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We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which are dual objects to dessins d'enfant. Furthermore, we give a proof of the quantum spectral curve equation for this pr ...
We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H ...
Why are classical theories often sufficient to describe the physics of our world even though everything around us is entirely composed of microscopic quantum systems? The boundary between these two fundamentally dissimilar theories remains an unsolved prob ...
The philosophy of "X-Mechanics" is introduced, and a few examples of its application by the author and collaborators to study "Y-Mechanics" problems are presented. ...
Due to their very nature, ultrafast phenomena are often accompanied by the occurrence of nonadiabatic effects. From a theoretical perspective, the treatment of nonadiabatic processes makes it necessary to go beyond the (quasi) static picture provided by th ...
After their formation, mountainous landscapes gradually evolve toward smoother geometries controlled by the interplay of erosion and sedimentation. The statistical mechanical properties of this process and the link between topography and geology have remai ...
One of the most prominent consequences of the quantum nature of light atomic nuclei is that their kinetic energy does not follow a Maxwell-Boltzmann distribution. Deep inelastic neutron scattering (DINS) experiments can measure this effect. Thus, the nucle ...
Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear ...
Nuclear quantum effects influence the structure and dynamics of hydrogen-bonded systems, such as water, which impacts their observed properties with widely varying magnitudes. This review highlights the recent significant developments in the experiment, th ...
Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of th ...
