![]() ![]() For example, any thermal emitter is fundamentally characterized by two key quantities: the angular spectral absorptivity \(\alpha \left(\omega ,-\widehat\right).\) Conversely, breaking these symmetries can remove such constraints. These symmetries have important implications for thermal radiation. The non-geometric symmetries include reciprocity, energy conservation, and time-reversal symmetry, which are invariance under the corresponding internal transformations of linear photonic systems. The geometric symmetries refer to the invariance of the system, including both the thermal emitter and its environment, under the usual spatial transformation such as rotation, reflection, and inversion. In this context, the relevant symmetries include the geometric and non-geometric ones. Symmetries also play an important role in thermal radiation. For example, the temporal translation symmetry gives rise to the conservation of energy. The continuous symmetries of a physical system are intimately related to the conservation laws characterizing that system. Continuous symmetries are described by Lie groups while discrete symmetries are described by finite groups. Symmetries are mathematically described by groups. The transformations may be continuous or discrete, which give rise to the corresponding types of symmetries. ![]() A symmetry of a physical system is a physical feature that remains invariant under some transformation. Symmetries are of fundamental importance in physics. Several review papers have comprehensively overviewed the field of thermal photonics, specifically the radiative heat transfer in near-field and far-field. Fruitful achievements propel the development of thermal photonics which improves energy utilization efficiency and revolutionizes many energy applications. Narrowband, directional, or polarized thermal emissions are all proposed and experimentally demonstrated using metamaterials. Thanks to the rapid development of nanophotonics, researchers demonstrated that thermal emission, similar to spontaneous emission of light, can be engineered or manipulated with the use of artificial or naturally occurring micro/nanostructures. In conventional systems, thermal emission tends to be broadband, incoherent, omnidirectional, and unpolarized, due to fluctuating electromagnetic fields thermally generated inside materials. ![]() The second law of thermodynamics governs the irreversibility of energy transfer in thermal emission. Planck’s law characterizes the spectral distribution of emitted power. In physics, thermal emission originates from electromagnetic radiation induced by the thermal motion of charged particles inside materials. Any object with a temperature above absolute zero exchanges thermal energy with the environment. A general group-theoretic description of this method is developed using the technique of harmonic expansions on the phase space.Radiative heat transfer is a ubiquitous physical process in our universe. In particular, we consider the reconstruction method based on measurements of displaced projectors, which comprises a number of recently proposed quantum-optical schemes and is also related to the standard methods of signal processing. The phase-space formalism is used to study the problem of the reconstruction of quantum states. The symbol calculus for the phase-space functions is given by means of the generalized twisted product. The concept of generalized coherent states and the method of harmonic analysis are used to construct explicitly a family of phase-space functions which are postulated to satisfy the Stratonovich-Weyl correspondence with a generalized tracing condition. This theory provides a unified phase-space formulation of quantum mechanics for physical systems possessing Lie-group symmetries. We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors. ![]()
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