Related papers: Duality between the quantum inverted harmonic osci…
In Quantum Machine Learning (QML) and Quantum Finance, amplitude encoding is often motivated by its logarithmic storage capacity arXiv:1307.0411. This paradigm typically relies on the mapping $\psi = \sqrt{P}$, treating the quantum state as…
We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $\alpha$ being proportional to the average degree of overlapping. Under critical conditions, a…
In this paper we expand our previous investigation of a quantum particle subject to the action of a random potential plus a fixed harmonic potential at a finite temperature T. In the classical limit the system reduces to a well-known…
A number of physical systems exhibit a particular form of asymptotic conformal invariance: within a particular range of distances, they are characterized by a long-range conformal interaction (inverse square potential), the absence of…
Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time…
A technique to reconstruct one-dimensional, reflectionless potentials and the associated quantum wave functions starting from a finite number of known energy spectra is discussed. The method is demonstrated using spectra that scale like the…
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model…
The inverse scale factor, which in classical cosmological models diverges at the singularity, is quantized in isotropic models of loop quantum cosmology by using techniques which have been developed in quantum geometry for a quantization of…
We consider the perturbed harmonic oscillator $T_D\psi=-\psi''+x^2\psi+q(x)\psi$, $\psi(0)=0$ in $L^2(R_+)$, where $q\in H_+=\{q', xq\in L^2(R_+)\}$ is a real-valued potential. We prove that the mapping $q\mapsto{\rm spectral data}={\rm…
Theory of the quantum quartic oscillator is developed with close attention to the energy cutoff one needs to impose on the system in order to approximate the smallest eigenvalues and corresponding eigenstates of its Hamiltonian by…
We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure…
The static second hyperpolarizability is derived from the space-fractional Schr\"{o}dinger equation in the particle-centric view. The Thomas-Reiche-Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second…
Conventional weak-coupling Rayleigh-Schr\"odinger perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale analysis, a powerful and sophisticated…
We demonstrate the possibility of controlling the border between the quantum and the classical world by performing nonselective measurements on quantum systems. We consider a quantum harmonic oscillator initially prepared in a Schroedinger…
Given a direct system of Hilbert spaces $s\mapsto \mathcal H_s$ (with isometric inclusion maps $\iota_s^t:\mathcal H_s\rightarrow \mathcal H_t$ for $s\leq t$) corresponding to quantum systems on scales $s$, we define notions of scale…
The function exp(iwt) describes an oscillating motion. Energy of the oscillator is proportional to the square of w. exp(iwt) is the solution of a differential equation. We have replaced this differential equation by the corresponding…
A new nonlinear scheme of high harmonics generation in a wide class of time-reversal invariant materials with broken spatial inversion symmetry (where recently the nonlinear Hall effect has been established) due to the nontrivial topology…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
The conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian defines a quantum theory with an…
The initial-to-final-state inverse problem consists in determining a quantum Hamiltonian assuming the knowledge of the state of the system at some fixed time, for every initial state. We formulated this problem to establish a theoretical…