A Quantum Crystal with Multidimensional Anharmonic Oscillators

Alexander V. Turbiner, Juan Carlos del Valle Rosales

Yuri V. Kozitsky, Yurij V. Holovatch, Bertrand Berche +2 more

For a system of interacting quantum anharmonic (double‐welled) oscillators (quantum anharmonic crystal), it is shown that a phase transition can cause the equilibrium dynamics of a given oscillator to be reducible. This means that the oscillator prefers one of the wells. Sufficient conditions for this effect to occur at some temperature, or not to occur at all temperatures, are presented.

Uniwersytet Marii

Konstantin E. Dorfman, Shaul Mukamel

Abstract Coherent multidimensional optical spectroscopy is broadly applied across the electromagnetic spectrum ranging from NMR to UV. These techniques reveal the properties of matter through the correlation plots of signal fields generated in response to sequences of short pulses with variable delays. Here we discuss a new class of multidimensional techniques obtained by the time-and-frequency-resolved photon coincidence counting measurements of N photons, which constitute a 2 N dimensional spectrum. A compact description of these signals is developed based on time-ordered superoperators rather than the normally ordered ordinary operators used in Glauber's photon counting formalism. The independent control of the time and frequency gate parameters reveals fine details of matter dynamics not available otherwise. These signal are illustrated for application to an anharmonic oscillator model with fluctuating energy and anharmonicity.

Yuri V. Kozitsky

Mojtaba Jafarpour, Davood Afshar

We present a new Lie algebraic method to study the eigenvalues and eigenfunctions of quantum anharmonic oscillators. We consider the Hamiltonians for the simple harmonic and anharmonic oscillator as the two generators of a Lie algebra, whose other generators may be found exactly or up to any order of the parameter involved. Speciflcally, the closed commutator algebra for the quartic anharmonic oscillator is established in a perturbation sense. An element of this Lie group, turning out to be the four-photon operator, transforms the quartic anharmonic oscillator Hamiltonian to the harmonic one in a perturbation sense; thus, facilitating the calculation of the eigenvalues and eigenfunctions of the former.