Related papers: Self-Similarity Among Energy Eigenstates
We suggest a general ansatz for the energy-eigenstates when a complex one-dimensional PT-symmetric potential possesses real discrete spectrum. Several interesting features of PT-symmetric quantum mechanics have been brought out using this…
The ETH ansatz for matrix elements of a given operator in the energy eigenstate basis results in a notion of thermalization for a chaotic system. In this context for a certain quantity - to be found for a given model - one may impose a…
We examine the quantum mechanical eigensolutions of the two-dimensional infinite well or quantum billiard system consisting of a circular boundary with an infinite barrier or baffle along a radius. Because of the change in boundary…
By introducing a phase field and solving the eigen-functional equation of particles, we obtain the exact expressions of the ground state energy as a functional of the particle density for interacting electron/boson systems, and a…
Experiments reveal that a confined electron system with two equally-populated layers at zero magnetic field can spontaneously break this symmetry through an interlayer charge transfer near the magnetic quantum limit. New fractional quantum…
We investigate the extent to which the eigenstate thermalization hypothesis~(ETH) is valid or violated in the non-integrable and the integrable spin-$1/2$ XXZ chain. We perform the energy-resolved analysis of the statistical properties of…
There is an extensive philosophical literature on the interrelated issues of identity, individuality, and distinguishability in quantum systems. A key consideration is whether quantum systems are subject to a strong form of individuality…
While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…
We investigate the energy spectrum structure of a system of two (identical) interacting bosonic wells occupied by N bosons within the Schwinger realization of the angular momentum. This picture enables us to recognize the symmetry…
The quantum self-organization is introduced as one of the major underlying mechanisms of the quantum many-body systems, for instance, atomic nuclei. It is shown that atomic nuclei are not necessarily like simple rigid vases containing…
We investigate the implications of integrability for the existence of quantum disentangled liquid (QDL) states in the half-filled one-dimensional Hubbard model. We argue that there exist finite energy-density eigenstates that exhibit QDL…
We propose a method to study the transition to chaos in isolated quantum systems of interacting particles. It is based on the concept of delocalization of eigenstates in the energy shell, controlled by the Gaussian form of the strength…
The shape space of k labelled points on a plane can be identified with the space of pure quantum states of dimension k-2. Hence, the machinery of quantum mechanics can be applied to the statistical analysis of planar configurations of…
We identify new universal properties of the energy eigenstates of chaotic systems with local interactions, which distinguish them both from integrable systems and from non-local chaotic systems. We study the relation between the energy…
The set of covariance matrices of a continuous-variable quantum system with a finite number of degrees of freedom is a strict subset of the set of real positive-definite matrices due to Heisenberg's uncertainty principle. This has the…
The spectrum of eigenenergies of a quantum integrable system whose hamiltonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in 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…
This work investigates in which form quantities with Planck dimensions occur already in the common quantum theory with local Lorentz symmetry. Since such Planck quantities as Planck length or Planck mass involve the Planck constant h, the…
Generic rotationally invariant random matrix models satisfy a simple relation: the probability distribution of off-diagonal elements and the one of half the difference between any two diagonal elements coincide. In the spirit of the…