Related papers: Lie Algebraic Quantum Phase Reduction
Phase reduction is a powerful technique in the study of nonlinear oscillatory systems. Under certain assumptions, it allows us to describe each multidimensional oscillator by a single phase variable, giving rise to simple phase models such…
The catastrophe theory is applied to a nuclear cluster model and an effective model for QCD at low energy. The study of quantum phase transitions in the cluster model was considered in an earlier publication, but restricted to spherical…
The phase reduction method is a dimension reduction method for weakly driven limit-cycle oscillators, which has played an important role in the theoretical analysis of synchro- nization phenomena. Recently, we proposed a generalization of…
We present a phase-amplitude reduction framework for analyzing collective oscillations in networked dynamical systems. The framework, which builds on the phase reduction method, takes into account not only the collective dynamics on the…
The phase diffusion in a self-sustained oscillator, which produces oscillator's spectral linewidth, is inherently governed by a nonlinear Langevin equation. Over past 40 years, the equation has been treated with linear approximation,…
We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with…
The dynamics of a quantum nonlinear oscillator is studied in terms of its quasi-flow, a dynamical mapping of the classical phase plane that represents the time-evolution of the quantum observables. Explicit expressions are derived for the…
Response theory has a successful history of connecting experimental observations with theoretical predictions. Of particular interest is the optical response of matter, from which spectroscopy experiments can be modelled. However, the…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
Parametrically driven oscillators can emerge as a basis for the next generation of qubits. Classically, these systems exhibit two stable oscillatory states with opposite phases. Upon quantization, these states turn into a pair of closely…
We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is…
Optimal entrainment of a quantum nonlinear oscillator to a periodically modulated weak harmonic drive is studied in the semiclassical regime. By using the semiclassical phase reduction theory recently developed for quantum nonlinear…
Linear response theory describes quantum measurement with an arbitrary detector weakly coupled to a measured system. This description produces generic quantitative relation characterizing the detector that is analogous to the…
A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised…
In order to address the measurement problem of quantum theory we make the assumption that quantum state reduction should be regarded as a genuine physical process deserving of a dynamical description. Generalizing the nonrelativistic…
Quantum trajectories describe the stochastic evolution of an open quantum system conditioned on continuous monitoring of its output, such as by an ideal photodetector. In practice an experimenter has access to an output filtered through…
We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [Tsang, Shapiro, and Lloyd, Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and…
We quantitatively analyze the dynamics of the quantum phase distribution associated with the reduced density matrix of a system, as the system evolves under the influence of its environment with an energy-preserving quantum nondemolition…