Structure and time-dependence of quantum breathers

Abstract

Quantum states of a discrete breather are studied in two ways. One method involves numerical diagonalization of the Hamiltonian, the other uses the path integral to examine correlations in the eigenstates. In both cases only the central nonlinearity is retained. To reduce truncation effects in the numerical diagonalization, a basis is used that involves a quadratic local mode. A similar device is used in the path integral method for deducing localization. Both approaches lead to the conclusion that aside from quantum tunneling the quantized discrete breather is stable.

Discrete breathers — Advances in theory and applications

“…It turns out to be impossible, for very much the same reasons as in the purely classical treatment (see [118]). This result implies, that there is almost no other source of decay for a localized initial state in a quantum lattice, but to slowly tunnel as a whole along the lattice, if nonlinearities allow for the formation of exact classical DB states [359,360]. Numerical calculations for such a case, but with few quanta, were performed by Proville [324], and, similar to the above trimer discussion, showed that if quantum breather states exist in the system, then localized excitations stay localized for times which are much longer than the typical phonon diffusion times in the absence of anharmonicity.…”

Quantumq-breathers in a finite Bose-Hubbard chain: The case of two interacting bosons

“…In many cases quantum dynamics is important. Quantum breathers consist of superpositions of nearly degenerate many-quanta bound states, with very long times to tunnel from one lattice site to another [4,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29]. Remarkably quantum breathers, though being extended states in a translationally invariant system, are characterized by exponentially localized weight functions, in full analogy to their classical counterparts.…”

Intrinsic Localized Modes in Metamaterials

“…It should be mentioned that a damping value up to 0.18 does not disturb the breather profile to a significant extent, and from a value of 0.20, it starts showing the effect of damping. In metamaterials, the value of damping is generally not considered very high [5] so that breather oscillations could be considered stable.…”

“…The formulation is accomplished using a Taylor-expansion in the x-dimension. The magnetization of the metamaterial [5] is considered to study the field behavior in SRRs. The dynamical equation thus obtained gives a reliable solution for device application as supported by the numerical solutions.…”