Historically they were sometimes called Feynman-Dyson diagrams or Dyson graphs, because when they were introduced the path integral was unfamiliar, and Freeman Dyson's derivation from old-fashioned perturbation theory was easier to follow for physicists trained in earlier methods.

Thus, the perturbation introduced to the system is described by a velocity field of infinitesimally small amplitude,.

The phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956, and later developed by Alexei Abrikosov and I. M. Khalatnikov using diagrammatic perturbation theory.

Erwin Schrödinger discussed at length the Stark effect in his third paper on quantum theory ( in which he introduced his perturbation theory ), once in the manner of the 1916 work of Epstein ( but generalized from the old to the new quantum theory ) and once by his ( first-order ) perturbation approach.

The problem is whether or not a small perturbation of a conservative dynamical system results in a lasting quasiperiodic orbit.

The KAM theorem states that if the system is subjected to a weak nonlinear perturbation, some of the invariant tori are deformed and survive, while others are destroyed.

Scientists and engineers are able to use liquid crystals in a variety of applications because external perturbation can cause significant changes in the macroscopic properties of the liquid crystal system.

On December 7 the gas supply in the attitude control system was exhausted, and on December 10 and 11 a total of 83 micrometeoroid hits were recorded which caused perturbation of the attitude and degradation of the signal strength.

* 1888 – Henri-Louis Le Chatelier states his principle that the response of a chemical system perturbed from equilibrium will be to counteract the perturbation.

When a new perturbation of temperature of this type happens, temperatures within the system will change in time toward a new equilibrium with the new conditions, provided that these do not change.

At the turn of the 20th century, this problem led Henri Poincaré to make one of the first deductions of the existence of chaos, or what is prosaically called the " butterfly effect ": that even a very small perturbation can have a very large effect on a system.

To keep the exposition simple, a crucial assumption is made: that the solutions to the unperturbed system are not degenerate, so that the perturbation series can be inverted.

Perturbation theory can fail when the system can transition to a different " phase " of matter, with a qualitatively different behaviour, that cannot be modelled by the physical formulas put into the perturbation theory ( e. g., a solid crystal melting into a liquid ).

The TRANSIT system satellites broadcast two UHF carrier signals that provided precise time hacks ( every two minutes ), plus the satellite's six orbit elements and orbit perturbation variables.

In contrast, positive feedback is feedback in which the system responds so as to increase the magnitude of any particular perturbation, resulting in amplification of the original signal instead of stabilization.

Positive feedback is a process in which the effects of a small disturbance on a system can include an increase in the magnitude of the perturbation.

If there are no tidal effects, no perturbation from other forces, and no transfer of mass from one star to the other, such a system is stable, and both stars will trace out an elliptical orbit around the center of mass of the system indefinitely.

Note that a naive perturbation theory around one of those two vacua would never show this non-perturbative tunneling effect, dramatically changing the picture of the vacuum structure of this quantum mechanical system.

In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one.

This happens when the system we wish to describe cannot be described by a small perturbation imposed on some simple system.

This is simply the expectation value of the perturbation Hamiltonian while the system is in the unperturbed state.

This result can be interpreted in the following way: suppose the perturbation is applied, but we keep the system in the quantum state ', which is a valid quantum state though no longer an energy eigenstate.

The reason we go to this trouble is that when the system starts in the state and no perturbation is present, the amplitudes have the convenient property that, for all t, c < sub > j </ sub >( t ) = 1 and if.

So, the system, initially in the unperturbed state, due to the perturbation can go into the state.

This means that, at each contribution of the perturbation series, we have to add a multiplicative factor in the integrands so that, the limit will give back the final state of the system by eliminating all oscillating terms but keeping the secular ones.

Anomalous operation, also known as anomalous perturbation, is any paranormal phenomena in which it is said that an individual ( a ) uses Psi ( parapsychology ) to influence a physical event, or ( b ) to effect a physical change, in object.

Alternatively, anomalous perturbation is defined as an interaction with matter without the use of all known physical mechanisms.

where q ' is the heat release rate perturbation and p ' is the pressure fluctuation.

This theory, completed in the 1940s, is known as quantum electrodynamics ( or " QED "), and, in situations where perturbation theory is applicable, is one of the most accurate theories known to physics.

The number of times the interaction Hamiltonian acts is the order of the perturbation expansion, and the time-dependent perturbation theory for fields is known as the Dyson series.

When the intermediate states at intermediate times are energy eigenstates ( collections of particles with a definite momentum ) the series is called old-fashioned perturbation theory.

Although the statement of the theory in terms of graphs may imply perturbation theory, use of graphical methods in the many-body problem shows that this formalism is flexible enough to deal with phenomena of nonperturbative characters ...

In the canonical quantum field theory the S-matrix is represented within the interaction picture by the perturbation series in the powers of the interaction Lagrangian,

The second order perturbation term in the S-matrix is

This has been demonstrated in the famous Lamb-Retherford experiment and was the starting point for the development of the theory of Quantum electrodynamics ( which is able to deal with these vacuum fluctuations and employs the famous Feynman diagrams for approximations using perturbation theory ).

When a body at these points is perturbed, it moves away from the point, but the factor opposite of that which is increased or decreased by the perturbation ( either gravity or angular momentum-induced speed ) will also increase or decrease, bending the object's path into a stable, kidney-bean-shaped orbit around the point ( as seen in the rotating frame of reference ).

( It is assumed that H does not depend on time and that the perturbation starts at ; otherwise one must use the Dyson series, formally written as

The Dirac picture is the one used in perturbation theory, and is specially associated to quantum field theory and many-body physics.

An orbital perturbation is when a force or impulse which is much smaller than the overall force or average impulse of the main gravitating body and which is external to the two orbiting bodies causes an acceleration, which changes the parameters of the orbit over time.

With the possible exception of gravitation, these interactions can usually be described in a set of calculational approximation methods known as perturbation theory, as being mediated by the exchange of gauge bosons between particles.

In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum.

The effect was first described by Jun Kondo, who applied third-order perturbation theory to the problem, which predicted that the scattering rate of conduction electrons off the magnetic impurity should diverge as the temperature approaches 0 K. The temperature dependence of the resistivity including the Kondo effect is written as:

Each of the examples described below shows how a naive perturbation analysis, which assumes that the problem is regular instead of singular, will fail.

As stated, the quadratic Stark effect is described by second-order perturbation theory.

In this case it is well described by an expansion in powers of g, called perturbation theory.

If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator ( or more accurately, the ground state of a QM problem ).

In 1865, Bernard described the perturbation of this internal state “… there are protective functions of organic elements holding living materials in reserve and maintaining without interruption humidity, heat and other conditions indispensable to vital activity.

In mathematics and physics, a non-perturbative function or process is one that cannot be accurately described by perturbation theory.

This is the equilibrium state that exists before any perturbation is added to the system, and is described by the mean velocity field where the gravitational field is An interface at separates the fluids of densities in the upper region, and in the lower region.

In addition, current quarks possess one asymptotic freedom within the perturbation theory described limits.

Emily Murphy, speaking for the five petitioners, originally objected to this change in the wording of the question, which she described in a letter to the Deputy Minister of Justice as "... a matter of amazement and perturbation to us.