Photon Number Density Research Articles

Non-Wiener Dynamics of Open Systems for Nonzero Number Density of Surrounding Photons

We propose a collective decay model for a localized ensemble of identical atoms in a vacuum broadband electromagnetic field with a nonzero photon number density considering second-order terms in the atom–field interaction constant. The model is based on the stochastic differential equation for the evolution operator for the atomic ensemble and surroundings, which is controlled by the main quantum random processes and independent classical Wiener processes. It is shown that in some cases, nonzero photon number density does not influence the suppression of collective emission of atoms, and its existence is manifested as an additional mechanism of redistribution of atoms over collective sublevels.

On the radiative and thermodynamic properties of the cosmic radiations using COBE FIRAS instrument data: IV. Sunyaev-Zel’dovich ( μ $\mu$ -type) distortion effect

The Sunyaev-Zel’dovich (SZ) effect represents a small spectral distortion to the cosmic microwave background (CMB) radiation, caused by the Compton scattering of CMB photons by the hot gas of galaxy clusters. In an early stage of universe, the SZ effect generates $\mu$ -type of distortions for the CMB spectrum. A $\mu$ -type distortion is created between the double Compton scattering decoupling ( $z \sim 10^{6}$ ) and the thermalization decoupling by the Compton scattering ( $z \sim 10^{5}$ ). In this case, to describe the small spectral distortion of the CMB spectrum, we use the Bose-Einstein ( $\mu$ -type) distribution with a non-zero chemical potential. At present, it is interesting to investigate the effect of this spectral distortion on the integral characteristics of the Bose-Einstein ( $\mu$ -type) spectrum. The thermal radiative and thermodynamic functions are such integral characteristics. These functions are as follows: a) the total radiation power per unit area; b) total energy density; c) number density of photons; d) grand potential density; e) Helmholtz free energy density; f) entropy density; g) heat capacity at constant volume; h) enthalpy density; and i) pressure. Precise analytical expressions are obtained for the temperature dependences of these functions. Using the observational data obtained by the COBE FIRAS, PIXIE, PRISM, and Planck missions, the thermal radiative and thermodynamic functions are calculated. A comparative analysis of the results obtained with the results for the same functions of the CMB spectrum at $T = 2.72548~\mbox{K}$ is carried out. Very small distortions are observed for the thermal radiative and thermodynamic functions. In the redshift range $10^{5} < z < 3 \times10^{6}$ , these functions are calculated. The expressions are obtained for new astrophysical parameters, such as the entropy density/Boltzmann constant and number density, created by the Bose-Einstein ( $\mu$ -type) spectrum.

Optical bistability in a low-photon-density regime

We give a microscopic description of the optical bistability, where the transmission coefficient has two different values as a function of input light intensity, and the system exhibits a discontinuous jump with a hysteresis loop. We developed an efficient numerical algorithm to treat the quantum master equation for hybridized systems of many photons and a large number of two-level atoms. By using this method, we characterize the bistability from the viewpoint of eigenmodes and eigenvalues of the time evolution operator of the quantum master equation. We investigate the optical bistability within the low photon-density regime, where the hybridization of photon and atom degrees of freedom occurs and the resonance spectrum has a double peak structure. We compared it with the standard optical bistability between the low photon-density regime and the high photon-density regime, where the photons can be treated as a classical electromagnetic field and the resonance spectrum has a single peak structure. We discuss the steady-state properties of the optical bistability: dependencies of the photon number density on the intensity and the double peak structure of the photon number distribution inside the bistable region. As for the dynamical properties, we find that the relaxation timescale shows an exponential growth with the system size, and reveal how the hysteresis loop of the optical bistability depends on the size of the system and the sweeping rate of the driving amplitude. Finally, by investigating the effects of detuning frequency of the input field, we clarify the characteristic properties of the present optical bistability within the low photon-density regime, which are qualitatively different from the standard optical bistable phenomena.

Room for New Physics in the Rayleigh-Jeans Tail of the Cosmic Microwave Background.

We show that, despite stringent constraints on the shape of the main part of the cosmic microwave background (CMB) spectrum, there is considerable room for its modification within its Rayleigh-Jeans (RJ) end, ω≪T_{CMB}. We construct explicit new physics models that give an order one (or larger) increase of photon count in the RJ tail, which can be tested by existing and upcoming experiments aiming to detect the cosmological 21cm emission or absorption signal. This class of models stipulates the decay of unstable particles to dark photons A^{'} that have a small mass, m_{A^{'}}∼10^{-14}-10^{-9} eV, nonvanishing mixing angle ε with electromagnetism, and energies much smaller than T_{CMB}. The nonthermal number density of dark photons can be many orders of magnitude above the number density of CMB photons, and even a small probability of A^{'}→A oscillations, for values as small as ε∼10^{-9}, can significantly increase the number of RJ photons. In particular, we show that resonant oscillations of dark photons into regular photons in the interval of redshifts 20<z<1700 can be invoked as an explanation of the recent tentative observation of a stronger-than-expected absorption signal of 21cm photons. We present a model that realizes this possibility, where meV mass dark matter decays to dark photons, with a lifetime longer than the age of the Universe.

Kinetic Equation for the Density Matrix of Atoms in the Field of a Broadband One-Photon Packet Taking into Account the Non-Wiener Dynamics

We have derived the quantum master kinetic equation for the density matrix of an atomic system in the field of a narrow-beam one-photon broadband packet in the conditions when the latter plays the role of a thermostat. This equation takes into account the Stark interaction of atoms with the broadband field of surroundings of the system, which are in the state with zero photon number density, as well as the interaction of broadband fields at the atomic system.

Nonradiative recombination centers in GaAs:N δ-doped superlattice revealed by two-wavelength-excited photoluminescence

We use two-wavelength-excited photoluminescence (PL) to investigate nonradiative recombination (NRR) centers in GaAs:N δ-doped superlattice (SL) structures grown by molecular beam epitaxy. The change in photoluminescence (PL) intensity due to the superposition of below-gap excitation at energies of 0.75, 0.80, 0.92, and 0.95 eV and above-gap excitation at energies of 1.69 or 1.45 eV into the GaAs conduction band and the E− band implies the presence of NRR centers inside the GaAs:N δ-doped SL and/or GaAs layers. The change in PL intensity as a function of the photon number density of below-gap excitation is examined for both bands, which enables us to determine the distribution of NRR centers inside the GaAs:N δ-doped SL and GaAs layers. We propose recombination models to explain the experimental results. Defect-related parameters that give a qualitative insight into the samples are investigated systematically by fitting the rate equations to the experimental data.

Gravitational leptogenesis in axion inflation with SU(2) gauge field

We present an intrinsic leptogenesis mechanism in models of axion inflation with a classical SU(2) gauge field. The gauge field is coupled to the axion with a Chern-Simons interaction and comprises a tiny fraction of the total energy, ρYM/ρtot ≲ ϵ2. However, it has spin-2 fluctuations which breaks the parity and leads to the generation of chiral gravitational waves during inflation. By the gravitational anomaly in SM, it naturally creates a net lepton number density, sufficient to explain the matter asymmetry. We show that this mechanism can generate the observed value of baryon to photon number density in a natural range of parameters and yet has a small chiral tensor power spectrum on large scales.

Breaking Be: a sterile neutrino solution to the cosmological lithium problem

The possibility that the so-called ``lithium problem'', i.e., the disagreement between the theoretical abundance predicted for primordial 7Li assuming standard nucleosynthesis and the value inferred from astrophysical measurements, can be solved through a non-thermal Big Bang Nucleosynthesis (BBN) mechanism has been investigated by several authors. In particular, it has been shown that the decay of a MeV-mass particle, like, e.g., a sterile neutrino, decaying after BBN not only solves the lithium problem, but also satisfies cosmological and laboratory bounds, making such a scenario worth to be investigated in further detail. In this paper, we constrain the parameters of the model with the combination of current data, including Planck 2015 measurements of temperature and polarization anisotropies of the Cosmic Microwave Background (CMB), FIRAS limits on CMB spectral distortions, astrophysical measurements of primordial abundances and laboratory constraints. We find that a sterile neutrino with mass MS = 4.35−0.17+0.13 MeV (at 95% c.l.), a decay time τS = 1.8−1.3+2.5 · 105 s (at 95% c.l.) and an initial density n̄S/n̄cmb = 1.7−0.6+3.5 · 10−4 (at 95% c.l.) in units of the number density of CMB photons, perfectly accounts for the difference between predicted and observed 7Li primordial abundance. This model also predicts an increase of the effective number of relativistic degrees of freedom at the time of CMB decoupling ΔNeffcmb ≡ Neffcmb −3.046 = 0.34−0.14+0.16 at 95% c.l.. The required abundance of sterile neutrinos is incompatible with the standard thermal history of the Universe, but could be realized in a low reheating temperature scenario. We also provide forecasts for future experiments finding that the combination of measurements from the COrE+ and PIXIE missions will allow to significantly reduce the permitted region for the sterile lifetime and density.

Thermal radiative and thermodynamic properties of solid and liquid uranium and plutonium carbides in the visible–near-infrared range

The knowledge of thermal radiative and thermodynamic properties of uranium and plutonium carbides under extreme conditions is essential for designing a new metallic fuel materials for next generation of a nuclear reactor. The present work is devoted to the study of the thermal radiative and thermodynamic properties of liquid and solid uranium and plutonium carbides at their melting/freezing temperatures. The Stefan-Boltzmann law, total energy density, number density of photons, Helmholtz free energy density, internal energy density, enthalpy density, entropy density, heat capacity at constant volume, pressure, and normal total emissivity are calculated using experimental data for the frequency dependence of the normal spectral emissivity of liquid and solid uranium and plutonium carbides in the visible-near infrared range. It is shown that the thermal radiative and thermodynamic functions of uranium carbide have a slight difference during liquid-to-solid transition. Unlike UC, such a difference between these functions have not been established for plutonium carbide. The calculated values for the normal total emissivity of uranium and plutonium carbides at their melting temperatures is in good agreement with experimental data. The obtained results allow to calculate the thermal radiative and thermodynamic properties of liquid and solid uranium and plutonium carbides for any size of samples. Based on the model of Hagen-Rubens and the Wiedemann-Franz law, a new method to determine the thermal conductivity of metals and carbides at the melting points is proposed.

Bose--Einstein Condensation in a Hyperbolic Model for the Kompaneets Equation

In low-density or high-temperature plasmas, Compton scattering is the dominant process responsible for energy transport. Kompaneets in 1957 derived a nonlinear degenerate parabolic equation for the photon energy distribution. In this paper we consider a simplified model obtained by neglecting diffusion of the photon number density in a particular way. We obtain a nonlinear hyperbolic PDE with a position-dependent flux, which permits a one-parameter family of stationary entropy solutions to exist. We completely describe the long-time dynamics of each nonzero solution, showing that it approaches some nonzero stationary solution. While the total number of photons is formally conserved, if initially large enough it necessarily decreases after finite time through an out-flux of photons with zero energy. This corresponds to formation of a Bose--Einstein condensate, whose mass we show can only increase with time.

Polylogarithmic Representation of Radiative and Thermodynamic Properties of Thermal Radiation in a Given Spectral Range: II. Real-Body Radiation

The general analytical expressions for the thermal radiative and thermodynamic properties of a real-body are obtained in a finite range of frequencies at different temperatures. The frequency dependence of the spectral emissivity is represented as a power series. The Stefan-Boltzmann law, total energy density, number density of photons, Helmholtz free energy density, internal energy density, enthalpy density, entropy density, heat capacity at constant volume, pressure, and total emissivity are expressed in terms of the polylogarithm functions. The general expressions for the thermal radiative and thermodynamic functions are applied for the study of thermal radiation of liquid and solid zirconium carbide. These functions are calculated using experimental data for the frequency dependence of the normal spectral emissivity in the visible-near infrared range at the melting (freezing) point. The gaps between the thermal radiative and thermodynamic functions of liquid and solid zirconium carbide are observed. The general analytical expressions obtained can easily be presented in wavenumber domain.

Photon-conserving Comptonization in simulations of accretion discs around black holes

We introduce a new method for treating Comptonization in computational fluid dynamics. By construction, this method conserves the number of photons. Whereas the traditional ‘blackbody Comptonization’ approach assumes that the radiation is locally a perfect blackbody and therefore uses a single parameter, the radiation temperature, to describe the radiation, the new ‘photon-conserving Comptonization’ approach treats the photon gas as a Bose–Einstein fluid and keeps track of both the radiation temperature and the photon number density. We have implemented photon-conserving Comptonization in the general relativistic radiation magnetohydrodynamical code koral and we describe its impact on simulations of mildly supercritical black hole accretion discs. We find that blackbody Comptonization underestimates the gas and radiation temperature by up to a factor of 2 compared to photon-conserving Comptonization. This discrepancy could be serious when computing spectra. The photon-conserving simulation indicates that the spectral colour correction factor of the escaping radiation in the funnel region of the disc could be as large as 5.

On the radiative and thermodynamic properties of the cosmic radiations using COBE FIRAS instrument data: III. Galactic far-infrared radiation

Using the three-component spectral model describing the FIRAS average continuum spectra, the exact analytical expressions for thermodynamic and radiative functions of Galactic far-infrared radiation are obtained. The COBE FIRAS instrument data in the 0.15–2.88 THz frequency interval at the mean temperatures of T1 = 17.72 K, T2 = 14 K and T3 = 6.73 K are used for calculating the radiative and thermodynamic functions, such as the total radiation power per unit area, total energy density, total emissivity, number density of photons, Helmholtz free energy density, entropy density, heat capacity at constant volume and pressure for the warm, intermediate-temperature and very cold components of the Galactic continuum spectra. The generalized Stefan-Boltzmann law for warm, intermediate-temperature and very cold components is constructed. The temperature dependence of each component is determined by the formula IS–B(T) = σ′T6. This result is important when we construct the cosmological models of radiative transfer that can be applied inside the Galaxy. Within the framework of the three-component spectral model, the total number of photons in our Galaxy and the total radiation power (total luminosity) emitted from a surface of the Galaxy are calculated. Their values are NGtotal = 1.3780 × 1068 and IGtotal(T) = 1.0482 × 1036 W. Other radiative and thermodynamic properties of the Galactic far-infrared radiation (photon gas) of the Galaxy are calculated. The expressions for astrophysical parameters, such as the entropy density/Boltzmann constant and number density of the Galactic far-infrared photons are obtained. We assume that the obtained analytical expressions for thermodynamic and radiative functions may be useful for describing the continuum spectra of the far-infrared radiation for other galaxies.

Polylogarithmic Representation of Radiative and Thermodynamic Properties of Thermal Radiation in a Given Spectral Range: I. Blackbody Radiation

There are several classes of materials and space objects for which the frequency dependence of the spectral emissivity is represented as a power series. Therefore, the study of the properties of thermal radiation for these real bodies is an important task for both fundamental science and industrial applications. The general analytical expressions for the thermal radiative and thermodynamic functions of a real body are obtained in a finite range of frequencies at different temperatures. The Stefan–Boltzmann law, total energy density, number density of photons, Helmholtz free energy density, internal energy density, enthalpy density, entropy density, heat capacity at constant volume, pressure, and total emissivity are expressed in terms of the polylogarithm functions. The obtained general expressions for the thermal radiative and thermodynamic functions are applied for the study of thermal radiation of liquid and solid zirconium carbide. These functions are calculated using experimental data for the frequency dependence of the normal spectral emissivity in the visible and near-infrared range at the melting (freezing) point. The gaps between the thermal radiative and thermodynamic functions of liquid and solid zirconium carbide are observed. The general analytical expressions obtained can easily be presented in the wavenumber domain.

Chiral gravity waves and leptogenesis in inflationary models with non-Abelian gauge fields

We present a leptogenesis scenario associated with inflationary models involving non-Abelian gauge fields within the standard model of particle physics (SM). We show that this class of inflationary models generates intrinsic birefringent gravitational waves that through the gravitational chiral anomaly in SM, can naturally create a net lepton number density. The CP violating interaction is produced by tensor fluctuations of the gauge field, while the efficiency of this process is determined by the effective background value of the gauge field. We demonstrate that this mechanism can create the observed value of baryon to photon number density in a natural range of parameters of these models.

Asymptotic description of finite lifetime effects on the photon emission from a quark-gluon plasma

Direct photons play an important role as electromagnetic probes from the quark-gluon plasma (QGP) which occurs during ultrarelativistic heavy-ion collisions. In this context, it is of particular interest how the finite lifetime of the QGP affects the resulting photon production. Earlier investigations on this question were accompanied by a divergent contribution from the vacuum polarization and by the remaining contributions not being integrable in the ultraviolet (UV) domain. In this work, we provide a different approach in which we do not consider the photon number density at finite times, but for free asymptotic states obtained by switching the electromagnetic interaction according to the Gell-Mann and Low theorem. This procedure eliminates a possible unphysical contribution from the vacuum polarization and, moreover, renders the photon number density UV integrable. It is emphasized that the consideration of free asymptotic states is, indeed, crucial to obtain such physically reasonable results.

The photon detection operator and complementarity between an electric detector and a magnetic detector

It has been a long-standing problem that there is no consistent definition of the photon position operator or photon number density in the context of quantum theory. In this paper, we derive the photon detection operator, which defines the location of photon absorption, by applying the theory of indirect measurement to quantum electrodynamics. It is shown that the photon detection probability depends on the properties of a photon-absorbing atom, in particular, on both electric and magnetic dipole moments of the atom. An experiment is proposed in which the complementarity of wave–particle nature of light will be tested. It is also discussed that the complementarity is related to the non-commutativity of the electric and the magnetic fields. (When this work was presented at the conference CEWQO2013, it had the title ‘Photon position operators and complementarity between electric detector and magnetic detector’.)

On the radiative and thermodynamic properties of the cosmic radiations using COBE FIRAS instrument data: I. Cosmic microwave background radiation

Using the explicit form of the functions to describe the monopole and dipole spectra of the Cosmic Microwave Background (CMB) radiation, the exact expressions for the temperature dependences of the radiative and thermodynamic functions, such as the total radiation power per unit area, total energy density, number density of photons, Helmholtz free energy density, entropy density, heat capacity at constant volume, and pressure in the finite range of frequencies v1≤v≤v2 are obtained. Since the dependence of temperature upon the redshift z is known, the obtained expressions can be simply presented in z representation. Utilizing experimental data for the monopole and dipole spectra measured by the COBE FIRAS instrument in the 60–600 GHz frequency interval at the temperature T=2.72548 K, the values of the radiative and thermodynamic functions, as well as the radiation density constant a and the Stefan-Boltzmann constant σ are calculated. In the case of the dipole spectrum, the constants a and σ, and the radiative and thermodynamic properties of the CMB radiation are obtained using the mean amplitude Tamp=3.358 mK. It is shown that the Doppler shift leads to a renormalization of the radiation density constant a, the Stefan-Boltzmann constant σ, and the corresponding constants for the thermodynamic functions. The expressions for new astrophysical parameters, such as the entropy density/Boltzmann constant, and number density of CMB photons are obtained. The radiative and thermodynamic properties of the Cosmic Microwave Background radiation for the monopole and dipole spectra at redshift z≈1089 are calculated.

On the radiative and thermodynamic properties of the cosmic radiations using COBE FIRAS instrument data: II. Extragalactic far infrared background radiation

Using the three-component spectral model describing the FIRAS average continuum spectra, the analytical expressions for the temperature dependence of the thermodynamic and radiative functions of the galactic far-infrared radiation are obtained. The COBE FIRAS instrument data in the 0.15 - 2.88 THz frequency interval at the mean temperatures T = 17.72 K, T = 14 K, and T =6.73 K are used for calculating the radiative and thermodynamic functions, such as the total radiation power per unit area, total energy density, total emissivity, number density of photons, Helmholtz free energy density, entropy density, heat capacity at constant volume and pressure for the warm, intermediate-temperature and very cold components of the Galactic continuum spectra. The generalized Stefan-Boltzmann laws for the warm, intermediate-temperature and very cold components are constructed. This result is important when we construct the cosmological models of radiative transfer in the inner Galaxy. Within the framework of the three- component spectral model, the total number of photons in our Galaxy and the total radiation power (total luminosity) emitted from the surface of the Galaxy are calculated. Other radiative and thermodynamic properties of the galactic far-infrared radiation (photon gas) for the Galaxy are presented. The expressions for astrophysical parameters, such as the entropy density/Boltzmann constant, and number density of the galactic far-infrared photons are obtained. We assume that the obtained analytical expressions for thermodynamic and radiative functions may be useful for describing the continuum spectra of the far-infrared radiation for outer galaxies.

NON-RELATIVISTIC RADIATION MEDIATED SHOCK BREAKOUTS. III. SPECTRAL PROPERTIES OF SUPERNOVA SHOCK BREAKOUT

The spectrum of radiation emitted following shock breakout from a star's surface with a power-law density profile ρ∝xn is investigated. Assuming planar geometry, local Compton equilibrium, and bremsstrahlung emission as the dominant photon production mechanism, numerical solutions are obtained for the photon number density and temperature profiles as a function of time for hydrogen–helium envelopes. The temperature solutions are determined by the breakout shock velocity v0 and the pre-shock breakout density ρ0 and depend weakly on the value of n. Fitting formulae for the peak surface temperature at breakout as a function of v0 and ρ0 are provided, with , and the time dependence of the surface temperature is tabulated. The time integrated emitted spectrum is a robust prediction of the model, determined by and v0 alone and insensitive to details of light travel time or slight deviations from spherical symmetry. Adopting commonly assumed progenitor parameters, breakout luminosities of ≈1045 erg s−1 and ≈1044 erg s−1 in the 0.3–10 keV band are expected for blue supergiant (BSG) and red supergiant (RSG)/He-WR progenitors, respectively ( is well below the band for RSGs, unless their radius is ∼1013 cm). >30 detections of SN 1987A-like (BSG) breakouts are expected over the lifetime of ROSAT and XMM-Newton. An absence of such detections would imply either that the typical parameters assumed for BSG progenitors are grossly incorrect or that their envelopes are not hydrostatic. The observed spectrum and duration of XRF 080109/SN 2008D are in tension with a non-relativistic breakout from a stellar surface interpretation.