Light-induced fractal energy spectrum of ultracold fermions on the two-dimensional optical lattice with {\cal T}_3 symmetry

2009 ◽  
Vol 42 (16) ◽  
pp. 165302
Author(s):  
Jing-Min Hou
Keyword(s):  
Energy Spectrum ◽  
Optical Lattice ◽  
Two Dimensional

Peculiarities of Stark-phonon Resonance in Two-dimensional Superlattices with Non-additive Energy Spectrum

2016 ◽  
Vol 8 (1) ◽  
pp. 01019-1-01019-3
Author(s):  
D. V. Zav’yalov ◽  
◽  
S. V. Kruchkov ◽  
E. S. Ionkina ◽  
◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Two Dimensional ◽  
Additive Energy

GAP-LABELING PROPERTIES OF THE ENERGY SPECTRUM FOR TWO-DIMENSIONAL FIBONACCI QUASILATTICES

1995 ◽  
Vol 09 (01) ◽  
pp. 55-66
Author(s):  
YOUYAN LIU ◽  
WICHIT SRITRAKOOL ◽  
XIUJUN FU
Keyword(s):  
Energy Spectrum ◽  
Density Of States ◽  
Energy Gap ◽  
Fractional Part ◽  
Numerical Results ◽  
Step Height ◽  
Integrated Density Of States ◽  
Two Dimensional

We have analytically obtained the occupation probabilities on subbands of the hierarchical energy spectrum and the step heights of the integrated density of states for two-dimensional Fibonacci quasilattices. Based on the above results, the gap-labeling properties of the energy spectrum are found, which claim that the step height is equal to {mτ}, where the braces denote the fractional part, and m is an integer that can be used to label the corresponding energy gap. Numerical results confirm these results very well.

Dirac oscillator in a uniform electric field: Path integral treatment

2019 ◽  
Vol 34 (30) ◽  
pp. 1950246
Author(s):  
Hassene Bada ◽  
Mekki Aouachria
Keyword(s):  
Energy Spectrum ◽  
Electric Field ◽  
Path Integral ◽  
Uniform Electric Field ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Fermionic Model ◽  
Internal Motions ◽  
Integral Treatment ◽  
The One

In this paper, the propagator of a two-dimensional Dirac oscillator in the presence of a uniform electric field is derived by using the path integral technique. The fact that the globally named approach is used in this work redirects, beforehand, our search for the propagator of the Dirac equation to that of the propagator of its quadratic form. The internal motions relative to the spin are represented by two fermionic oscillators, which are described by Grassmannian variables, according to Schwinger’s fermionic model. Once the integration over the anticommuting variables (Grassmannian variables) is accomplished, the problem becomes the one of finding a non-relativistic propagator with only bosonic variables. The energy spectrum of the electron and the corresponding eigenspinors are also obtained in this work.

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