Coherent Quantum Dynamics: What Fluctuations Can Tell

Abstract

Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values of products of arbitrary operators within both oscillator coherent states and SU(2) coherent states. In particular, we generally prove that the energy fluctuations of an arbitrary Hamiltonian are in leading order entirely due to the time dependence of the classical variables. These results add to the list of wellknown properties of coherent states and are applied here to the Lipkin-Meshkov-Glick model, the Dicke model, and to coherent intertwiners in spin networks as considered in Loop Quantum Gravity.

13 pages. Some remarks and references added, typos corrected. Version to appear in Phys. Rev. A

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• Driven-Dissipative Quantum Dynamics in Ultra Long-lived Dipoles in an Optical Cavity
• Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring
• Analytical description of the survival probability of coherent states in regular regimes
• Quantum scarring in a spin-boson system: fundamental families of periodic orbits
• Anomalous Thermalization in Quantum Collective Models
• Coherent States of su(1,1): Correlations, Fluctuations, and the Pseudoharmonic Oscillator
• Nielsen complexity of coherent spin state operators
• Quantum multifractality as a probe of phase space in the Dicke model
• Optimal Spin Squeezed Steady State induced by the dynamics of non-hermtian hamiltonians
• Noncentrosymmetric Triangular Magnet CaMnTeO${}_6$: Strong Quantum Fluctuations and Role of s0 vs. s2 Electronic States in Competing Exchange Interactions
• Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach
• Exact solutions and Dynamical phase transitions in the Lipkin-Meshkov-Glick model with Dual nonlinear interactions