scholarly journals TIME OPERATORS OF A HAMILTONIAN WITH PURELY DISCRETE SPECTRUM

2008 ◽  
Vol 20 (08) ◽  
pp. 951-978 ◽  
Author(s):  
ASAO ARAI ◽  
YASUMICHI MATSUZAWA
Keyword(s):  
Perturbation Theory ◽  
Discrete Spectrum ◽  
Spectral Properties ◽  
Mathematical Theory ◽  
Time Operator ◽  
Regular Perturbation ◽  
Time Operators

We develop a mathematical theory of time operators of a Hamiltonian with purely discrete spectrum. The main results include boundedness, unboundedness and spectral properties of them. In addition, possible connections of a time operator of H with regular perturbation theory are discussed.

REMARKS ON THE GROUND STATE ENERGY OF THE SPIN-BOSON MODEL: AN APPLICATION OF THE WIGNER–WEISSKOPF MODEL

2001 ◽  
Vol 13 (02) ◽  
pp. 221-251 ◽  
Author(s):  
MASAO HIROKAWA
Keyword(s):  
Perturbation Theory ◽  
Spectral Analysis ◽  
Ground State Energy ◽  
Ground State ◽  
Spectral Properties ◽  
State Energy ◽  
Regularity Condition ◽  
Infrared Singularity ◽  
Regular Perturbation ◽  
Boson Model

For the ground state energy of the spin-boson (SB) model, we give a new upper bound in the case with infrared singularity condition (i.e. without infrared cutoff), and a new lower bound in the case of massless bosons with infrared regularity condition. We first investigate spectral properties of the Wigner–Weisskopf (WW) model, and apply them to SB model to achieve our purpose. Then, as an extra result of the spectral analysis for WW model, we show that a non-perturbative ground state appears, and its ground state energy is so low that we cannot conjecture it by using the regular perturbation theory.

scholarly journals EXISTENCE OF SOLITARY WAVES AND PERIODIC WAVES TO A PERTURBED GENERALIZED KDV EQUATION

2014 ◽  
Vol 19 (4) ◽  
pp. 537-555 ◽  
Author(s):  
Weifang Yan ◽  
Zhengrong Liu ◽  
Yong Liang
Keyword(s):  
Perturbation Theory ◽  
Solitary Waves ◽  
Wave Speed ◽  
Kdv Equation ◽  
Upper And Lower Bounds ◽  
Singular Perturbation Theory ◽  
Geometric Singular Perturbation Theory ◽  
Periodic Waves ◽  
Regular Perturbation ◽  
Generalized Kdv Equation

In this paper, the existence of solitary waves and periodic waves to a perturbed generalized KdV equation is established by applying the geometric singular perturbation theory and the regular perturbation analysis for a Hamiltonian system. Moreover, upper and lower bounds of the limit wave speed are obtained. Some previous results are extended.

STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALS

1990 ◽  
Vol 02 (04) ◽  
pp. 479-494 ◽  
Author(s):  
PETER D. HISLOP ◽  
SHU NAKAMURA
Keyword(s):  
Perturbation Theory ◽  
Spectral Properties ◽  
Trace Class ◽  
Random Perturbations ◽  
Absolutely Continuous Spectrum ◽  
Random Potentials ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Accumulation Points ◽  
Mourre Estimate

Spectral properties of one-dimensional Schrödinger operators with unbounded potentials are studied. The main example is the Stark Hamiltonian with unbounded Anderson-type random perturbations. In this case, it is shown that if the perturbation is o(x) then the spectrum is the real line and absolutely continuous except for eigenvalues with no accumulation points. If the perturbation is larger than O(x), then the Hamiltonian has no absolutely continuous spectrum. The methods of proof involve the Mourre estimate and trace-class perturbation theory as recently used by Simon and Spencer.

Nonlinear Wave Forces Acting on Submerged Horizontal Cylinders

1988 ◽  
Vol 110 (1) ◽  
pp. 62-70 ◽  
Author(s):  
R. Inoue ◽  
Y. Kyozuka
Keyword(s):  
Perturbation Theory ◽  
Free Surface ◽  
Nonlinear Wave ◽  
Wave Breaking ◽  
Nonlinear Effects ◽  
Second Order ◽  
Experimental Results ◽  
Wave Forces ◽  
Regular Perturbation ◽  
Horizontal Cylinders

This paper is to present experimental results of the first and second-order wave forces acting on three kinds of horizontally submerged cylinders. Wave height, wave frequency and the models’ submergence were varied in the experiments. These results are compared with the numerical calculations based on the regular perturbation theory. Through this study, it was found that the calculations of both the first and second-order wave forces coincide with the experiments when the cylinders are submerged at a sufficient depth. However, in the case that the cylinders are close to the free surface and/or wave amplitudes are relatively large, the experimental results become small compared with the calculations because of nonlinear effects, such as wave breaking observed in the experiments.

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