Related papers: Quantum asymptotic amplitude for quantum oscillato…
We study numerically the damping of quantum oscillations and the increase of entropy with time in model spin systems decohered by a spin bath. In some experimentally relevant cases, the oscillations of considerable amplitude can persist…
This study is devoted to the asymptotic spectral analysis of multiscale Schr\"odinger operators with oscillating and decaying electric potentials. Different regimes, related to scaling considerations, are distinguished. By means of a normal…
Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the…
We introduce a framework for implementing quantum operations as steady states of a subsystem in an extended Hilbert space. Each operation has a spectral criterion for reaching the steady state. This adds a `spectral switch' mechanism to the…
Quantum computers have now appeared in our society and are utilized for the investigation of science and engineering. At present, they have been built as intermediate-size computers containing about fifty qubits and are weak against noise…
Systems of coupled optical parametric oscillators (OPOs) forming an Ising machine are emerging as large-scale simulators of the Ising model. The advances in computer science and nonlinear optics have triggered not only the physical…
We study theoretically the nonlinear optical response of a two-dimensional semiconductor quantum dot supercrystal under a resonant continuous wave excitation. A single quantum dot is modeled as a three-level ladder-like system with the…
Interaction with a thermal environment decoheres the quantum state of a mechanical oscillator. When the interaction is sufficiently strong, such that more than one thermal phonon is introduced within a period of oscillation, quantum…
The accurate description and robust computational modeling of the nonequilibrium properties of quantum systems remain a challenge in condensed matter physics. In this work, we develop a linear-scale computational simulation technique for…
We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from the threshold of the essential spectrum and give the…
We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a…
Quantum criticality of open many-body systems has attracted lots of interest for emergent phenomena and universality. Here we present the exact steady state of the quantum van der Pol oscillator using the complex $P$-representation. We show…
The purpose of this article is to describe the singularities of one-dimensional oscillatory integrals, whose phases have a certain singularity, in the form of an asymptotic expansion. In the case of the Laplace integral, an analogous result…
Quantum mechanics imposes that any amplifier that works independently on the phase of the input signal has to introduce some excess noise. The impossibility of such a noiseless amplifier is rooted into unitarity and linearity of quantum…
While Koopman operator lifts a nonlinear system into an infinite-dimensional function space and represents it as a linear dynamics, its definition is restricted to autonomous systems, i.e., does not incorporate inputs or disturbances. To…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
We study the dynamics of a nonlinear oscillator near the critical point where period-two vibrations are first excited with the increasing amplitude of parametric driving. Above the threshold, quantum fluctuations induce transitions between…
It is demonstrated that a nonrelativistic quantum scale anomaly manifests itself in the appearance of composite operators with complex scaling dimensions. In particular, we study nonrelativistic quantum mechanics with an inverse square…
Parametric fluctuations or stochastic signals are introduced into the control pulse sequence to investigate the feasibility of random control over quantum open systems. In a large parameter error region, the out-of-order control pulses work…
The nonlinear quantum regime is crucial for implementing interesting quantum effects, which have wide applications in modern quantum science. Here we propose an effective method to reach the nonlinear quantum regime in a modulated…