Continuous solutions for balance laws

Abstract The paper employs the method of characteristics to show that continuous solutions of scalar conservation laws do not incur entropy production and to recover, in a direct and elementary way the (known) properties of solutions to the Hunter-Saxton equation. Keywords: Balance laws, Characteristics, Hunter-Saxton equation Mathematics Subject Classification (2000): 35L65, 35Q58     

Dancy Cartwright: Particularism in the philosophy of science

This paper aims to explore the space of possible particularistic approaches to Philosophy of Science by examining the differences and similarities between Jonathan Dancy’s moral particularism—as expressed in both his earlier writings (e.g., Moral Reasons, 1993), and, more explicitly defended in his book Ethics without Principles (2004)—and Nancy Cartwright’s particularism in the philosophy of science, as defended in her early collection of essays, How the Laws of Physics Lie (1983), and her later book, The Dappled World: A Study of the Boundaries of Science (1999). I shall argue that Dancy’s particularism is more radical, but also more plausible, than Cartwright’s, concluding that we have good reason to embrace a scientific particularism that is far closer to Dancy’s ethical particularism than any view defended by Nancy Cartwright, or any other philosopher from the ‘Stanford school’ of scientific theory.     

Low-frequency stimulated emission and induced absorption in a three-level atom

We consider the excitation spectra of a bichromatically driven three-level atom in the lambda configuration and in the low-frequency domain. These dynamically induced spectra occur when the excitation fields operate at low intensities and are neither one- nor two-photon resonant with the various transitions of the system.     

Dopant-enhanced ablation of nitrocellulose by a nitrogen laser

The photoetching behavior of pure nitrocellulose and of nitrocellulose dyed with stilbene-420, coumarin-120 and rhodamine 6G by 337 nm nitrogen laser pulses has been studied. Ablation with a low power nitrogen laser is hereby reported for the first time. A two step photochemical mechanism is proposed to account for the ablation of the pure material. With the addition of dyes strongly absorbing at 337 nm the photoetching rate of nitrocellulose can be increased significantly. This increase is proportional to the molar extinction coefficient of the dye at 337 nm and its concentration in the polymer. The photoetching mechanism and the energy transfer processes from the dye to the polymer are discussed in detail.     

Quantum beats in two-photon resonance fluorescence

The two-photon resonance fluorescence spectrum of a three-level atom is shown to consist of the low frequency modes in addition to the high frequency ones in the limit of high photon densities. The spectral function for the low frequency modes consists of two lorentzian lines describing: the peak occuring at the renormalized beat frequency Δ₊ and that of the zero-photon excitation at the frequency Δ_-, where Δ_±=Δ-3Ω²/2ω_a±Ω²u/2ω_a, u²=1+(2Δω_a/Ω ²)². Here, 2Δ is the energy splitting between the two excited states, ω_a is the photon energy of the pump field and Ω is the Rabi frequency. The peak at the renormalized beat frequency Δ₊ occurs provided that the condition (2Δω_a/Ω²)² > 1 is satisfied. The two-photon laser spectroscopy is expected to be a useful tool for the observation of the low frequency modes in question.     

Cooperative and interference effects in the resonance fluorescence of two identical three-level atoms at high photon densities

The excitation spectrum of two identical three-level atoms is considered when a strong electromagnetic field operates resonantly between two levels of the atoms. While undergoing the transition into the excited state, the atoms interact through their dipole-dipole interaction and radiate to each other as well, and subsequently, they decay radiatively into another excited state. For such a system, the spectral functions are calculated describing the cooperative and interference spectra for the symmetric and antisymmetric modes arising from the decay of the atoms from one excited state into another. In the absence of the pump field, the spectral function for the symmetric modes consists of two peaks, which are described by Lorentzian lines peaked at the frequencies ω = ω₂₃ + V_AB and ω = ω₂₃ ? V_AB and having spectral widths of the order of γ⁰₂₁ + γ⁰₂₃ and γ⁰₂₃, respectively, where ω₂₃ is the transition frequency between the two excited states, V_AB is the dipole-dipole interaction and $\text{1}\text{2}\text{γ}{}^0{}_{21}$ is the natural width for a photon spontaneously emitted from the 2 → 1 transition of an isolated atom. The splitting of the central peak for the transition in question and the broadening of the spectral widths are due entirely to the dipole-dipole and radiative interactions between the atoms. The spectral function for the antisymmetric modes describes a stable mode at the frequency ω = ω₂₃ ? V_AB, which has a delta-function distribution, and a Lorentzian line peaked at the frequency ω = ω₂₃ + V_AB and has a spectral width of the order of γ⁰₂₁. In the presence of the pump field, the spectral function for the symmetric modes contains, in addition to the central peaks, two pairs of sidebands, one pair of which is induced by the pump field with an energy shift equal to $\text{Ω}{}_{\mathrm{<mtext>a</mtext>}}\text{/√2}$, while the other pair of sidebands is due to the dipole-dipole interaction between the atoms; the probability of occurrence of the latter pair of sidebands is proportional to $\text{V}{}_{\mathrm{AB}}\text{/Ω}{}_{\mathrm{<mtext>a</mtext>}}$, while the induced energy shift is equal to $\text{3Ω}{}_{\mathrm{<mtext>a</mtext>}}\text{/√2}$, where $\text{√2Ω}{}_{\mathrm{<mtext>a</mtext>}}$ is the induced by the laser field energy shift (Rabi frequency) for a single two-level atom. The spectral widths for both pairs of sidebands are of the order of γ⁰₂₁ + γ⁰₂₃. The excitation spectrum of the antisymmetric modes consists of, in addition to the central peaks, a pair of stable sidebands, which have delta-function distributions, and two pairs of sidebands, which are similar but sharper than those for the symmetric modes. Detail comparisons are given between the one- and two-atom excitation spectra for the systems under investigation.     

Stimulated emission at the sum-frequency generation of a bichromatic field interacting with a three-level atom

The Maximum-Entropy formalism is used to obtain approximations to the spherically averaged charge and momentum densities. The only information required is the first few radial expectation values. Analytical and numerical approximations to the central values of the densities are calculated. Moreover, the unused or unknown radial expectation values are estimated by means of the moments of these Maximum-Entropy densities. As illustration, the accuracy of these approximations are numerically studied in a Hartree-Fock framework. This method is complementary to the one which makes use of the Stieltjes-Chebyshev inequalities and leads to the least biased approximate densities compatible with the information we use.     

One- and two-photon resonance fluorescence of a three-level atom at high photon densities

We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.