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Combinatorics of Loop Equations for Branched Covers of Sphere

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Path integral approach to the quantum fidelity amplitude

Jiri Vanicek

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 ...

Royal Soc2016

Quantum description of a rotating and vibrating molecule

Jean-Philippe Ansermet, Sylvain Bréchet, François Reuse, Klaus Maschke

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 ...

Springer Verlag2015

An introduction to the problem of bridging quantum and classical dynamics

Sara Bonella

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 ...

Springer Heidelberg2015

Rotational Heisenberg Inequalities

Jean-Philippe Ansermet, Sylvain Bréchet, François Reuse, Klaus Maschke

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 ...

EDP Sciences2015

Combinatorics of loop equations for branched covers of sphere

Nicolas Gerson Orantin

We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which in a certain way generalize the notion of dessins d'enfant. Furthermore, we give a proof of the quantum spectral curv ...

2014

The research program of Stochastic Deformation (with a view toward Geometric Mechanics)

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 ...

2012

PT-Symmetric Periodic Optical Potentials

In quantum theory, any Hamiltonian describing a physical system is mathematically represented by a self-adjoint linear operator to ensure the reality of the associated observables. In an attempt to extend quantum mechanics into the complex domain, it was r ...

Springer US2011

The quantum mechanics of perfect fluids

Riccardo Rattazzi, Solomon G Shamsuddin Osman Endlich

We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vo ...

2011

Controlling Biological Functions

Majed Chergui

A review. Manipulation of the quantum properties of matter can influence the course of biochem. reactions. Can biol. functions, such as vision or photosynthesis, that are driven by incoherent phenomena have anything to do with quantum mechanics, where the ...

2006

Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions

Jiri Vanicek

Due to the Heisenberg uncertainty principle, various classical systems differing only on the scale smaller than Planck's cell correspond to the same quantum system. We use this fact to find a unique semiclassical representation without the Van Vleck determ ...

2004