Von Neumann equations with time-dependent Hamiltonians and supersymmetric quantum mechanics

Details Von Neumann equations with time-dependent Hamiltonians and supersymmetric quantum mechanics Von Neumann equations with time-dependent Hamiltonians and supersymmetric quantum mechanics

1999-07-17

arxiv.org/abs/quant-ph/9907059v1

Phys.Rev.E61:3325-3329,2000

Physics

Quantum Physics

revtex, 3 eps files

Scientific paper

10.1103/PhysRevE.61.3325

Starting with a time-independent Hamiltonian $h$ and an appropriately chosen solution of the von Neumann equation $i\dot\rho(t)=[ h,\rho(t)]$ we construct its binary-Darboux partner $h_1(t)$ and an exact scattering solution of $i\dot\rho_1(t)=[h_1(t),\rho_1(t)]$ where $h_1(t)$ is time-dependent and not isospectral to $h$. The method is analogous to supersymmetric quantum mechanics but is based on a different version of a Darboux transformation. We illustrate the technique by the example where $h$ corresponds to a 1-D harmonic oscillator. The resulting $h_1(t)$ represents a scattering of a soliton-like pulse on a three-level system.

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