Renormalized unitary transformation in the adiabatic theorem

1991 ◽  
Vol 44 (1) ◽  
pp. 59-64 ◽  
Author(s):  
Kazuo Takayanagi
Keyword(s):  
Unitary Transformation ◽  
Adiabatic Theorem

Ground state molecular parameters of phosphine, PH3, from the simultaneous analysis of the high-resolution infrared, microwave and submillimeterwave spectra

1985 ◽  
Vol 50 (11) ◽  
pp. 2480-2492 ◽  
Author(s):  
Soňa Přádná ◽  
Dušan Papoušek ◽  
Jyrki Kauppinen ◽  
Sergei P. Belov ◽  
Andrei F. Krupnov ◽  
...  
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Ground State ◽  
Unitary Transformation ◽  
Point Of View ◽  
Acoustic Detection ◽  
Molecular Parameters ◽  
Microwave Spectrometer ◽  
Fourier Transform Spectra ◽  
First Time

Fourier transform spectra of the ν2 band of PH3 have been remeasured with 0.0045 cm-1 resolution. Ground state combination differences from these data have been fitted simultaneously with the microwave and submillimeterwave data to determine the ground state spectroscopical parameters of PH3 including the parameters of the Δk = ± 3n interactions. The correlation between the latter parameters has been discussed from the point of view of the existence of two equivalent effective rotational operators which are related by a unitary transformation. The ΔJ = 0, +1, ΔK = 0 (A1 ↔ A2, E ↔ E) rotational transitions in the ν2 and ν4 states have been measured for the first time by using a microwave spectrometer and a radiofrequency spectrometer with acoustic detection.

scholarly journals Persistence of the spectral gap for the Landau–Pekar equations

2021 ◽  
Vol 111 (1) ◽  
Author(s):  
Dario Feliciangeli ◽  
Simone Rademacher ◽  
Robert Seiringer
Keyword(s):  
Initial Data ◽  
Spectral Gap ◽  
Effective Hamiltonian ◽  
Adiabatic Theorem ◽  
Strongly Coupled

AbstractThe Landau–Pekar equations describe the dynamics of a strongly coupled polaron. Here, we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for all times. For such initial data, this allows us to extend the results on the adiabatic theorem for the Landau–Pekar equations and their derivation from the Fröhlich model obtained in previous works to larger times.

scholarly journals Time-Rescaling of Dirac Dynamics: Shortcuts to Adiabaticity in Ion Traps and Weyl Semimetals

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 81
Author(s):  
Agniva Roychowdhury ◽  
Sebastian Deffner
Keyword(s):  
Time Dependence ◽  
Unitary Transformation ◽  
Ion Traps ◽  
Time Frame ◽  
Effective Potentials ◽  
Shortcuts To Adiabaticity ◽  
Weyl Semimetals ◽  
Adiabatic Dynamics

Only very recently, rescaling time has been recognized as a way to achieve adiabatic dynamics in fast processes. The advantage of time-rescaling over other shortcuts to adiabaticity is that it does not depend on the eigenspectrum and eigenstates of the Hamiltonian. However, time-rescaling requires that the original dynamics are adiabatic, and in the rescaled time frame, the Hamiltonian exhibits non-trivial time-dependence. In this work, we show how time-rescaling can be applied to Dirac dynamics, and we show that all time-dependence can be absorbed into the effective potentials through a judiciously chosen unitary transformation. This is demonstrated for two experimentally relevant scenarios, namely for ion traps and adiabatic creation of Weyl points.

QUANTUM EFFECTS OF A DOMAIN WALL IN THE FERROMAGNETIC SYSTEM

2011 ◽  
Vol 25 (06) ◽  
pp. 413-418
Author(s):  
JI-SUO WANG ◽  
KE-ZHU YAN ◽  
BAO-LONG LIANG
Keyword(s):  
Domain Wall ◽  
Unitary Transformation ◽  
Energy Levels ◽  
Canonical Quantization ◽  
Classical Equation ◽  
Quantization Method ◽  
Damping Term ◽  
Quantum Energy ◽  
Moving Wall ◽  
Ferromagnetic System

Starting from the classical equation of the motion of a domain wall in the ferromagnetic systems, the quantum energy levels of the wall and the corresponding eigenfunctions in the case of considering damping term are given by using the canonical quantization method and unitary transformation. The quantum fluctuations of displacement and momentum of the moving wall has also been given as well as the uncertain relation.

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