On particle creation by black holes

Hawking's analysis of particle creation by black holes is extended by explicitly obtaining the expression for the quantum mechanical state vector ψ which results from particle creation starting from the vacuum during gravitational collapse. (Hawking calculated only the expected number of particles in each mode for this state.) We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. In agreement with previously known results, we find that we are led to a unique quantum scattering theory which is completely well behaved mathematically provided a certain condition is satisfied by the operators which describe the scattering of classical positive frequency solutions. In terms of these operators we derive the expression for the state vector describing particle creation from the vacuum, and we prove that S-matrix is unitary. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. There is some ambiguity in the theory in this case arising from freedom involved in defining what one means by “positive frequency” at the future event horizon. However, it is proven that the expression for the density matrix formed from ψ describing the emission of particles to infinity is independent of this choice, and thus unambiguous predictions for the results of all possible measurements at infinity are obtained. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail (i.e., not only in expected number of particles) with black body emission.     

在高密度下核物质的色超导性

建立了相变热力学理论和场论的关系. 强调在量子场论中必须引进序参量场， 则相变的讨论就类似于Goldstone bosons 的产生. 如果只讨论一级相变， Goldstone bosons场就足够了; 如果要讨论二级相变， 则必须讨论一系列的场， 这些场构成一个对称群的表示. 另外, 也将这一思想用到色超导中. In this paper we built a relation between the thermodynamical theory of the phase transition and field theory. We emphasized that in the quantum field theory we have to introduce the order parameter fields. Then the discussion of the phase transition is closed to the creation of the Goldstone bosons. If we only discuss the first order transition, the Goldstone bosons fields are sufficient. If we want to discuss the second order transition, we have to discuss a set of fields that constructs a representation of a symmetry group. We also apply this concept to color superconductivity.     

Dynamically assisted pair production for scalar QED by two fields

By solving the quantum Vlasov equation, the dynamically assisted pair production for scalar quantum electrodynamics (QED) is investigated. It is verified that this mechanism still holds true for boson pair production. Two combinations of two electric fields having different time scales under various time delays are considered; it is found that the oscillations of the momentum spectrum and the number density of created bosons decrease with increasing time delay, and the latter has a maximum value when the time delay equals zero. Furthermore, the differences in vacuum pair production between bosons and fermions are also studied, and they are helpful for distinguishing the created bosons from fermions.     

Non-abelian gauge bosons in the compactified bosonic membrane theory

We consider the bosonic membrane compactified on a torus. The membrane motion is stabilized by a topologically non-trivial background. We find that, in the narrow membrane limit, the mass formula to O(ħ;) reduces to exactly the same form as that of the compactified closed bosonic string theory, and we obtain (almost) massless vector bosons in the adjoint representation of a simply laced Lie group in D = 27. This is only dimension at which the gravitation and gauge bosons may coexist in that background.     

Kinetics of the Bose-Einstein condensation

We study the bosonic Boltzmann-Nordheim kinetic equation, which describes the kinetic regime of weakly interacting bosons with s-wave scattering only. We consider a spatially homogeneous fluid with an isotropic momentum distribution. The issue of the dynamical formation of a Bose-Einstein condensate has been studied extensively. We supply here the completed equations of motion for the coupled system, the energy density distribution of the normal fluid and the density of the condensate. With this information the post-nucleation self-similar solution is investigated in more detail than before.     

A Time-Dependent Nonequilibrium Calculational Scheme towards the Study of Temperature Fluctuations

A new perturbative scheme for interacting nonequilibrium thermal quantum fields using thermo field dynamics is outlined by explicitly considering the temporal change of the thermal vacuum as it moves through many inequivalent state vector spaces. One is then naturally led to two sources of time dependence, one from the dynamics and the other from the change of thermal vacuum, which are taken care of by the Hamiltonian and the thermal generator, respectively. To obtain a practical scheme we restrict ourselves by the demand that a spectral representation for the full propagator exists. This leads to a time dependent temperature. The addition of a diagonalization condition for the quasi-particle Hamiltonian provides the master equation for the number density. We show that our formalism is equivalent to an extended form of the path-ordering method. This formalism is a first step towards the study of the origin of heat and temperature in high-energy heavy ion collisions.     

Compton scattering in the Buchholz–Roberts framework of relativistic QED

We consider a Haag–Kastler net in a positive energy representation, admitting massive Wigner particles and asymptotic fields of massless bosons. We show that massive single-particle states are always vacua of the massless asymptotic fields. Our argument is based on the Mean Ergodic Theorem in a certain extended Hilbert space. As an application of this result, we construct the outgoing isometric wave operator for Compton scattering in QED in a class of representations recently proposed by Buchholz and Roberts. In the course of this analysis, we use our new technique to further simplify scattering theory of massless bosons in the vacuum sector. A general discussion of the status of the infrared problem in the setting of Buchholz and Roberts is given.     

Scalar particles in a narrow-band periodic potential

A system of an infinite number of spinless particles in a narrow-band periodic potential is treated. The dimension of the space is arbitrary, the tight-binding approximation is used, and it is assumed that the filling fraction is nearly one electron per atom. After a preliminary discussion of the Hartree approximation, the full Schrödinger equation is considered and a rigorous spectral perturbation theory in the kinetic energy term is set up. To get rid of the lack of relative boundedness of this perturbation, a vacuum state is constructed and its energy renormalized to zero, and passage is made to an excitonic representation in which the quasiparticles appear naturally as local perturbations of the vacuum. In this representation, relative boundedness is recovered and Rayleigh-Schrödinger expansions can be used to find cluster expansions for all local observables.     

Laser Driven Electron‐Positron Pair Creation–Kinetic Theory Versus Analytical Approximations

The dynamical Schwinger effect of vacuum pair creation driven by an intense external laser pulse is studied on the basis of quantum kinetic theory. The numerical solutions of these kinetic equations exhibit a complex time dependence which makes an analysis of the physical processes difficult. In particular, the question of secondary effects, such as creation of secondary annihilation photons from the focus spot of the colliding laser beams, remains an important open problem. In the present work we, therefore, develop a perturbation theory which is able to capture the dominant time dependence of the produced electron‐positron pair density. The theory shows excellent agreement with the exact kinetic results during the laser pulse, but fails to reproduce the residual pair density remaining in the system after termination of the pulse. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evolution of the single-mode squeezed vacuum state in amplitude dissipative channel

Using the way of deriving infinitive sum representation of density operator as a solution to the master equation describing the amplitude dissipative channel by virtue of the entangled state representation, we show manifestly how the initial density operator of a single-mode squeezed vacuum state evolves into a definite mixed state which turns out to be a squeezed chaotic state with decreasing-squeezing and deeoherence. We investigate average photon number, photon statistics distributions for this mixed state.     

Robustness of wave functions of interacting many bosons in a leaky Box

We study the robustness, against the leakage of bosons, of wave functions of interacting many bosons confined in a finite box by deriving and analyzing a general equation of motion for the reduced density operator. We identify a robust wave function that remains a pure state, whereas other wave functions, such as the Bogoliubov's ground state and the ground state with a fixed number of bosons, evolve into mixed states. Although these states all have the off-diagonal long-range order, and the same energy, we argue that only the robust state is realized as a macroscopic quantum state.     

Nonequilibrium perturbation theory in Liouville-Fock space for inelastic electron transport

We use a superoperator representation of the quantum kinetic equation to develop nonequilibrium perturbation theory for an inelastic electron current through a quantum dot. We derive a Lindblad-type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville-Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron-vibronic and electron-electron interactions. Our perturbation theory becomes equivalent to a Keldysh nonequilibrium Green's function perturbative treatment provided that the buffer zone is large enough to alleviate the problems associated with approximations of the Lindblad kinetic equation.     

Spontaneous Lorentz violation via QED with non-exact gauge invariance

We reconsider an alternative theory of QED with the photon as a massless vector Nambu–Goldstone boson and show that the underlying spontaneous Lorentz violation caused by the vector field vacuum expectation value, while being superficial in gauge invariant theory, becomes physically significant in QED with a tiny gauge non-invariance. This leads, through special dispersion relations appearing for charged fermions, to a new class of phenomena, which could be of distinctive observational interest in particle physics and astrophysics. They include a significant change in the GZK cutoff for UHE cosmic-ray nucleons, stability of high-energy pions and W bosons, a modification of nucleon beta decays, and some other ones.     

Pair production and optical lasers

Electron-positron pair creation in a standing wave is explored using a parameter-free quantum kinetic equation. Field strengths and frequencies corresponding to modern optical lasers induce a material polarization of the QED vacuum, which may be characterized as a plasma of e+e- quasiparticle pairs with a density of approximately 10(20) cm-3. The plasma vanishes almost completely when the laser field is zero, leaving a very small residual pair density n(r) which is the true manifestation of vacuum decay. The average pair density per period is proportional to the laser intensity but independent of the frequency nu. The density of residual pairs also grows with laser intensity but n(r) proportional to nu(2). With optical lasers at the forefront of the current generation, these dynamical QED vacuum effects can plausibly generate 5-10 observable two-photon annihilation events per laser pulse.     

Variational wave equations of two fermions interacting via scalar,pseudoscalar, vector,pseudovector and tensor fields

We consider a method for deriving relativistic two-body wave equations for fermions in the coordinate representation. The Lagrangian of the theory is reformulated by eliminating the mediating fields by means of covariant Green's functions. Then, the nonlocal interaction terms in the Lagrangian are reduced to local expressions which take into account retardation effects approximately. We construct the Hamiltonian and two-fermion states of the quantized theory, employing an unconventional “empty” vacuum state, and derive relativistic two-fermion wave equations. These equations are a generalization of the Breit equation for systems with scalar, pseudoscalar, vector, pseudovector and tensor coupling.     

Diagonalization of theXXZ Hamiltonian by vertex operators

We diagonalize the anti-ferroelectricXXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of . Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit—thesu(2)-invariant Thirring model.Dedicated to Professors Huzihiro Araki and Noboru Nakanishi on the occasion of their sixtieth birthdays     

固体电介质的电老化与击穿新理论和实验

根据一级捕获动力学方程,导出高电场下固体电介质中新陷阱产生的动力学理论,从该理论出发,以陷阱密度增加到一定程度作为介质发生电击穿的临界条件,获得高电场下电介质的寿命与电场的指数成正比,这一理论结果与广泛应用的电老化经验公式一致,也与实验结果相符。 关键词：     

A continuum model of gas flows with localized density variations

We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows.     

Search for hidden sector photons with the ADMX detector

Hidden U(1) gauge symmetries are common to many extensions of the standard model proposed to explain dark matter. The hidden gauge vector bosons of such extensions may mix kinetically with standard model photons, providing a means for electromagnetic power to pass through conducting barriers. The axion dark matter experiment detector was used to search for hidden vector bosons originating in an emitter cavity driven with microwave power. We exclude hidden vector bosons with kinetic couplings χ>3.48×10?? for masses less than 3 μeV. This limit represents an improvement of more than 2 orders of magnitude in sensitivity relative to previous cavity experiments.