A classical mechanics technique for quantum linear response

A method for classical and quantum mechanics

In many physical problems it is not possible to find an exact solution. However, when some parameter in the problem is small, one can obtain an approximate solution by expanding in this parameter. This is the basis of perturbative methods, which have been applied and developed practically in all areas of Physics. Unfortunately many interesting problems in Physics are of non-perturbative nature ...

Continuum mechanics for quantum many-body systems: Linear response regime

We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave function. By describing the many-body system in terms of a single collective field we provide an alternative to traditional approaches, which emphasize one-partic...

Classical Limit of Quantum Mechanics

para o valor esperado de uma dada observável fı́sica A = A(p, q, t) representada pelo operador Â. As equações (1) e (2) são válidas desde que o potencial externo V varie vagarosamente dentro de um pacote de onda bem localizadoψPE (Pacote de Ehrenfest). Assim, de acordo com os livros-texto [1], as equações de Newton são obtidas como limite clássico da equação de Schrödinger. No entanto, Ballentin...

Mixing Quantum and Classical Mechanics

Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket is antisymmetric and satisfies the Jacobi identity, and, therefore, leads to a natural description of interaction between quantum and classical degrees of f...

Classical models of quantum mechanics