Related papers: Quantum anharmonic oscillator and its statistical …
The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
The main purpose of this paper is to demonstrate and illustrate, once again, the potency of the variational technique as an approximation procedure for the quantization of quantum mechanical systems. By choosing particle-in-a-box…
The solution of one--dimensional asymmetric quantum harmonic oscillator is presented. The asymmetry can be realized, for example, by using two springs, one spring is glued with the mass, and the second spring is freely connected with the…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0< q < 1, these normalized states form an overcomplete set that resolves the unity with respect to an explicit…
In this paper we consider eigenvalues asymptotics of the energy operator in the one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator of this…
Present quantum Monte Carlo codes use statistical techniques adapted to find the amplitude of a quantum system or the associated eigenvalues. Thus, they do not use a true physical random source. It is demonstrated that, in fact, quantum…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
A linear quantum harmonic oscillator factors into one dimensional oscillators and can be solved using creation and annihilation operators. We consider a spherical analogue. This analogue does not factor. The two dimensional case is…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation…
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…
We study the eigen-energy and eigen-function of a quantum particle acquiring the probability density-dependent effective mass (DDEM) in harmonic oscillators. Instead of discrete eigen-energies, continuous energy spectra are revealed due to…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first con- tribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i)…