Solute reencounter effects. 5. Equivalence of isolated pair and concentration gradient models in the long-time limit

1981 ◽  
Vol 85 (24) ◽  
pp. 3552-3554 ◽  
Author(s):  
B. Stevens
Keyword(s):  
Concentration Gradient ◽  
Time Limit ◽  
Long Time ◽  
Gradient Models

scholarly journals A Discontinuity of the Energy of Quantum Walk in Impurities

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1134
Author(s):  
Kenta Higuchi ◽  
Takashi Komatsu ◽  
Norio Konno ◽  
Hisashi Morioka ◽  
Etsuo Segawa
Keyword(s):  
Unit Circle ◽  
Stationary State ◽  
Discrete Time ◽  
Quantum Walk ◽  
Time Limit ◽  
The Other ◽  
Unitary Matrix ◽  
Initial State ◽  
Time Quantum ◽  
Long Time

We consider the discrete-time quantum walk whose local dynamics is denoted by a common unitary matrix C at the perturbed region {0,1,⋯,M−1} and free at the other positions. We obtain the stationary state with a bounded initial state. The initial state is set so that the perturbed region receives the inflow ωn at time n(|ω|=1). From this expression, we compute the scattering on the surface of −1 and M and also compute the quantity how quantum walker accumulates in the perturbed region; namely, the energy of the quantum walk, in the long time limit. The frequency of the initial state of the influence to the energy is symmetric on the unit circle in the complex plain. We find a discontinuity of the energy with respect to the frequency of the inflow.

LONG‐TIME RESPONSE PREDICTED BY EXACT ELASTIC RAY THEORY

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 363-368 ◽  
Author(s):  
T. W. Spencer
Keyword(s):  
Formal Solution ◽  
Intermediate Stage ◽  
Time Limit ◽  
Time Interval ◽  
Individual Response ◽  
Axially Symmetric ◽  
Long Time ◽  
The Difference ◽  
The Individual ◽  
Significant Figures

The formal solution for an axially symmetric radiation field in a multilayered, elastic system can be expanded in an infinite series. Each term in the series is associated with a particular raypath. It is shown that in the long‐time limit the individual response functions produced by a step input in particle velocity are given by polynomials in odd powers of the time. For rays which suffer m reflections, the degree of the polynomials is 2m+1. The total response is obtained by summing all rays which contribute in a specified time interval. When the rays are selected indiscriminately, the difference between the magnitude of the partial sum at an intermediate stage of computation and the magnitude of the correct total sum may be greater than the number of significant figures carried by the computer. A prescription is stated for arranging the rays into groups. Each group response function varies linearly in the long‐time limit and goes to zero when convolved with a physically realizable source function.

scholarly journals Cancellation of vacuum diagrams and the long-time limit in out-of-equilibrium diagrammatic quantum Monte Carlo

2019 ◽  
Vol 100 (8) ◽  
Author(s):  
Alice Moutenet ◽  
Priyanka Seth ◽  
Michel Ferrero ◽  
Olivier Parcollet
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Time Limit ◽  
Long Time

scholarly journals Quasi equilibrium construction for the long time limit of glassy dynamics

2015 ◽  
Vol 2015 (10) ◽  
pp. P10010
Author(s):  
Silvio Franz ◽  
Giorgio Parisi ◽  
Federico Ricci-Tersenghi ◽  
Pierfrancesco Urbani
Keyword(s):  
Time Limit ◽  
Quasi Equilibrium ◽  
Glassy Dynamics ◽  
Long Time

ENERGY RELAXATION AND TRANSFER IN TRIMER

2001 ◽  
Vol 15 (28n30) ◽  
pp. 3781-3784
Author(s):  
PAVEL HEŠMAN ◽  
IVAN BARVÍK
Keyword(s):  
Energy Transfer ◽  
Density Matrix ◽  
Initial Conditions ◽  
Energy Relaxation ◽  
Time Limit ◽  
Matrix Elements ◽  
Arbitrary Time ◽  
Initial Excitation ◽  
Long Time ◽  
Secular Approximation

We consider the relaxation and transfer in a symmetric trimer coupled to a phonon bath. The energy transfer within the trimer occurs via resonance interactions and coupling between the trimer and the bath occurs via modulation of the monomer energies by phonons. We compare the model introduced by Čápek with the Redfield model used commonly with secular approximation. We discuss two initial conditions: a) The highest eigenstate of the trimer is initially excited, and b) the initial excitation is local. We find that the occupation probabilities in the representation of eigenstates are the same in both models. But it is not so for off-diagonal density matrix elements. Only if the off-diagonal elements vanish initially (initial conidtion a), they vanish at arbitrary time in both models. If the initial excitation is local, off-diagonal elements differ essentially even in the long time limit.

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