Related papers: The quantum double well anharmonic oscillator in a…
Multiparametric quantum $gl(2)$ algebras are presented according to a classification based on their corresponding Lie bialgebra structures. From them, the non-relativistic limit leading to quantum harmonic oscillator algebras is implemented…
The O(N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions. The problem is directly related to that of a quantum double well anharmonic oscillator in an…
We study the synchronization of a van der Pol self-oscillator with Kerr anharmonicity to an external drive. We demonstrate that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase…
Quantum noise with exchange and tunneling is studied within time-dependent wave packets. A novel expression for the quantum noise of two identical particles injected simultaneously from opposite sides of a tunneling barrier is presented.…
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…
We prove a reducibility result for a quantum harmonic oscillator in arbitrary dimensions with arbitrary frequencies perturbed by a linear operator which is a polynomial of degree two in $x_j$, $-i \partial_j$ with coefficients which depend…
The purpose of this short paper is to give a summary of the derivation of a perturbative method to assess the impact of an arbitrary 3D magnetic field configuration, whose energy is everywhere small relative to the gravitational binding…
We study the entanglement evolution of two coupled qubits in interaction with an external environment and in the presence of an external magnetic field with a stochastic component. The results show the expected degradation of entanglement…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
Nonlinearity of electromagnetic field vibrations described by q-oscillators is shown to produce essential dependence of second correlation functions on intensity and deformation of Planck distribution. Experimental tests of such…
We investigate the convergence properties of a perturbation method proposed some time ago and reveal some of it most interesting features. Anharmonic oscillators in the strong--coupling limit prove to be appropriate illustrative examples…
We propose an approach based on a generalized quantum mechanics to deal with the basic features of the intrinsic spin Hall effect. This can be done by considering two decoupled harmonic oscillators on the noncommutative plane and evaluating…
We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter $\lambda $. The ground state can be obtained exactly and its energy…
The quantum anomalous Hall effect refers to the quantization of Hall effect in the absence of applied magnetic field. The quantum anomalous Hall effect is of topological nature and well suited for field-free resistance metrology and…
The aim of this work is to study the physical properties of a one-way quantum computer in an effective low-energy cluster state. We calculate the optimal working conditions as a function of the temperature and of the system parameters. The…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…
In this work an observation concerning a positivity property of the quantum anharmonic oscillator is made. This positivity property is suggested by the BMV conjecture.
We introduce and review briefly the phenomenon of quantum annealing and analog computation. The role of quantum fluctuation (tunneling) in random systems with rugged (free) energy landscapes having macroscopic barriers are discussed to…
This book chapter describes the dynamics of a modulated oscillator for resonant and nonresonant modulation. Two types of resonant modulation are considered: additive, with frequency close to the oscillator eigenfrequency, and parametric,…
Coupling two or more self-oscillating systems may stabilize their zero-amplitude rest-state, therefore quenching their oscillation. This phenomenon is termed "amplitude death". Well-known and studied in classical self-oscillators, amplitude…