Stochastic classical trajectory approach to relaxation phenomena. III. Comparison of trajectory results to quantum mechanical perturbation theory

1983 ◽  
Vol 78 (6) ◽  
pp. 3959-3963 ◽  
Author(s):  
Abraham Nitzan ◽  
John C. Tully
Keyword(s):  
Perturbation Theory ◽  
Classical Trajectory ◽  
Quantum Mechanical ◽  
Relaxation Phenomena ◽  
Mechanical Perturbation ◽  
Trajectory Approach

scholarly journals One-loop non-planar anomalous dimensions in super Yang-Mills theory

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tristan McLoughlin ◽  
Raul Pereira ◽  
Anne Spiering
Keyword(s):  
Perturbation Theory ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Mechanical Perturbation ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Dilatation Operator ◽  
Scalar Products

Abstract We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.

General method for removing resonance singularities in quantum mechanical perturbation theory

1996 ◽  
Vol 104 (12) ◽  
pp. 4664-4671 ◽  
Author(s):  
Kathleen M. Kuhler ◽  
Donald G. Truhlar ◽  
Alan D. Isaacson
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanical ◽  
Mechanical Perturbation ◽  
General Method

A remark on quantum-mechanical perturbation theory

1954 ◽  
Vol 50 (4) ◽  
pp. 632-633
Author(s):  
N. Kemmer
Keyword(s):  
Perturbation Theory ◽  
Quantum Theory ◽  
High Order ◽  
Quantum Mechanical ◽  
Quantum Field ◽  
Mechanical Perturbation

In the course of preparing lectures on elementary quantum theory the author developed a way of presenting time-independent perturbation theory that seems to have some advantages over more familiar presentations. There is nothing fundamentally new in the method, and if any claim of greater power can be made for the new version, it is at best for situations in which high-order perturbations are of interest. Quantum-field theorists will no doubt recognize the relation of this presentation to much that has been done in their subject recently.

Operator equations in perturbation theory

1967 ◽  
Vol 301 (1467) ◽  
pp. 507-512 ◽  
Keyword(s):  
Perturbation Theory ◽  
Harmonic Oscillator ◽  
Quantum Mechanical ◽  
Unperturbed System ◽  
Mechanical Perturbation ◽  
Operator Equations ◽  
Linear Harmonic Oscillator

Quantum mechanical perturbation theory is discussed in terms of solutions W of commutator equations of the type [ h , W ] = A . The operators W lead to perturbation corrections for any eigenstate of the unperturbed system. The theory is illustrated by considering the linear harmonic oscillator perturbed by the N th power of the displacement.

Complementary variational principles in perturbation theory

1968 ◽  
Vol 303 (1475) ◽  
pp. 503-509 ◽  
Keyword(s):  
Perturbation Theory ◽  
Lower Bound ◽  
Harmonic Oscillator ◽  
Lower Bounds ◽  
Upper Bound ◽  
Variational Principles ◽  
Upper And Lower Bounds ◽  
Quantum Mechanical ◽  
Simple Application ◽  
Mechanical Perturbation

Complementary upper and lower bounds are derived for second-order quantum-mechanical perturbation energies. The upper bound is equivalent to that of Hylleraas. The lower bound appears to be new, but reduces to that of Prager & Hirschfelder if a certain constraint is applied. A simple application to a perturbed harmonic oscillator is presented.

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