Non-adiabatic quantum evolution: The S matrix as a geometrical phase factor

2012 ◽  
Vol 376 (16) ◽  
pp. 1328-1334 ◽  
Author(s):  
Y. Saadi ◽  
M. Maamache
Keyword(s):  
Phase Factor ◽  
Quantum Evolution ◽  
Geometrical Phase ◽  
S Matrix

A MODIFIED MOYAL REPRESENTATION AND THE PANCHARATNAM PHASE OF TWO-LEVEL SYSTEMS

2002 ◽  
Vol 16 (30) ◽  
pp. 4641-4648
Author(s):  
LING LI ◽  
BO-ZANG LI
Keyword(s):  
Quantum Phase ◽  
Phase Factor ◽  
Quantum Evolution ◽  
Level System ◽  
Pancharatnam Phase ◽  
General Quantum ◽  
Two Level Systems

By including a pre-phase-factor, the Moyal representation for the spin-1/2 (or two-level) system is modified. Such a modification is necessary for describing completely the quantum evolution and calculating exactly the quantum phase. In our modified Moyal representation (MMR) the geometrical expression of the most general quantum phase, i.e., the Pancharatnam phase, is deduced in a much simpler way and without the restriction of cyclic evolution. Two simple examples of application of the MMR are given.

scholarly journals Geometrical Phase Factor for a Non-Hermitian Hamiltonian

1991 ◽  
Vol 14 (1) ◽  
pp. 91-91
Author(s):  
Ch Miniatura ◽  
C Sire ◽  
J Baudon ◽  
J Bellissard
Keyword(s):  
Phase Factor ◽  
Geometrical Phase

WEYL'S GAUGE TRANSFORM AND QUANTUM GEOMETRIC PHASE FACTORS

2007 ◽  
Vol 22 (07n10) ◽  
pp. 645-650
Author(s):  
HUA-ZHONG LI
Keyword(s):  
Gauge Theory ◽  
Gauge Transformation ◽  
Quantum State ◽  
Geometric Phase ◽  
State Vector ◽  
Parallel Transport ◽  
Phase Factor ◽  
Geometrical Phase ◽  
Phase Loop ◽  
Gauge Transform

The historical and geometrical origin of Gauge Transformation and Yang's phase loop of gauge theory are discussed. In the present talk, we present the following points: 1. Parallel transport of a vector; 2. Weyl 1918 gauge transformation 3. Concept of non-integrable phase factor; 4. Berry's quantum geometrical phase; 5. Parallel transport of quantum state vector produces the phase physics.

scholarly journals ON THE SCATTERING PHASE FOR AdS5 × S5 STRINGS

2007 ◽  
Vol 22 (06) ◽  
pp. 415-424 ◽  
Author(s):  
NIKLAS BEISERT
Keyword(s):  
Phase Factor ◽  
S Matrix ◽  
Scattering Phase

We propose a phase factor of the worldsheet S-matrix for strings on AdS5 × S5 apparently solving Janik's crossing relation exactly.

Quantal phase factors accompanying adiabatic changes

1984 ◽  
Vol 392 (1802) ◽  
pp. 45-57 ◽  
Keyword(s):  
Phase Factor ◽  
Symmetric Matrices ◽  
Sign Reversal ◽  
Dynamical Phase ◽  
Geometrical Phase ◽  
Sign Change ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Special Case ◽  
Quantal System

A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.

Geometrical Phase Factor for a Non-Hermitian Hamiltonian

1990 ◽  
Vol 13 (3) ◽  
pp. 199-203 ◽  
Author(s):  
Ch Miniatura ◽  
C Sire ◽  
J Baudon ◽  
J Bellissard
Keyword(s):  
Phase Factor ◽  
Geometrical Phase

scholarly journals A general definition of $JT_a$ -- deformed QFTs

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Tarek Anous ◽  
Monica Guica
Keyword(s):  
Energy Levels ◽  
Finite Size ◽  
Flow Equation ◽  
Phase Factor ◽  
General Definition ◽  
Size Spectrum ◽  
Geometric Flow ◽  
Flow Equations ◽  
S Matrix ◽  
Definition Of

We propose a general path-integral definition of two-dimensional quantum field theories deformed by an integrable, irrelevant vector operator constructed from the components of the stress tensor and those of a U(1) current. The deformed theory is obtained by coupling the original QFT to a flat dynamical gauge field and ``half'' a flat dynamical vielbein. The resulting partition function is shown to satisfy a geometric flow equation, which perfectly reproduces the flow equations for the deformed energy levels that were previously derived in the literature. The S-matrix of the deformed QFT differs from the original S-matrix only by an overall phase factor that depends on the charges and momenta of the external particles, thus supporting the conjecture that such QFTs are UV complete, although intrinsically non-local. For the special case of an integrable QFT, we check that this phase factor precisely reproduces the change in the finite-size spectrum via the Thermodynamic Bethe Ansatz equations.

Unitary bounds and controllability of quantum evolution in NMR spectroscopy

1999 ◽  
Vol 96 (12) ◽  
pp. 1739-1744 ◽  
Author(s):  
T. S. UNTIDT, S. J. GLASER, C. GRIESIN
Keyword(s):  
Nmr Spectroscopy ◽  
Quantum Evolution
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