scholarly journals Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model

2020 ◽  
Vol 5 (1) ◽  
pp. 7 ◽  
Author(s):  
Eduardo Jonathan Torres-Herrera ◽  
Lea F. Santos
Keyword(s):  
Cold Atoms ◽  
Matrix Theory ◽  
Energy Levels ◽  
Ion Traps ◽  
Special Issue ◽  
Number Operator ◽  
One Dimensional ◽  
Quantum Domain ◽  
Level Statistics ◽  
The One

The analysis of level statistics provides a primary method to detect signatures of chaos in the quantum domain. However, for experiments with ion traps and cold atoms, the energy levels are not as easily accessible as the dynamics. In this work, we discuss how properties of the spectrum that are usually associated with chaos can be directly detected from the evolution of the number operator in the one-dimensional, noninteracting Aubry-André model. Both the quantity and the model are studied in experiments with cold atoms. We consider a single-particle and system sizes experimentally reachable. By varying the disorder strength within values below the critical point of the model, level statistics similar to those found in random matrix theory are obtained. Dynamically, these properties of the spectrum are manifested in the form of a dip below the equilibration point of the number operator. This feature emerges at times that are experimentally accessible. This work is a contribution to a special issue dedicated to Shmuel Fishman.

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 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>

scholarly journals DECONFINEMENT AND COLD ATOMS IN OPTICAL LATTICES

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5169-5178
Author(s):  
M. A CAZALILLA ◽  
A. F. HO ◽  
T. GIAMARCHI
Keyword(s):  
Optical Lattices ◽  
Cold Atoms ◽  
Three Dimensional ◽  
Optical Traps ◽  
High Dimensional ◽  
Interacting Particles ◽  
Controllable System ◽  
One Dimensional ◽  
Physical Systems ◽  
The One

Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems.

A NEW SUPERSYMMETRIC VERSION OF THE ABRAHAM-MOSES METHOD FOR SYMMETRIC POTENTIALS

1996 ◽  
Vol 08 (05) ◽  
pp. 655-668
Author(s):  
J. CASAHORRÁN
Keyword(s):  
Hilbert Space ◽  
Energy Levels ◽  
Wave Functions ◽  
Symmetric Potential ◽  
One Dimensional ◽  
Supersymmetric Version ◽  
Discrete And Continuous Spectra ◽  
The One ◽  
Original Potential ◽  
General Method

Starting from the one-dimensional Schrodinger equation with symmetric potential Vs(x), a general method is presented in order to obtain a family of partially isospectral hamiltonians. Arguments concerning supersymmetric transformations, factorization procedures and Riccati equations are invoked along the article. As a result of the appearance of singular superpotentials, the physical meaning of our method can be summarized as follows: only the odd wave-functions of the original potential Vs(x) are transported via supersymmetry into the Hilbert space associated with the partner Vp(x). In such a case the degeneracy of energy levels is partially broken. Supersymmetry is neither exact nor spontaneously broken but realizes itself acting on wave functions vanishing at x=0. While the domain of the original hamiltonian H extends along the whole real axis, the susy partner Hp reduces to the half-line (x≤0 or x≥0). To illustrate how the procedure works in practice we resort to a symmetric potential in the Posch-Teller class containing both discrete and continuous spectra.

MAGNETIC RESONANCES IN THE ONE-DIMENSIONAL S=1 SPIN SYSTEM NENP

1993 ◽  
Vol 07 (01n03) ◽  
pp. 1016-1019 ◽  
Author(s):  
W. PALME ◽  
H. KRIEGELSTEIN ◽  
B. LÜTHI ◽  
T.M. BRILL ◽  
T. YOSIDA ◽  
...  
Keyword(s):  
Energy Levels ◽  
Frequency Range ◽  
Resonance Signal ◽  
Temperature Dependent ◽  
Critical Fields ◽  
One Dimensional ◽  
The One ◽  
Magnetic Resonances ◽  
Field Theoretical Model ◽  
Signal Intensities

Magnetic resonance experiments in the frequency range 55–404 GHz in magnetic fields up to 14 T are presented. Comparison with an existing field theoretical model leads to gap parameters and critical fields that are only slightly different from those obtained by neutron scattering experiments at q=π. Temperature dependent resonance signal intensities of various branches are compared to calculated intensities in the framework of Boltzmann statistics for temperatures between 1.5 K and 18 K. In this way resonance branches are assigned to transitions within a scheme of energy levels.

EFFECT OF INTERACTION IN ONE-DIMENSIONAL TOPOLOGICAL INSULATOR

2013 ◽  
Vol 27 (07) ◽  
pp. 1361001
Author(s):  
HUAIMING GUO ◽  
SHUN-QING SHEN
Keyword(s):  
Topological Insulator ◽  
Cold Atoms ◽  
Berry Phase ◽  
Repulsive Interaction ◽  
Edge States ◽  
One Dimensional ◽  
Diagonalization Method ◽  
Half Filling ◽  
The One ◽  
Exact Diagonalization Method

The one-dimensional interacting topological insulator is studied by means of exact diagonalization method. The topological properties are examined with the existence of the edge states and the quantized berry phase at half-filling. It is found that the topological phases are not only robust to small repulsive interactions but also are stabilized by small attractive interactions and also finite repulsive interaction can drive a topological nontrivial phase into a trivial one while the attractive interaction can drive a trivial phase into a nontrivial one. These results could be realized experimentally using cold atoms trapped in the 1D optical lattice.

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