Quantum mechanics of the damped harmonic oscillator

2002 ◽  
Vol 80 (6) ◽  
pp. 645-660 ◽  
Author(s):  
M Blasone ◽  
P Jizba
Keyword(s):  
Harmonic Oscillator ◽  
Ground State ◽  
Geometric Phase ◽  
State Energy ◽  
Dimensional System ◽  
One Dimensional ◽  
Damped Harmonic Oscillator ◽  
Linear Harmonic Oscillator ◽  
Two Dimensional System ◽  
The One

We quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. By using the Feynman–Hibbs method, the time-dependent quantum states of such a system are constructed entirely in the framework of the classical theory. The geometric phase is calculated and found to be proportional to the ground-state energy of the one-dimensional linear harmonic oscillator to which the two-dimensional system reduces under appropriate constraint. PACS Nos.: 03.65Ta, 03.65Vf, 03.65Ca, 03.65Fd

scholarly journals GROUND-STATE ENERGY OF THE ONE-DIMENSIONAL HUBBARD MODEL IN A SIMPLE SELF-CONSISTENT VERSION OF THE LADDER APPROXIMATION

1995 ◽  
Vol 09 (18) ◽  
pp. 1149-1157 ◽  
Author(s):  
F.D. BUZATU
Keyword(s):  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Consistency Condition ◽  
Ladder Approximation ◽  
Model Parameters ◽  
Simple Assumption ◽  
One Dimensional ◽  
The One

The ground-state energy of the one-dimensional Hubbard model is calculated within the ladder approximation; from the comparison with the exact results in the repulsive case, it follows that the approximation is good at low densities or small couplings. The ladder approximation can be improved by imposing a self-consistency condition; using a simple assumption, the results become close to the exact ones in a large range of the model parameters.

scholarly journals Dimerization in Quantum Spin Chains with O(n) Symmetry

2021 ◽  
Author(s):  
Jakob E. Björnberg ◽  
Peter Mühlbacher ◽  
Bruno Nachtergaele ◽  
Daniel Ueltschi
Keyword(s):  
Phase Diagram ◽  
Ground State ◽  
Quantum Spin ◽  
Spin Chains ◽  
Dimensional System ◽  
Quantum Spin Chains ◽  
One Dimensional ◽  
Open Region ◽  
Quantum Spins ◽  
The One

AbstractWe consider quantum spins with $$S\ge 1$$ S ≥ 1 , and two-body interactions with $$O(2S+1)$$ O ( 2 S + 1 ) symmetry. We discuss the ground state phase diagram of the one-dimensional system. We give a rigorous proof of dimerization for an open region of the phase diagram, for S sufficiently large. We also prove the existence of a gap for excitations.

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