Generalized Kinetic Theory of Electrons and Phonons

A Generalized Kinetic Theory was proposed in order to have the possibility to treat particles which obey a very general statistics. By adopting the same approach, we generalize here the Kinetic Theory of electrons and phonons. Equilibrium solutions and their stability are investigated.Comment: Proceedings of the International School and Workshop on Nonextensive Thermodynamics and Physical Applications, NEXT 2001, 23-30 May 2001, Cagliari (Italy) (To appear in Physica A

Decoherence Effects in Reactive Scattering

Decoherence effects on quantum and classical dynamics in reactive scattering are examined using a Caldeira-Leggett type model. Through a study of dynamics of the collinear H+H2 reaction and the transmission over simple one-dimensional barrier potentials, we show that decoherence leads to improved agreement between quantum and classical reaction and transmission probabilities, primarily by increasing the energy dispersion in a well defined way. Increased potential nonlinearity is seen to require larger decoherence in order to attain comparable quantum-classical agreement.Comment: 25 pages, 6 figures, to be published in J. Chem. Phy

Minimum of η/s\eta/s and the phase transition of the Linear Sigma Model in the large-N limit

We reexamine the possibility of employing the viscosity over entropy density ratio as a diagnostic tool to identify a phase transition in hadron physics to the strongly coupled quark-gluon plasma and other circumstances where direct measurement of the order parameter or the free energy may be difficult. It has been conjectured that the minimum of eta/s does indeed occur at the phase transition. We now make a careful assessment in a controled theoretical framework, the Linear Sigma Model at large-N, and indeed find that the minimum of eta/s occurs near the second order phase transition of the model due to the rapid variation of the order parameter (here the sigma vacuum expectation value) at a temperature slightly smaller than the critical one.Comment: 22 pages, 19 figures, v2, some references and several figures added, typos corrected and certain arguments clarified, revised for PR

Bose-Einstein Condensate Driven by a Kicked Rotor in a Finite Box

We study the effect of different heating rates of a dilute Bose gas confined in a quasi-1D finite, leaky box. An optical kicked-rotor is used to transfer energy to the atoms while two repulsive optical beams are used to confine the atoms. The average energy of the atoms is localized after a large number of kicks and the system reaches a nonequilibrium steady state. A numerical simulation of the experimental data suggests that the localization is due to energetic atoms leaking over the barrier. Our data also indicates a correlation between collisions and the destruction of the Bose-Einstein condensate fraction.Comment: 7 pages, 8 figure

The Nonlinear Permittivity Including Non-Abelian Self-interaction of Plasmons in Quark-Gluon Plasma

By decomposing the distribution functions and color field to regular and fluctuation parts, the solution of the semi-classical kinetic equations of quark-gluon plasma is analyzed. Through expanding the kinetic equations of the fluctuation parts to third order, the nonlinear permittivity including the self-interaction of gauge field is obtained and a rough numerical estimate is given out for the important \vk =0 modes of the pure gluon plasma.Comment: 7 pages, shortened version accepted by Chin.Phys.Let

Levy distribution in many-particle quantum systems

Levy distribution, previously used to describe complex behavior of classical systems, is shown to characterize that of quantum many-body systems. Using two complimentary approaches, the canonical and grand-canonical formalisms, we discovered that the momentum profile of a Tonks-Girardeau gas, -- a one-dimensional gas of $N$ impenetrable (hard-core) bosons, harmonically confined on a lattice at finite temperatures, obeys Levy distribution. Finally, we extend our analysis to different confinement setups and demonstrate that the tunable Levy distribution properly reproduces momentum profiles in experimentally accessible regions. Our finding allows for calibration of complex many-body quantum states by using a unique scaling exponent.Comment: 7 pages, 6 figures, results are generalized, new examples are adde

The non-self-adjointness of the radial momentum operator in n dimensions

The non self-adjointness of the radial momentum operator has been noted before by several authors, but the various proofs are incorrect. We give a rigorous proof that the $n$-dimensional radial momentum operator is not self- adjoint and has no self-adjoint extensions. The main idea of the proof is to show that this operator is unitarily equivalent to the momentum operator on $L^{2}[(0,\infty),dr]$ which is not self-adjoint and has no self-adjoint extensions.Comment: Some text and a reference adde

Deriving Boltzmann Equations from Kadanoff-Baym Equations in Curved Space-Time

To calculate the baryon asymmetry in the baryogenesis via leptogenesis scenario one usually uses Boltzmann equations with transition amplitudes computed in vacuum. However, the hot and dense medium and, potentially, the expansion of the universe can affect the collision terms and hence the generated asymmetry. In this paper we derive the Boltzmann equation in the curved space-time from (first-principle) Kadanoff-Baym equations. As one expects from general considerations, the derived equations are covariant generalizations of the corresponding equations in Minkowski space-time. We find that, after the necessary approximations have been performed, only the left-hand side of the Boltzmann equation depends on the space-time metric. The amplitudes in the collision term on the right--hand side are independent of the metric, which justifies earlier calculations where this has been assumed implicitly. At tree level, the matrix elements coincide with those computed in vacuum. However, the loop contributions involve additional integrals over the the distribution function.Comment: 14 pages, 5 figures, extended discussion of the constraint equations and the solution for the spectral functio

Decoherence and dephasing errors caused by D.C. Stark effect in rapid ion transport

We investigate the error due to D.C. Stark effect for quantum information processing for trapped ion quantum computers using the scalable architecture proposed in J. Res. Natl. Inst. Stan. 103, 259 (1998) and Nature 417, 709 (2002). As the operation speed increases, dephasing and decoherence due to the D.C. Stark effect becomes prominent as a large electric field is applied for transporting ions rapidly. We estimate the relative significance of the decoherence and dephasing effects and find that the latter is dominant. We find that the minimum possible of dephasing is quadratic in the time of flight, and an inverse cubic in the operational time scale. From these relations, we obtain the operational speed-range at which the shifts caused by D.C. Stark effect, no matter follow which trajectory the ion is transported, are no longer negligible. Without phase correction, the maximum speed a qubit can be transferred across a 100 micron-long trap, without excessive error, in about 10 ns for Calcium ion and 50 ps for Beryllium ion. In practice, the accumulated error is difficult to be tracked and calculated, our work gives an estimation to the range of speed limit imposed by D.C. Stark effect.Comment: 7 pages, 1 figure. v2: Title is changed in this version to make our argument more focused. Introduction is rewritten. A new section IV is added to make our point more prominent. v3: Title is changed to make our argument more specific. Abstract, introduction, and summary are revise