This paper is devoted to the theory of quantum electromagnetic field in an optically dense medium. Self-consistent equations describing interaction between a quantum field and a quantum dielectric medium are obtained from the first principles, i.e., outside a phenomenological description. Using these equations, we found a transformation (of the Bogoliubov transformation type) that converts the operators of the "vacuum" field into operators of collective perturbations of the field and an ensemble of atoms, that is, photons in the medium. Transformation parameter is the refractive index of the wave mode considered. It is shown that besides the energy of the collective electromagnetic field, the energy of photons in the medium includes the energy of the internal degrees of freedom of the substance and the energy of near-field dipole interaction between atoms in the polarized medium. The concept of negative energy photons is introduced on the basis of self-consistent equations.Keywords: Optically dense medium, quantum field, Bogoliubov transformation, photons in the medium 2 cuum). For example, for the medium with polarizability and refractive index 4 1 2 2 n ck the result obtained within this approach corresponds to the approximation of small optical density, 12 n . Despite the obvious constraints, this approach can be very effective. The point is that the approximation of small optical depth, i.e., the assumption that 11 n in a fairly narrow frequency band, does not contradict, in principle, the condition of strong frequency dispersion, 1 n . As an example, we mention the effect of electromagnetically induced transparency (EIT) [24][25][26][27]: which suggests that within the "transparency window" there is a frequency range in which a small group velocity is combined with an almost "vacuum" phase velocity. However, in general (including some of the EIT modes, see [26,27]), the constraint 11 n is awkward. To our knowledge, the analysis which is free of both the constraints of the phenomenological approach and the small optical density approximation, was carried out only in terms of a two-level model [5,[28][29][30].This paper is devoted to the development of the theory of quantum field in a medium with an arbitrary optical density and an arbitrary energy-level structure. Selecting as the initial model an ensemble of atoms interacting through a collective field, we came to fairly universal operator equations of quantum electrodynamics of a dielectric medium without spatial dispersion. Using these equations, it was found that the exact dispersion relation k for photons in the medium corresponds to the quanta of collective excitations of the field and the medium, and the energy k of a quantum includes the energy of the macroscopic field, the energy of the internal degrees of freedom, and the energy of the near-field dipole interaction in the polarized medium. It is shown that the operators of creation and annihilation the photon in the medium are related with t...
Ultracompact nonlinear optical devices utilizing two-dimensional (2D) materials and nanostructures are emerging as important elements of photonic circuits. Integration of the nonlinear material into a subwavelength cavity or waveguide leads to a strong Purcell enhancement of the nonlinear processes and compensates for a small interaction volume. The generic feature of such devices which makes them especially challenging for analysis is strong dissipation of both the nonlinear polarization and highly confined modes of a subwavelength cavity. Here we solve a quantum-electrodynamic problem of the spontaneous and stimulated parametric down-conversion in a nonlinear quasi-2D waveguide or cavity. We develop a rigorous Heisenberg-Langevin approach which includes dissipation and fluctuations in the electron ensemble and in the electromagnetic field of a cavity on equal footing. Within a relatively simple model, we take into account the nonlinear coupling of the quantized cavity modes, their interaction with a dissipative reservoir and the outside world, amplification of thermal noise and zero-point fluctuations of the electromagnetic field, and other relevant effects. We derive closed-form analytic results for relevant quantities such as the spontaneous parametric signal power and the threshold for parametric instability. We find a strong reduction in the parametric instability threshold for 2D nonlinear materials in a subwavelength cavity and provide a comparison with conventional nonlinear photonic devices. arXiv:1801.07227v2 [physics.optics]
<p>We investigate the Middle Pleistocene Transition (MPT) - a rapid change in the periodicity of the Pleistocene glacial cycles&#160;from 41 kyr to about 100 kyr, which occurred about a million years ago - using the data-driven model [1]. Here we estimate stability of the model using a novel concept of interval stability [2-4], referring to the behavior of the perturbed model during a finite time interval. In a few words we define the class of 'safe' perturbations after which the system (our data-driven model) returns back to the initial dynamical regime and 'unsafe' perturbation of minimal amplitude needed to disrupt the system.</p><p>We demonstrate that the MPT is likely associated with decreasing of the climate system's interval stability to rapid disturbances (millennial and shorter). This confirms the statement made in the paper [1] that the main factor in the onset of the long-period glacial cycles is strongly nonlinear oscillations induced by the short-scale variability.</p><ol><li>D. Mukhin, A. Gavrilov, E. Loskutov, J. Kurths, A. Feigin. Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition. Scientific Reports, 9 7328 (2019).</li> <li>P. Menck, J. Heitzig, N. Marwan, J. Kurths. How basin stability complements the linear-stability paradigm. Nature Phys, 9 89&#8211;92 (2013).</li> <li>V. Klinshov, V. Nekorkin, J. Kurths. Stability threshold approach for complex dynamical systems. New Journal Physics, 18 013004 (2016).</li> <li>V. Klinshov, S. Kirillov, J. Kurths, V. Nekorkin. Interval stability for complex systems. New Journal Physics, 18 013004 (2018).</li> </ol>
<p>The global climate system is an aggregate of a huge number of interacting components, each having an intrinsic time scale. Such a complex dynamical system demonstrates nontrivial behavior and can exhibit a variety of possible modes of evolution. Gradual change of the parameters of the global climate system can lead to transitions (e.g., the Mid-Pleistocene Transition or to abrupt climate changes) from the observed to a new mode.<br>In this work, we investigate the stability of the global climate system against strong sudden perturbations in the last 2.5 million years. This case is fundamentally different from the small perturbations case: in particularly, the system response cannot be described by a linearized evolution operator. To estimate the climate system&#8217;s nonlinear stability during the last 2.5 million years, we use a nonlinear data-driven model of climate dynamics in Pleistocene [1] and basin stability criterion [2]. Our results indicate that the stabilityof the Pleistocene climate to large perturbations decreases with time: past climates being much more stable compared to the present one.<br>This work was supported by RFBR grant 19-02-00502.</p><p>1. D. Mukhin, A. Gavrilov, E. Loskutov, J. Kurths, A. Feigin. &#8220;Bayesian Data Analysis for Revealing Causes of the Middle Pleistocene Transition&#8221;. ScientificReports, 9 7328 (2019).<br>2. V. Klinshov, S. Kirillov, J. Kurths, V. Nekorkin. &#8220;Interval stability for complex systems&#8221;. New Journal of Physics, v. 20, p. 043040.</p>
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