A matrix model is constructed which describes a chiral version of the large N U (N ) gauge theory on a two-dimensional sphere of area A. This theory has three separate phases. The large area phase describes the associated chiral string theory. An exact expression for the free energy in the large area phase is used to derive a remarkably simple formula for the number of topologically inequivalent covering maps of a sphere with fixed branch points and degree n.
We use a modified Thomas-Fermi approximation to estimate analytically the critical velocity for the formation of vortices in harmonically trapped BEC. We compare this analytical estimate to numerical calculations and to recent experiments on trapped alkali condensates.
exchange of energy between excitons and photons is faster than any loss process. The momentum-energy dispersions of cavity polaritons are characterized by anticrossing of the exciton and cavity dispersions consisting of an upper-polariton (UP) branch (UPB) and a lower-polariton (LP) branch (LPB), with the minimal energy separation between UPB and LPB at the anticrossing point referred as the vacuum Rabi splitting energy (ℏΩ R ). [1] Due to the large oscillator strength and binding energy of organic materials, organic cavity polaritons exhibit large ℏΩ R even at room temperature. [2][3][4] When ℏΩ R is comparable (20%) to the uncoupled exciton energy (E Ex ), the system is characterized by the ultrastrong coupling (USC) regime, where the rotating wave approximation (RWA) is no longer applicable, and the antiresonant exciton-photon coupling terms can significantly modify cavity-polariton properties. [5][6][7][8] The hybrid light-matter characteristics of both single and multiple cavity polaritons are of significant theoretical and practical importance, such as organic light-emitting diodes (LEDs), [9,10] roomtemperature polariton condensation and lasing, [11][12][13] polaritonmediated energy transfer, [14][15][16] conductivity enhancement, [17,18] and superfluidity. [19] However, nonlinear optical processes, such as the optical Kerr effect and optical harmonic generation, arising from cavity polaritons in organic materials are now beginning to receive attention. Importantly, optical harmonic spectral dispersion measurements, which are widely used to study the excited states of organic molecular materials, [20,21] can be utilized to study the intrinsic nonlinearity of the hybrid light-matter system. Recently, the enhancement of resonant second-harmonic generation (SHG) of the lower polariton is reported from strongly coupled organic crystalline nanofiber microcavities, where the SHG wavelength is resonant with the lower polariton. [22] Also, the enhanced third-harmonic generation (THG) was observed from cavity polaritons in the ultrastrong coupling regime when the pump wavelength is resonant with the lower polariton. [23] Here, we experimentally and theoretically demonstrate the dispersion of the upper-polariton-enhanced THG using anglevarying reflection configuration in the ultrastrong coupling regime, and observe the THG intensity is largest when the THG wavelength is resonant with the upper polariton, in contrast to Organic cavity polaritons are bosonic quasiparticles arising from the strong interaction between organic molecular excitons and photons within microcavities. The spectral dispersion of third-harmonic generation near resonance with cavity polaritons is studied experimentally via angle-resolved reflected third-harmonic generation measurements with several pump wavelengths. Moreover, a three-step nonlinear optical transfer matrix model is used to simulate the third-harmonic generation using the sum-overstates dispersive nonlinear coefficients, which include polariton states. The angle-dependent experimen...
We compute the metrics of the [Formula: see text] and [Formula: see text], characterize their geometry and explore the “duality” k1=k2 of the target space. In particular limits of the ratio k1/k2 the latter coset becomes [Formula: see text] where k is either k1 or k2. This analysis is a starting point for investigating some properties of three-dimensional stringy gravity.
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