Related papers: Not-so-normal mode decomposition
In this work we introduce the concept of a sub-space decomposition, subject to a partition of the coordinates. Considering metrics determined by partial orders in the set of coordinates, the so called poset metrics, we show the existence of…
We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall…
Synchronization and emergence of a collective mode is a general phenomenon, frequently observed in ensembles of coupled self-sustained oscillators of various natures. In several circumstances, in particular in cases of neurological…
Definition of generalized normal form for a system of ODEs corresponding to an infinitesimal symplectic or contact transformation near a singular point, with an arbitrary polynomial unperturbed part, and a method of its finding are…
Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
We address the decomposition of a multi-mode pure Gaussian state with respect to a bi-partite division of the modes. For any such division the state can always be expressed as a product state involving entangled two-mode squeezed states and…
We describe an extension to the density matrix renormalization group method incorporating real time evolution into the algorithm. Its application to transport problems in systems out of equilibrium and frequency dependent correlation…
We derive simplified normal forms for an area-preserving map in a neighbourhood of a degenerate resonant elliptic fixed point. Such fixed points appear in generic two-parameter families of area-preserving maps. We also derive a simplified…
We show the emergence of spontaneous synchronization between a pair of detuned quantum oscillators within a harmonic network. Our model does not involve any nonlinearity, driving, or external dissipation, thus providing the simplest…
It is well known that the quasinormal modes (or resonant states) of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the…
The composite systems can be non-uniquely decomposed into parts (subsystems). Not all decompositions (structures) of a composite system are equally physically relevant. In this paper we answer on theoretical ground why it may be so. We…
We consider a generalized Jaynes-Cummings model of a two-level atom interacting with a multimode nondegenerate coherent field. The sum of the mode frequencies is equal to the two-level transition frequency, creating the resonance condition.…
A universal approach is proposed for suppression of collective synchrony in a large population of interacting rhythmic units. We demonstrate that provided that the internal coupling is weak, stabilization of overall oscillations with…
A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions…
We give an approach to open quantum systems based on formal deformation quantization. It is shown that classical open systems of a certain type can be systematically quantized into quantum open systems preserving the complete positivity of…
Despite the several novel features arising from the dissipative optomechanical coupling, such effect remains vastly unexplored due to the lack of a simple formalism that captures non-Hermiticity in optomechanical systems. In this Letter, we…
Medical images can be decomposed into normal and abnormal features, which is considered as the compositionality. Based on this idea, we propose an encoder-decoder network to decompose a medical image into two discrete latent codes: a normal…
We propose a novel scheme to normalize scattering modes of the electromagnetic field. By relying on analytical solutions for Maxwell's equations in the homogenous medium outside the scatterer, we derive normalization conditions that only…
Schmidt modes of non-collinear biphoton angular wave functions are found analytically. The experimentally realizable procedure is described for their separation. Parameters of the Schmidt decomposition are used for evaluation of the degree…