Multidimensional quantum rate theory

Gennady Mil’nikov, António J. C. Varandas

The paper presents a new semiclassical theory of multidimensional tunneling and its application to the decay problem. A simple semiclassical expression for the decay rate constant is derived in terms of complex valued family of classical trajectories in the decay valley while the algebraic form of the family in the tunneling region is found by means of classical canonical perturbation theory. This provides a tool to analytically continue the classical trajectories into the decay valley, with a numerical illustration of such a continuation being done for a model 2D decay rate problem. The calculated results for the rate constant are found to be in good agreement with the exact ones for the high levels where the suggested perturbative treatment is applicable. It is also shown that the formulated theory can be directly compared with a previously proposed hopping method which gives a way to examine the accuracy of the latter without exact quantum calculations.

Jiřı́ Pokorný, Tsu-Ming Wu

Fatih Dinç, Lauren E. Hayward Sierens, Agata M. Brańczyk

We study the collective decay rates of multidimensional quantum networks in which one-dimensional waveguides form an intersecting hyperrectangular lattice, with qubits located at the lattice points.We introduce and motivate the dimensional reduction of poles (DRoP) conjecture, which identifies all collective decay rates of such networks via a connection to waveguides with a one-dimensional topology (e.g., a linear chain of qubits).Using DRoP, we consider many-body effects such as superradiance, subradiance, and bound states in continuum in multidimensional quantum networks.We find that, unlike one-dimensional linear chains, multidimensional quantum networks have superradiance in distinct levels, which we call multidimensional superradiance.Furthermore, we generalize the N -3 scaling of subradiance in a linear chain to d-dimensional networks.

Brittany L. Hyland, Craig C. Martens

Hans‐Dieter Meyer, Fabien Gatti, Graham A. Worth

Multidimensional Quantum Dynamics: MCTDH Theory and Applications