Combinatorics of loop equations for branched covers of sphere
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Since their discovery in 1927, the Heisenberg Inequalities have become an icon of quantum mechanics. Often inappropriately referred to as the Uncertainty Principle, these inequalities relating the standard deviations of the position and momentum observable ...
Simulating the exact quantum dynamics of realistic interacting systems is presently a task beyond reach but for the smallest of them, as the numerical cost for solving the time-dependent Schrodinger equation scales exponentially with the number of degrees ...
In 1906, Theodore Lyman discovered his eponymous series of transitions in the extreme-ultraviolet region of the atomic hydrogen spectrum(1,2). The patterns in the hydrogen spectrum helped to establish the emerging theory of quantum mechanics, which we now ...
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 ...
Traditional simulated annealing uses thermal fluctuations for convergence in optimization problems. Quantum tunneling provides a different mechanism for moving between states, with the potential for reduced time scales and different outcomes. Thermal and q ...
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and its applications, suc ...
The electronic configuration of the molecule is the foundation of its structure and reactivity. The spin state is one of the key characteristics arising from the ordering of electrons within the molecule’s set of orbitals. Organic molecules that have open-s ...
This is an overview of a program of stochastic deformation of the mathematical tools of classical mechanics, in the Lagrangian and Hamiltonian approaches. It can also be regarded as a stochastic version of Geometric Mechanics.The main idea is to construct ...
A rigorous quantum description of molecular dynamics with a particular emphasis on internal observables is developed accounting explicitly for kinetic couplings between nuclei and electrons. Rotational modes are treated in a genuinely quantum framework by ...
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 ...
