S-matrix formalism of transmission through two quantum billiards coupled by a waveguide

2005 ◽  
Vol 38 (49) ◽  
pp. 10647-10661 ◽  
Author(s):  
Almas F Sadreev ◽  
Evgeny N Bulgakov ◽  
Ingrid Rotter
Keyword(s):  
Matrix Formalism ◽  
S Matrix

scholarly journals Formale Mehrkanal-Streutheorie

1960 ◽  
Vol 15 (4) ◽  
pp. 311-319
Author(s):  
Gerald Gbawert ◽  
Joachim Petzold
Keyword(s):  
Quantum Mechanics ◽  
Particle System ◽  
Formal Theory ◽  
Exclusion Principle ◽  
Alternative Formulation ◽  
Matrix Formalism ◽  
Nonrelativistic Quantum ◽  
System A ◽  
S Matrix ◽  
Nonrelativistic Quantum Mechanics

An alternative formulation is presented of the formal theory of multi-channel scattering in nonrelativistic quantum mechanics. We start by defining spaces of state vectors, where two particles either stay together or separate in the limit t →+∞ (or — ∞), when the state vector develops in time by e–i H t (H is the complete Hamiltonian of the n-particle system). A channel is defined as a space of state vectors with the following property: Developing in time by e-i H t they asymptotically describe a state of the n-particle system, where the particles are grouped in fragments. Defining a Hamiltonian Hγ for each channel, in which—compared to H—the interactions acting between particles from different fragments are missing, it is physically plausible that lim eiH e—iHt Ψ exists for vectors Ψ in the channel. Having discussed the limit vectors (asymptotic states), the S-matrix formalism can be introduced as usual. Finally the introduction of the exclusion principle is discussed.

Interacting Hadron resonance gas model within S-matrix formalism

2019 ◽  
Vol 28 (09) ◽  
pp. 1940001 ◽  
Author(s):  
Ashutosh Dash ◽  
Subhasis Samanta
Keyword(s):  
Virial Coefficients ◽  
Heavy Ion ◽  
Phase Shifts ◽  
Matrix Formalism ◽  
Ion Collisions ◽  
S Matrix ◽  
Scattering Phase ◽  
Thermodynamic Variables ◽  
K Matrix ◽  
Dynamical Information

A noninteracting hadron resonance gas model is used often to study the hadronic phase formed in heavy ion collisions. Interaction among various hadronic constituents can be included using an S-matrix-based virial expansion approach. The virial coefficients require the dynamical information about the scattering phase shifts, which is used to compute various thermodynamic observables of an interacting hadronic gas. The attractive part of the phase shifts are calculated using K-matrix formalism while the repulsive part is obtained by fitting to experimental data. Calculation of various thermodynamic variables like pressure, energy density, specific heat capacity, etc., along with the second and higher-order correlations and fluctuations of conserved charges are done, first with only attraction and then with both attraction and repulsion included. Comparison of S-matrix results indicate a better agreement with lattice QCD data than the ideal HRG model across all thermodynamic variables.

Resonance Widths and Unitarity

1972 ◽  
Vol 50 (2) ◽  
pp. 84-92 ◽  
Author(s):  
C. T. Tindle
Keyword(s):  
Energy Dependence ◽  
Cross Section ◽  
Matrix Theory ◽  
Neutron Cross Section ◽  
Matrix Formalism ◽  
R Matrix ◽  
Level Width ◽  
S Matrix ◽  
The Difference ◽  
Energy Dependent

The low energy neutron cross section of 135Xe is analyzed using both the R-matrix theory of Wigner and Eisenbud and the S-matrix theory of Humblet and Rosenfeld. Particular attention is given to the role played by the total resonance level width for it is well known that the R-matrix widths are energy dependent but the S-matrix widths are not. This different energy dependence leads to different analytic forms for the cross section and the n + 135Xe reaction offers what may be the simplest and best physical example for comparing these two forms. To the accuracy of the present data the difference is not detectable. The different energy dependence of the resonance widths is shown to be related to unitarity. A general proof that the R-matrix formalism is always unitary is given. The difficulty of satisfying unitarity in the S-matrix formalism is discussed and it is shown for the n + 135Xe reactions that this can lead to physically unacceptable solutions. This "lack of unitarity" does not, however, lead to any difficulties in fitting the present experimental data.

S-matrix theory and the density matrix formalism

1979 ◽  
Vol 38 (2) ◽  
pp. 553-560 ◽  
Author(s):  
M. Roberts ◽  
W.E. Hagston
Keyword(s):  
Density Matrix ◽  
Matrix Theory ◽  
Matrix Formalism ◽  
Density Matrix Formalism ◽  
S Matrix

QUANTUM-ELECTRODYNAMIC PROCESSES IN A RADIATION-DOMINATED ROBERTSON-WALKER UNIVERSE

1992 ◽  
Vol 07 (09) ◽  
pp. 2055-2086 ◽  
Author(s):  
I.L. BUCHBINDER ◽  
L.I. TSAREGORODTSEV
Keyword(s):  
Quantum Electrodynamics ◽  
Line Element ◽  
Total Probability ◽  
Matrix Formalism ◽  
Differential Probability ◽  
Electron Positron ◽  
S Matrix ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Electron Positron Pair

Quantum electrodynamics in an expanding Robertson-Walker universe with the line element ds2=dt2 – a2(t)(dx2+dy2+dz2) (radiation-dominated universe) is considered. The differential probability of bremsstrahlung of an electron in the external gravitational field and the differential probability of an electron-positron pair and photon creation from the vacuum are calculated by using the perturbative S-matrix formalism. The behavior of these probabilities in different kinematic regions is investigated. The total probabilities are shown to be finite. In conclusion, the total probability of a pair and photon creation from vacuum We is compared with the total probability of pair production due to an expansion of the universe W0. The comparison shows that We=1.9·10−2W0 at about the Compton time of an electron.

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