Short-time behavior of the correlation functions for the quantum Langevin equation

1996 ◽  
Vol 53 (4) ◽  
pp. 2033-2037 ◽  
Author(s):  
Raffaella Blasi ◽  
Saverio Pascazio
Keyword(s):  
Langevin Equation ◽  
Correlation Functions ◽  
Time Behavior ◽  
Quantum Langevin Equation ◽  
Short Time

scholarly journals Low Density Limit and the Quantum Langevin Equation for the Heat Bath

2009 ◽  
Vol 16 (04) ◽  
pp. 351-370
Author(s):  
Ameur Dhahri
Keyword(s):  
Langevin Equation ◽  
Time Scale ◽  
Chemical Potential ◽  
Heat Bath ◽  
Interaction Model ◽  
Low Density ◽  
Density Limit ◽  
Quantum Langevin Equation ◽  
Low Density Limit ◽  
Short Time

We consider a repeated quantum interaction model describing a small system [Formula: see text] in interaction with each of the identical copies of the chain ⊗ℕ* ℂn+1, modeling a heat bath, one after another during the same short time intervals [0, h]. We suppose that the repeated quantum interaction Hamiltonian is split into two parts: a free part and an interaction part with time scale of order h. After giving the GNS representation, we establish the connection between the time scale h and the classical low density limit. We introduce a chemical potential µ related to the time h as follows: h2 = eβµ. We further prove that the solution of the associated discrete evolution equation converges strongly, when h tends to 0, to the unitary solution of a quantum Langevin equation directed by the Poisson processes.

Short time behavior and universal relations in polymer cyclization

1991 ◽  
Vol 1 (4) ◽  
pp. 471-486 ◽  
Author(s):  
Barry Friedman ◽  
Ben O'Shaughnessy
Keyword(s):  
Time Behavior ◽  
Short Time

An approach towards a simple quantum Langevin equation

2011 ◽  
Vol 511 (4-6) ◽  
pp. 471-481 ◽  
Author(s):  
Joshua M. Jackson ◽  
Pietrina L. Brucia ◽  
Michael Messina
Keyword(s):  
Langevin Equation ◽  
Quantum Langevin Equation ◽  
Simple Quantum

Asymptotic time behavior of correlation functions. II. Kinetic and potential terms

1976 ◽  
Vol 15 (1) ◽  
pp. 7-22 ◽  
Author(s):  
M. H. Ernst ◽  
E. H. Hauge ◽  
J. M. J. van Leeuwen
Keyword(s):  
Correlation Functions ◽  
Time Behavior ◽  
Asymptotic Time

Short Time Behavior of Solutions to Linear and Nonlinear Schrödinger Equations

2008 ◽  
Vol 60 (5) ◽  
pp. 1168-1200 ◽  
Author(s):  
Michael Taylor
Keyword(s):  
Broad Class ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Time Behavior ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Pinsky Phenomenon ◽  
Nonlinear Schrodinger Equations ◽  
Linear And Nonlinear ◽  
Short Time

AbstractWe examine the fine structure of the short time behavior of solutions to various linear and nonlinear Schrödinger equations ut = iΔu+q(u) on I×ℝn, with initial data u(0, x) = f (x). Particular attention is paid to cases where f is piecewise smooth, with jump across an (n−1)-dimensional surface. We give detailed analyses of Gibbs-like phenomena and also focusing effects, including analogues of the Pinsky phenomenon. We give results for general n in the linear case. We also have detailed analyses for a broad class of nonlinear equations when n = 1 and 2, with emphasis on the analysis of the first order correction to the solution of the corresponding linear equation. This work complements estimates on the error in this approximation.

scholarly journals Dissipative quantum tunneling: quantum Langevin equation approach

1988 ◽  
Vol 128 (1-2) ◽  
pp. 29-34 ◽  
Author(s):  
G.W. Ford ◽  
J.T. Lewis ◽  
R.F. O'Connell
Keyword(s):  
Langevin Equation ◽  
Quantum Tunneling ◽  
Equation Approach ◽  
Quantum Langevin Equation
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