Flavoured leptogenesis in the CTP formalism

Within the Closed Time Path (CTP) framework, we derive kinetic equations for particle distribution functions that describe leptogenesis in the presence of several lepton flavours. These flavours have different Standard-Model Yukawa couplings, which induce flavour-sensitive scattering processes and thermal dispersion relations. Kinetic equilibrium, which is rapidly established and maintained via gauge interactions, allows to simplify these equations to kinetic equations for the matrix of lepton charge densities. In performing this simplification, we notice that the rapid flavour-blind gauge interactions damp the flavour oscillations of the leptons. Leptogenesis turns out to be in the parametric regime where the flavour oscillations are overdamped and flavour decoherence is mainly induced by flavour sensitive scatterings. We solve the kinetic equations for the lepton number densities numerically and show that they interpolate between the unflavoured and the fully flavoured regimes within the intermediate parametric region, where neither of these limits is applicable.     

Quantum mechanics of leptogenesis

Thermal leptogenesis is an attractive mechanism that explains in a simple way the matter-antimatter asymmetry of the universe. It is usually studied via the Boltzmann equations, which describes the time evolution of particle densities or distribution functions in a thermal bath. The Boltzmann equations are classical equations and suffer from basic conceptual problems and they lack to include many quantum phenomena. We show how to address leptogenesis systematically in a purely quantum way, by describing non-equilibrium excitations of a Majorana particle in the Kadanoff-Baym equations with significant emphasis on the initial and boundary conditions of the solutions. We apply our results to thermal leptogenesis, computing analytically the asymmetry generated, comparing it with the semiclassical Boltzmann approach. The non-locality of the Kadanoff-Baym equations shows how off-shell effects can have a huge impact on the generated asymmetry. The insertion of standard model decay widths to the particles excitations of the bath is also discussed. We explain how with a trivial insertion of these widths we regain locality on the processes.     

Equation of state for warm dense lithium: A first principles investigation

The quantum molecular dynamics based on the density functional theory has been adopted to simulate the equation of state for the shock compressed lithium. In contrary to some earlier experimental measurement and theoretical simulation,there is not any evidence of the ‘kink' in the Hugoniot curve in our accurate simulation. Throughout the shock compression process, only a simple solid-to-liquid melting behavior is demonstrated, instead of complicated solid–solid phase transitions. Moreover, the x-ray absorption near-edge spectroscopy has been predicted as a feasible way to diagnose the structural evolution of warm dense lithium in this density region.     

The first second of the Universe

The history of the Universe after its first second is now tested by high quality observations of light element abundances and temperature anisotropies of the cosmic microwave background. The epoch of the first second itself has not been tested directly yet; however, it is constrained by experiments at particle and heavy ion accelerators. Here I attempt to describe the epoch between the electroweak transition and the primordial nucleosynthesis. The most dramatic event in that era is the quark‐hadron transition at 10 μs. Quarks and gluons condense to form a gas of nucleons and light mesons, the latter decay subsequently. At the end of the first second, neutrinos and neutrons decouple from the radiation fluid. The quark‐hadron transition and dissipative processes during the first second prepare the initial conditions for the synthesis of the first nuclei. As for the cold dark matter (CDM), WIMPs (weakly interacting massive particles) – the most popular candidates for the CDM – decouple from the presently known forms of matter, chemically (freeze‐out) at 10 ns and kinetically at 1 ms. The chemical decoupling fixes their present abundances and dissipative processes during and after thermal decoupling set the scale for the very first WIMP clouds.     

Off-equilibrium photon production during the chiral phase transition

In the early stage of ultrarelativistic heavy-ion collisions chiral symmetry is restored temporarily. During this so-called chiral phase transition, the quark masses change from their constituent to their bare values. This mass shift leads to the spontaneous non-perturbative creation of quark–antiquark pairs, which effectively contributes to the formation of the quark–gluon plasma. We investigate the photon production induced by this creation process. We provide an approach that eliminates possible unphysical contributions from the vacuum polarization and renders the resulting photon spectra integrable in the ultraviolet domain. The off-equilibrium photon numbers are of quadratic order in the perturbative coupling constants while a thermal production is only of quartic order. Quantitatively, we find, however, that for the most physical mass-shift scenarios and for photon momenta larger than 1 GeV the off-equilibrium processes contribute less photons than the thermal processes.     

Electronic correlation in the quantum Hall regime

Two‐dimensional interacting electron systems become strongly correlated if the electrons are subject to a perpendicular high magnetic field. After introducing the physics of the quantum Hall regime the incompressible many‐particle ground state and its excitations are studied in detail at fractional filling factors for spin‐polarized electrons. The spin degree of freedom whose importance was shown in recent experiments is considered by studying the thermodynamics at filling factor one and near one.     

On the effective non-Hermitian eigenvalue problems for resonant levels

Summary A class of non-Hermitian eigenvalue equations, which are aimed to determine positions and widths of resonant (decaying) levels, is derived quite generally through a projection operator procedure whereby the effects of the continuum states responsible for the decay is represented in an effective manner. The boundary conditions appropriate to these eigenvalue problems are discussed and the wave function renormalization is evaluated. A connection is drawn with the effective eigenvalue problems occurring in the many-body Green's functions theory. Features like the energy dependence of the self-energy for the single-particle Green's function and of the screened Coulomb interaction for the electron-hole Green's function are accordingly interpreted in terms of elimination of continuum channels.

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Riassunto é noto da tempo, soprattutto dai lavori di Feshbach sul metodo delle hamiltoniane efficaci per reazioni nucleari, che tecniche di operatori di proiezione sono particolarmente adatte a costruire hamiltoniane efficaci allo scopo di determinare i parametri rilevanti delle risonanze nella teoria della diffusione. In questo articolo si pone in maggiore risalto l'aspetto quasi-legato degli stati risonanti e si considera un problema modello dove un insieme di stati discreti é accoppiato con un insieme di stati continui, i quali sono poi eliminati dalla trattazione esplicita mediante operatori di proiezione. In questo modo la sottomatrice dell'operatore risolvente nel sottospazio degli stati discreti risulta espressa in termini di un'hamiltoniana efficace che è non hermitiana e dipendente dall'energia. Tale procedimento è poi collegato con la risoluzione della equazione di Schr?dinger soggetta alle condizioni al contorno del tipo Kapur-Peierls che sono appropriate agli stati quasi stazionari. Questo collegamento fornisce, tra l'altro, una relazione tra la rinormalizzazione della funzione d'onda e la dipendenza dall'energia dell'hamiltoniana efficace. I risultati generali così ottenuti sono poi applicati alla teoria delle funzioni di Green a molti corpi. In particolare, si mostra come sia l'equazione di Dyson che determina i livelli a quasi particella sia l'equazione agli autovalori per gli eccitoni con schermaggio dielettrico possano essere interpretate nel senso delle hamiltoniane efficaci.

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Резюме В общем виде выводится класс незрмитовых уравнений для собственных значений, которые преднаэначемы для определения положений и ширин резонансных (распадающих) уровней, используя процедуру операторов проектирования. В таком подходе влияние непрерывных состояний, ответственных за распад, учитывается эффективным образом. Обсуждаются граничные условия, соответствующие этим проблемам собственных значений, и вычисляется перенормировка волновой функции. Отмечается связь с проблемами эффективных собственных значений, которые имеют место в теории многочастичных гриновских функций. Такие особенности, как энергетическая зависимость собственной энергии для одночастичной функции Грина и экранированное кулоновское взаимодействие для электрон-дырочной гриновской функции, интерпретируются соответственно на основе исключения непрерывных каналов.

     

Nonequilibrium dynamics of scalar fields in a thermal bath

We study the approach to equilibrium for a scalar field which is coupled to a large thermal bath. Our analysis of the initial value problem is based on Kadanoff-Baym equations which are shown to be equivalent to a stochastic Langevin equation. The interaction with the thermal bath generates a temperature-dependent spectral density, either through decay and inverse decay processes or via Landau damping. In equilibrium, energy density and pressure are determined by the Bose-Einstein distribution function evaluated at a complex quasi-particle pole. The time evolution of the statistical propagator is compared with solutions of the Boltzmann equations for particles as well as quasi-particles. The dependence on initial conditions and the range of validity of the Boltzmann approximation are determined.     

Description of the viscosity of honeys in the supercooled regime

For several honeys from different countries, we study the dependence of the Logarithmic Shift Factor (LSF$LSF$) with temperature that obeys the Williams–Landel–Ferry equation. We find that the LSF$LSF$ may be expressed in terms of a linear equation. On the other hand, the viscosities of different honeys present a corresponding state behavior through a master plot in terms of an adimensional temperature. This kind of behavior has been reported for other glass formers.     

A Consistency Check for the Free Scalar Field Theory Realization of the Doubly Spacial Relativity *

We study a free scalar field theory in the framework of the Magueijo-Smolin model of the "Doubly Special Relativity" (DSR) which is a non-linear realization of the action of the Lorentz group on momentum space admitting an invariant energy cutoff. We show that unlike the standard quantum field theory, the Klein-Gordon equation obtained via Euler-Lagrange field equation and Heisenberg picture equation of motion of the field are not equivalent in this framework, at least up to the first order of the Planck length scale.     

Quasiparticle excitations in relativistic quantum field theory

We analyze the particle-like excitations arising in relativistic field theories in states different than the vacuum. The basic properties characterizing the quasiparticle propagation are studied using two different complementary methods. First we introduce a frequency-based approach, wherein the quasiparticle properties are deduced from the spectral analysis of the two-point propagators. Second, we put forward a real-time approach, wherein the quantum state corresponding to the quasiparticle excitation is explicitly constructed, and the time-evolution is followed. Both methods lead to the same result: the energy and decay rate of the quasiparticles are determined by the real and imaginary parts of the retarded self-energy, respectively. Both approaches are compared, on the one hand, with the standard field-theoretic analysis of particles in the vacuum and, on the other hand, with the mean-field-based techniques in general backgrounds.     

关于量子力学的基本原理

文章抽选关于量子力学基本原理的几个题目,包括量子力学与经典物理学的对比、量子概念的产生、薛定谔方程的出现、全同性原理和量子路径积分等,作些说明。目的在于激发读者思考量子力学的本质在哪里。     

Topological Entanglement Entropy from the Holographic Partition Function

We study the entropy of chiral 2+01-dimensional topological phases, where there are both gapped bulk excitations and gapless edge modes. We show how the entanglement entropy of both types of excitations can be encoded in a single partition function. This partition function is holographic because it can be expressed entirely in terms of the conformal field theory describing the edge modes. We give a general expression for the holographic partition function, and discuss several examples in depth, including abelian and non-abelian fractional quantum Hall states, and $p+ip$ superconductors. We extend these results to include a point contact allowing tunneling between two points on the edge, which causes thermodynamic entropy associated with the point contact to be lost with decreasing temperature. Such a perturbation effectively breaks the system in two, and we can identify the thermodynamic entropy loss with the loss of the edge entanglement entropy. From these results, we obtain a simple interpretation of the non-integer ‘ground state degeneracy’ which is obtained in 1+1-dimensional quantum impurity problems: its logarithm is a 2+1-dimensional topological entanglement entropy.     

The CPT Group of the Dirac Field

Using the standard representation of the Dirac equation, we show that, up to signs, there exist only two sets of consistent solutions for the matrices of charge conjugation (C), parity (P), and time reversal (T), which give the transformation of fields , and , where and . These sets are given by , , and , , . Then , and two successive applications of the parity transformation to fermion fields necessarily amount to a 2 rotation. Each of these sets generates a non abelian group of 16 elements, respectively, and , which are non isomorphic subgroups of the Dirac algebra, which, being a Clifford algebra, gives a geometric nature to the generators, in particular to charge conjugation. It turns out that and , where is the dihedral group of eight elements, the group of symmetries of the square, and 16E is a non trivial extension of by , isomorphic to a semidirect product of these groups; S₆ and S₈ are the symmetric groups of six and eight elements. The matrices are also given in the Weyl representation, suitable for taking the massless limit, and in the Majorana representation, describing self-conjugate fields. Instead, the quantum operators C, P and T, acting on the Hilbert space, generate a unique group , which we call the CPT group of the Dirac field. This group, however, is compatible only with the second of the above two matrix solutions, namely with , which is then called the matrix CPT group. It turns out that , where is the dicyclic group of 8 elements and S₁₀ is the symmetric group of 10 elements. Since , the quaternion group, and , the 0-sphere, then .     

量子场论中的自旋算符

从量子场论的角度对相对论粒子的运动自旋概念作了进一步深入研究.构造了场量子自旋以及场系统运动自旋两个新算符.给出了场量子自旋动量空间的显式表达式以及用Poincar啨群生成元表示的场系统运动自旋的显式表达式.借助这两个算符,可以干净地解决有关场自旋的问题,表明它们才是场自旋的恰当的算符.     

The Hyperbolic Volume of Knots from the Quantum Dilogarithm

The invariant of a link in three-sphere, associated with the cyclic quantum dilogarithm, depends on a natural number N. By the analysis of particularexamples, it is argued that, for a hyperbolic knot (link), the absolute valueof this invariant grows exponentially at large N, the hyperbolic volume of the knot (link) complement being the growth rate.     

Electronic structure of EuPtSi3 studied from the first principles calculation

We investigate the electronic structure of EuPtSi₃ using full potential linearized augmented plane wave method within the generalized gradient approximation. We reproduce the observed easy axis of magnetization as well as magnetic moment and propose that the magnetic configuration for this compound is incommensurate or noncollinear. We find that the spin configuration has only negligible effect on the band around Fermi energy. EuPtSi₃ and its isostructural superconductor BaPtSi₃ have similar band structures. Despite the shorter Pt-Si bond, EuPtSi₃ possesses larger density of state near the Fermi energy compared with BaPtSi₃, thus the structural difference and the associated difference in band structure cannot explain the non-superconductivity of EuPtSi₃.     

Photon-assisted Shot noise of the double quantum dot interferometer in weak Kondo regime

The shot noise of a parallel double quantum dot (DQD) system under the perturbation of microwave fields is investigated in the weak Kondo regime. Peak-valley structures exhibit in the differential conductance and shot noise, and side resonant peaks emerge around the Kondo peak due to the absorption and emission of photons. The shot noise is sensitively dependent on the adjusting approach through changing the gate voltages. Large resonant Fano factor accompanying photon-induced side peaks appear by simultaneously varying the two gate voltages. The photon suppression and enhancement of shot noise have been evaluated corresponding to the coherent and incoherent current correlation. The destructive interference causes the suppression of shot noise by changing the Aharonov–Bohm phase.     

The realistic QCD equation of state in relativistic heavy-ion collisions and the early Universe

The realistic equation of state of strongly interacting matter, that has been successfully applied in the recent hydrodynamic studies of hadron production in relativistic heavy-ion collisions at RHIC, is used in the Friedmann equation to determine the precise time evolution of thermodynamic parameters in the early Universe. A comparison with the results obtained with simple ideal-gas equations of state is made. The realistic equation of state describes a crossover rather than the first-order phase transition between the quark–gluon plasma and hadronic matter. Our numerical calculations show that small inhomogeneities of strongly interacting matter in the early Universe are moderately damped during such crossover.