scholarly journals Spectral Statistics of the Triaxial Rigid Rotator: Semiclassical Origin of Their Pathological Behavior

2003 ◽  
Vol 17 (15) ◽  
pp. 803-812
Author(s):  
V. R. Manfredi ◽  
V. Penna ◽  
L. Salasnich
Keyword(s):  
Angular Momentum ◽  
Spectral Properties ◽  
Total Angular Momentum ◽  
Energy Levels ◽  
Rigid Rotator ◽  
One Dimensional ◽  
Spectral Statistics ◽  
Rotational Motions ◽  
Pathological Behavior ◽  
The One

In this paper we investigate the local and global spectral properties of the triaxial rigid rotator. We demonstrate that, for a fixed value of the total angular momentum, the energy spectrum can be divided into two sets of energy levels, whose classical analogs are librational and rotational motions. By using diagonalization, semiclassical and algebric methods, we show that the energy levels follow the anomalous spectral statistics of the one-dimensional harmonic oscillator.

scholarly journals On the spectral properties of the Schrödinger operator with a periodic PT-symmetric potential

2017 ◽  
Vol 14 (05) ◽  
pp. 1750065 ◽  
Author(s):  
Oktay Veliev
Keyword(s):  
Schrödinger Operator ◽  
Spectral Properties ◽  
Schrodinger Operator ◽  
Symmetric Potential ◽  
One Dimensional ◽  
Symmetric Complex ◽  
The One ◽  
Complex Valued

In this paper, we investigate the spectrum and spectrality of the one-dimensional Schrödinger operator with a periodic PT-symmetric complex-valued potential.

Spectral Properties of the One-Dimensional SILK Quasilattices

1991 ◽  
Vol 8 (10) ◽  
pp. 533-536 ◽  
Author(s):  
Liu Youyan ◽  
Luan Changfu ◽  
Deng Wenji ◽  
Han Hui ◽  
Zou Nanzhi
Keyword(s):  
Spectral Properties ◽  
One Dimensional ◽  
The One

scholarly journals The spectrum of the Schrödinger–Hamiltonian for trapped particles in a cylinder with a topological defect perturbed by two attractive delta interactions

2018 ◽  
Vol 15 (08) ◽  
pp. 1850135 ◽  
Author(s):  
Fassari Silvestro ◽  
Rinaldi Fabio ◽  
Viaggiu Stefano
Keyword(s):  
Quantum Dot ◽  
Harmonic Oscillator ◽  
Total Energy ◽  
Spectral Properties ◽  
Bound States ◽  
Three Dimensional ◽  
Point Interactions ◽  
One Dimensional ◽  
The One ◽  
Math Phys

In this paper, we exploit the technique used in [Albeverio and Nizhnik, On the number of negative eigenvalues of one-dimensional Schrödinger operator with point interactions, Lett. Math. Phys. 65 (2003) 27; Albeverio, Gesztesy, Hoegh-Krohn and Holden, Solvable Models in Quantum Mechanics (second edition with an appendix by P. Exner, AMS Chelsea Series 2004); Albeverio and Kurasov, Singular Perturbations of Differential Operators: Solvable Type Operators (Cambridge University Press, 2000); Fassari and Rinaldi, On the spectrum of the Schrödinger–Hamiltonian with a particular configuration of three one-dimensional point interactions, Rep. Math. Phys. 3 (2009) 367; Fassari and Rinaldi, On the spectrum of the Schrödinger–Hamiltonian of the one-dimensional harmonic oscillator perturbed by two identical attractive point interactions, Rep. Math. Phys. 3 (2012) 353; Albeverio, Fassari and Rinaldi, The Hamiltonian of the harmonic oscillator with an attractive-interaction centered at the origin as approximated by the one with a triple of attractive-interactions, J. Phys. A: Math. Theor. 49 (2016) 025302; Albeverio, Fassari and Rinaldi, Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive [Formula: see text]-impurities symmetrically situated around the origin II, Nanosyst. Phys. Chem. Math. 7(5) (2016) 803; Albeverio, Fassari and Rinaldi, Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive [Formula: see text]-impurities symmetrically situated around the origin, Nanosyst. Phys. Chem. Math. 7(2) (2016) 268] to deal with delta interactions in a rigorous way in a curved spacetime represented by a cosmic string along the [Formula: see text] axis. This mathematical machinery is applied in order to study the discrete spectrum of a point-mass particle confined in an infinitely long cylinder with a conical defect on the [Formula: see text] axis and perturbed by two identical attractive delta interactions symmetrically situated around the origin. We derive a suitable approximate formula for the total energy. As a consequence, we found the existence of a mixing of states with positive or zero energy with the ones with negative energy (bound states). This mixture depends on the radius [Formula: see text] of the trapping cylinder. The number of quantum bound states is an increasing function of the radius [Formula: see text]. It is also interesting to note the presence of states with zero total energy (quasi free states). Apart from the gravitational background, the model presented in this paper is of interest in the context of nanophysics and graphene modeling. In particular, the graphene with double layer in this framework, with the double layer given by the aforementioned delta interactions and the string on the [Formula: see text]-axis modeling topological defects connecting the two layers. As a consequence of these setups, we obtain the usual mixture of positive and negative bound states present in the graphene literature.

scholarly journals Spectral analysis of Hahn-Dirac system

2021 ◽  
Author(s):  
Bilender Allahverdiev ◽  
Hüseyin Tuna
Keyword(s):  
Spectral Analysis ◽  
Boundary Value Problem ◽  
Spectral Properties ◽  
Orthonormal Basis ◽  
Boundary Value ◽  
Dirac System ◽  
One Dimensional ◽  
Countable Sequence ◽  
Greens Function ◽  
The One

In this paper, we study some spectral properties of the one-dimensional Hahn-Dirac boundary-value problem, such as formally self-adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Greens function, the existence of a countable sequence of eigenvalues, eigenfunctions forming an orthonormal basis of L2w,q ((w0. a): E).

scholarly journals Effects of finite-range interactions on the one-electron spectral properties of one-dimensional metals: Application to Bi/InSb(001)

2019 ◽  
Vol 100 (3) ◽  
Author(s):  
José M. P. Carmelo ◽  
Tilen Čadež ◽  
Yoshiyuki Ohtsubo ◽  
Shin-ichi Kimura ◽  
David K. Campbell
Keyword(s):  
Spectral Properties ◽  
Finite Range ◽  
One Dimensional ◽  
The One

scholarly journals ON THE SPECTRUM OF THE ONE-DIMENSIONAL SCHRÖDINGER HAMILTONIAN PERTURBED BY AN ATTRACTIVE GAUSSIAN POTENTIAL

2017 ◽  
Vol 57 (6) ◽  
pp. 385 ◽  
Author(s):  
Silvestro Fassari ◽  
Manuel Gadella ◽  
Luis Miguel Nieto ◽  
Fabio Rinaldi
Keyword(s):  
Discrete Spectrum ◽  
Energy Levels ◽  
Trace Class ◽  
Bound State ◽  
Great Accuracy ◽  
Coupling Constant ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Gaussian Potential ◽  
The One

<p>We propose a new approach to the problem of finding the eigenvalues (energy levels) in the discrete spectrum of the one-dimensional Hamiltonian with an attractive Gaussian potential by using the well-known Birman-Schwinger technique. However, in place of the Birman-Schwinger integral operator we consider an isospectral operator in momentum space, taking advantage of the unique feature of this potential, that is to say its invariance under Fourier transform. <br />Given that such integral operators are trace class, it is possible to determine the energy levels in the discrete spectrum of the Hamiltonian as functions of <span>the coupling constant with great accuracy by solving a finite number of transcendental equations. We also address the important issue of the coupling constant thresholds of the Hamiltonian, that is to say the critical values of λ for which we have the emergence of an additional bound state out of the absolutely continuous spectrum. </span></p>

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