相关论文: Cyclotomy and Ramanujan sums in quantum phase lock…
We introduce a systematic study of "symmetric quantum circuits", a new restricted model of quantum computation that preserves the symmetries of the problems it solves. This model is well-adapted for studying the role of symmetry in quantum…
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…
With growing interest in quantum technologies, possibilities of synchronizing quantum systems has garnered significant recent attention. In experiments with dilute ensemble of laser cooled spin-1 $^{87}{Rb}$ atoms, we observe phase…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
A quantization scheme based on the extension of phase space with application of constrained quantization technic is considered. The obtained method is similar to the geometric quantization. For constrained systems the problem of scalar…
Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in terms of connections on composite Hilbert space bundles.
Ramanujan sums have attracted significant attention in both mathematical and engineering disciplines due to their diverse applications. In this paper, we introduce an algebraic generalization of Ramanujan sums, derived through polynomial…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
The Kuramoto model serves as a paradigm for describing spontaneous synchronization in a system of classical interacting rotors. In this study, we extend this model to the quantum domain by coupling quantum interacting rotors to external…
Classical and quantum theories of time-symmetric smoothing, which can be used to optimally estimate waveforms in classical and quantum systems, are derived using a discrete-time approach, and the similarities between the two theories are…
Many two-dimensional physical systems have symmetries which are mathematically described by quantum groups (quasi-triangular Hopf algebras). In this letter we introduce the concept of a spontaneously broken Hopf symmetry and show that it…
We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states…
Discovering pragmatic and efficient approaches to construct $\varepsilon$-approximations of quantum operators such as real (imaginary) time-evolution propagators in terms of the basic quantum operations (gates) is challenging. Prior…
Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance…
As examples of quantum-"classical" coupling systems, multi-component systems are studied by semiclassical evaluations of the Feynman kernels in the coherent-state representation. From the observation of the phase space caustics due to the…
We describe the effect of geometric phases induced by either classical or quantum electric fields acting on single electron spins in quantum dots in the presence of spin-orbit coupling. On one hand, applied electric fields can be used to…
Dynamical tunnelling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunnelling process is governed by nonlinear resonances that manifest within the regular…
We begin with the simple model of phase sychronization in open classical nonlinear system which is represented in the language of angular momentum variables. After that we propose the relevant quantum counterpart of this system. Using the…
The interrelation between classicality/quantumness and symmetry of states is discussed within the phase-space formulation of finite-dimensional quantum systems. We derive representations for classicality measures…
In many physical applications, bound states and/or resonances are observed, which raises the question whether these states are elementary or composite. Here we elaborate on several methods for calculating the compositeness $X$ of bound…