On the Theory of Shifts and Broadening of Electronic Spectra of Polar Solutes in Polar Media

When a polar‐solute molecule undergoes an electronic transition and forms a state of different polarity, the Franck—Condon principle shows that the new system is first formed in a nonequilibrium thermodynamic state. An expression for the spectral shift and broadening by a series of solvents of differing polarity is derived in the present paper in terms of thermodynamic properties of certain equilibrium distribution systems. For this purpose use is made of a recent particle description of nonequilibrium and equilibrium polar media, which emphasizes functional dependence and avoids, thereby, the usual more specific assumptions. A relation between the broadening and the shift is then deduced under certain conditions. Expressions are also derived for the effect of pressure and temperature on the shift, in terms of the polar contribution to the volume and entropy of solvation, respectively, and for the influence of applied electrical fields. An expression is obtained for the solvent‐reversal shift of Brooker in terms of the polarizability difference of the initial and final states of the solute. Introduction of more specific assumptions is then made for purposes of comparison with earlier works, which constitute special cases of the present one, and for estimation of dipole moments and polarizabilities of excited states from spectral and electrical shifts

On the space of elliptic genera

Invariance under modular transformations and spectral flow restrict the possible spectra of superconformal field theories (SCFT). This paper presents a technique to calculate the number of constraints on the polar spectra of N=(2,2) and N=(4,0) SCFT's by analyzing the elliptic genus. The polar spectrum corresponds to the principal part of a Laurent expansion derived from the elliptic genus. From the point of view of the AdS_3/CFT_2 correspondence, these are the states which lie below the cosmic censorship bound in classical gravity. The dimension of the space of elliptic genera is obtained as the number of coefficients of the principal part minus the number of constraints. As an additional illustration of the technique, the constraints on the spectrum of N=4 topologically twisted Yang-Mills on CP^2 are discussed.Comment: 31 pages, published versio

An electric charge has no screw sense--a comment on the twistfree formulation of electrodynamics by da Rocha & Rodrigues

Da Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and superfluous, and (ii) that they can derive the Lorentz force equation from Maxwell's equations. As to (i), we point out that the distinction of polar/axial and twisted/untwisted derives from the property of the electric charge of being a pure scalar, that is, not carrying any screw sense. Therefore, the mentioned distinctions are necessary ingredients in any fundamental theory of electrodynamics. If one restricted the allowed coordinate transformations to those with positive Jacobian determinants (or prescribed an equivalent constraint), then the RR scheme could be accommodated; however, such a restriction is illegal since electrodynamics is, in fact, also covariant under transformations with negative Jacobians. As to (ii), the "derivation" of the Lorentz force from Maxwell's equations, we point out that RR forgot to give the symbol F (the field strength) in Maxwell's equations an operational meaning in the first place. Thus, their proof is empty. Summing up: the approach of RR does not bring in any new insight into the structure of electrodynamics.Comment: Added answer to da Rocha & Rodrigues arXiv:0912.212

Basic differential forms for actions of Lie groups

A section of a Riemannian $G$-manifold $M$ is a closed submanifold $\Sigma$ which meets each orbit orthogonally. It is shown that the algebra of $G$-invariant differential forms on $M$ which are horizontal in the sense that they kill every vector which is tangent to some orbit, is isomorphic to the algebra of those differential forms on $\Sigma$ which are invariant with respect to the generalized Weyl group of this orbit, under some condition.Comment: 10 pages, ESI Preprint 87, AmSTe

Investigating nano-structuring within imidazolium ionic liquids: A thermodynamic study using photochromic molecular probes

Following previous studies involving the thermal relaxation of spirocyclic compounds we extended our studies to investigate the formation of nano-structured domains in ionic liquids (ILs). Two compounds, spiropyran (BSP) and spirooxazine (SO) were added to imidazolium cation based ionic liquids with increasing chain lenghts (C2 –C12). Increasing side-chain length was found to have only minor effects on the rate of thermal relaxation of BSP and SO. BSP was found to be a suitable probe molecule as linear correlations in parameters were observed for this compound. This is believed to be due to the fact that BSP-IL interactions were based on hydrogen bonding between MCBSP and the cation compared to MCSO which is limited to electrostatic interactions thus enhancing the sensitivity of MCBSP to the charged polar regions. Increasing the side-chain of the cation resulted in slight increases in MC-BSP activation energy from 96.93 kJ.mol-1 in [C4mIm][NTf2] to 105.27 kJ.mol-1 in [C12mIm][NTf2]. MC-BSP S‡ and H‡ values also increased with increasing side-chain. Expansion and dispersion of polar regions due to increasing non-polar interactions may be enhanced by introduction of the bulky probe molecule. The resulting reorganisation of the system produced positive entropies of activation, 13.79 J.K- 1.mol-1 for C4mIm to 46.15 J.K-1.mol-1 for C12mIm, following an increase in disorder due to probe dye closure from MC to BSP and migration of dye to regions of preferential solvation. The ability for spirocyclic compounds to form both polar and non-polar isomers resulted in the ability to analyse both solvent regions using a single probe dye. Ground state equilibrium, Ke, examined non-polar regions of the IL while equilibrium of activation, K‡, examined the polar regions. A linear response to side chain length to equilibrium of activation was believed to be due to the fact that polar regions were possibly expanding due to increasing influence of non-polar side chain interactions upon the over solvent structure. The result of such reordering and dispersion of polar regions reduces solvent-solute interactions which increases rate of MC-BSP relaxation

A study of magnetic storms and auroras

New notations for magnetic disturbance fields are proposed, based on the theoretical consideration of the electric current systems by which they are produced. A typical magnetic storm begins suddenly when the onrush of the front of the solar gas is halted by the earth's magnetic field. This effect (DCF field) is most markedly observed as a sudden increase of the horizontal component of the earth's field (the storm sudden commencement, abbreviated to ssc)— like a step function. In many cases, however, the change of the field during the ssc is more complicated, and different at different places. Such a complexity superposed on the simple increase (DCF) is ascribed to a complicated current system generated in the polar ionosphere (DP current). It is found that the changes of electromagnetic conditions in the polar regions are communicated, without delay, to lower latitudes, even down to the equatorial regions. It is inferred that the equatorial jet is affected by such a change and produces the abnormal enhancement of ssc along the magnetic dip equator. From the extensive analysis of several magnetic storms that occurred during the IGY and IGC, it is suggested that the capture of the solar particles in the outer geomagnetic field occurs when irregularities (containing tangled magnetic fields and high energy protons) embedded in the solar stream, impinge on the earth.. Thus the development of a magnetic storm depends on the distribution of such irregularities in the stream. The motions and resulting currents and magnetic fields of such "trapped" solar particles are studied in detail for a special model. It is inferred that a large decrease (DR field) must follow the initial increase; it is ascribed to the ring current produced by such motion of solar protons oi energy of order 500 Kev. It is proposed that during the storm there appears a transient 'storm-time1 belt well outside the outer radiation belt. It is predicted that the earth's magnetic field is reversed in limited regions when the ring current is appreciably enhanced. This involves the formation of neutral lines there. These may be of two kinds, called X lines or 0 lines according as they are crossed or encircled by magnetic lines of force. These may be entirely separated or may be joined to form a loop, called an OX loop. It is shown that one of them, the X line, which is connected with the auroral ionosphere by the lines of force, could be the proximate source of th<e particles that produce the aurora polaris. By postulating the existence of such X-type neutral lines at about 6 earth radii, an explanation is obtained of the detailed morphology of the aurora. This includes the auroral zones and their changes, the nighttime peak occurrence of auroras, their thin ribbon-like structure and their multiplicity, their diffuse and active forms and the transition between them (break-up) the required electron and proton flux, and the ray and wavy structures. Among the most important phenomena associated with the sudden change of the aurora from the diffuse to the active form are the simultaneous appearance of the auroral electrojet and the resulting polar magnetic disturbances (DP sub-storms). Several typical DP sub-storms are studied in detail. It is concluded that a westward auroral jet is produced by a southward electric field. It is shown that an instability of the sheetbeam issuing from along the X-type neutral line can produce a southward electric field of the required intensity. The southward electric field produces an eastward motion of the electrons in the ionosphere. This may be identified with the eastward motion of an active aurora and with the westward auroral electrojet. Besides such large changes- of the field, there often appear various quasi-sinusoidal changes of the field, much less intense. They are supposed to be hydromagnetic waves, some of which are generated in the outer atmosphere and propagated through the ionosphere, where a certain amount of their energy is dissipated. It is concluded however that Such a dissipation is not sufficient to produce any appreciable heating of the ionosphere.Chapter I The electromagnetic environment of the earth : The solar system in the Galaxy ; The sun and the interplanetary space ; The outer atmosphere, the Van Allen radiation belts and the ionosphere ; The earth’s permanent magnetic field ; Introduction to geomagnetic storms and auroras ; The analysis of the earth’s magnetic field – Chapter II The sudden commencement of magnetic storms : Introduction ; The studies of Sc and Si at individual observations ; A theory of the Sc of magnetic storms ; Transmission of the Sc from the inner boundary of the solar steam to the earth’s surface ; The sudden commencement DP currents – Chapter III The ring current and the van allen radiation belts : Introduction ; The motion of charged particles in the earth’s dipole magnetic field ; Electric currents in an ionized gas (general formulae) ; The steady ring current in a dipole field ; The magnetic field produced by the ring current ; The main phase of magnetic storms ; The ring current belt ; Discussion – Chapter IV A neural line discharge theory of the aurora Polaris : Introduction ; The formation of a neutral line ; The motions of charged particles close to a neutral line ; The auroral zones ; Particle injection associated with arcs ; Rayed arcs ; Instabilities of auroras – Chapter V Polar magnetic disturbances : Introduction ; The polar magnetic disturbances of 5 to 6 December 1958 (College, Alaska) ; The polar magnetic disturbances of 29 September 1957 (Worldwide) ; The polar magnetic disturbances of 23 September 1957 ; The eastward motion of auroras and the electric field of polar magnetic disturbances ; The origin of the electric field of polarmagnetic disturbances – Chapter VI Hydromagnetic waves in the ionosphere : Introduction ; Ionospheric heating by hydromagnetic waves connected with geomagnetic micropulsations – Acknowledgements -- ReferencesYe