Related papers: Nearest Neighbor Distances on a Circle: Multidimen…
The spacings between bound-state levels of the Schr\"odinger equation with the same principal quantum number $N$ but orbital angular momenta $\ell$ differing by unity are found to be nearly equal for a wide range of power potentials $V =…
Spectral statistics of quantum systems have been studied in detail using the nearest neighbour level spacings, which for generic chaotic systems follows random matrix theory predictions. In this work, the probability density of the closest…
In this paper,a systematic study of quantum phase transition within U(5) \leftrightarrow SO(6) limits is presented in terms of infinite dimensional Algebraic technique in the IBM framework. Energy level statistics are investigated with…
Exact solvability (typically, of harmonic oscillators) in quantum mechanics usually implies an elementary form of the spectrum while in all the "next-to-solvable" models, the energies E are only available in an implicit form (typically, as…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
We study the complexity of approximations to the normalized information distance. We introduce a hierarchy of computable approximations by considering the number of oscillations. This is a function version of the difference hierarchy for…
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…
We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies…
We address the old and widely debated question of the statistical properties of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of 1-d interacting bosons allows for the…
Energy spectra of quasi-one-dimensional quantum rings with a few electrons are studied using several different theoretical methods. Discrete Hubbard models and continuum models are shown to give similar results governed by the special…
Schroedinger bound-state problem in D dimensions is considered for a set of central polynomial potentials (containing 2q coupling constants). Its polynomial (harmonic-oscillator-like, quasi-exact, terminating) bound-state solutions of…
Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the…
We study statistical properties of excited levels of the E x (b_1+b_2) Jahn-Teller model. The multitude of avoided crossings of energy levels is generally claimed to be a testimony of quantum chaos. We found that apart from two limiting…
The connection between random matrices and the spectral fluctuations of complex quantum systems in a suitable limit can be explained by using the setup of random matrix theory. Higher-order spacing statistics in the $m$ superposed spectra…
We discuss how the thermalization of an elementary quantum system is modified when the system is placed in an environment out of thermal equilibrium. To this aim we provide a detailed investigation of the dynamics of an atomic system placed…
We study a $1$-dimensional chain of $N$ weakly anharmonic classical oscillators coupled at its ends to heat baths at different temperatures. Each oscillator is subject to pinning potential and it also interacts with its nearest neighbors.…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
A classic no-go theorem in one-dimensional quantum mechanics can be evaded when the potentials are unbounded below, thus allowing for novel parity-paired degenerate energy bound states. We numerically determine the spectrum of one such…
The statistical properties of spectra of quantum systems within the framework of random matrix theory is widely used in many areas of physics. These properties are affected, if two or more sets of spectra are superposed, resulting from the…