnetic and electric fields: Hall and diamagnetic fluctuations

Based on the classical Langevin equation, we have re-visited the problem of orbital motion of a charged particle in two dimensions for a normal magnetic field crossed with or without an in-plane electric bias. We are led to two interesting fluctuation effects: First, we obtain not only a longitudinal "work-fluctuation" relation as expected for a barotropic type system, but also a transverse work-fluctuation relation perpendicular to the electric bias. This "Hall fluctuation" involves the product of the electric and the magnetic fields. And second, for the case of harmonic confinement without bias, the calculated probability density for the orbital magnetic moment gives non-zero even moments, not derivable as field derivatives of the classical free energy.Comment: 4 pages, 2 figures, revised versio

High density quark matter in the NJL model with dimensional vs. cut-off regularization

We investigate color superconducting phase at high density in the extended Nambu--Jona-Lasinio model for the two flavor quarks. Because of the non-renormalizability of the model, physical observables may depend on the regularization procedure, that is why we apply two types of regularization, the cut-off and the dimensional one to evaluate the phase structure, the equation of state and the relationship between the mass and the radius of a dense star. To obtain the phase structure we evaluate the minimum of the effective potential at finite temperature and chemical potential. The stress tensor is calculated to derive the equation of state. Solving the Tolman-Oppenheimer-Volkoff equation, we show the relationship between the mass and the radius of a dense star. The dependence on the regularization is found not to be small for these phenomena in the color superconducting phase.Comment: 10 pages, 11 figures; a few points corrected and references adde

Phase diagram of the one dimensional Hubbard-Holstein Model at 1/2 and 1/4 filling

The Hubbard-Holstein model is one of the simplest to incorporate both electron-electron and electron-phonon interactions. In one dimension at half filling the Holstein electron-phonon coupling promotes onsite pairs of electrons and a Peierls charge density wave while the Hubbard onsite Coulomb repulsion U promotes antiferromagnetic correlations and a Mott insulating state. Recent numerical studies have found a possible third intermediate phase between Peierls and Mott states. From direct calculations of charge and spin susceptibilities, we show that (i) As the electron-phonon coupling is increased, first a spin gap opens, followed by the Peierls transition. Between these two transitions the metallic intermediate phase has a spin gap, no charge gap, and properties similar to the negative-U Hubbard model. (ii) The transitions between Mott/intermediate and intermediate/Peierls states are of the Kosterlitz-Thouless form. (iii) For larger U the two transitions merge at a tritical point into a single first order Mott/Peierls transition. In addition we show that an intermediate phase also occurs in the quarter-filled model.Comment: 10 pages, 10 eps figure

On compatibility and improvement of different quantum state assignments

When Alice and Bob have different quantum knowledges or state assignments (density operators) for one and the same specific individual system, then the problems of compatibility and pooling arise. The so-called first Brun-Finkelstein-Mermin (BFM) condition for compatibility is reobtained in terms of possessed or sharp (i. e., probability one) properties. The second BFM condition is shown to be generally invalid in an infinite-dimensional state space. An argument leading to a procedure of improvement of one state assifnment on account of the other and vice versa is presented.Comment: 8 page

Spin-Peierls Quantum Phase Transitions in Coulomb Crystals

The spin-Peierls instability describes a structural transition of a crystal due to strong magnetic interactions. Here we demonstrate that cold Coulomb crystals of trapped ions provide an experimental testbed in which to study this complex many-body problem and to access extreme regimes where the instability is triggered by quantum fluctuations alone. We present a consistent analysis based on different analytical and numerical methods, and provide a detailed discussion of its feasibility on the basis of ion-trap experiments. Moreover, we identify regimes where this quantum simulation may exceed the power of classical computers.Comment: slightly longer than the published versio

Path Integral of the Two Dimensional Su-Schrieffer-Heeger Model

The equilibrium thermodynamics of the two dimensional Su-Schrieffer-Heeger Model is derived by means of a path integral method which accounts for the variable range of the electronic hopping processes. While the lattice degrees of freedom are classical functions of time and are integrated out exactly, the electron particle paths are treated quantum mechanically. The free energy of the system and its temperature derivatives are computed by summing at any $T$ over the ensemble of relevant particle paths which mainly contribute to the total partition function. In the low $T$ regime, the {\it heat capacity over T} ratio shows un upturn peculiar of a glassy like behavior. This feature is more sizeable in the square lattice than in the linear chain as the overall hopping potential contribution to the total action is larger in higher dimensionality.Comment: Phys.Rev.B vol.71 (2005