In theoretical and mathematical physics, twistor theory is a mathematical theory mapping the geometric objects of conventional 3+1 space-time (Minkowski space) into geometric objects in a 4 dimensional space with metric signature (2,2). This space is called twistor space, and its complex valued coordinates are called “twistors.”

— Wikipedia on Twistor theory

2009.12.27 Sunday ACHK

In theoretical physics, mysterious duality is a set of mathematical similarities between some objects and laws describing M-theory on k-dimensional tori on one side, and geometry of del Pezzo surfaces on the other side.

In theoretical physics, mysterious duality is a set of mathematical similarities between some objects and laws (and perhaps all of them, if the conjecture is extended appropriately) describing M-theory on k-dimensional tori (i.e. type II superstring theory on T^{k-1} if k is positive) on one side, and geometry of del Pezzo surfaces (for example, the cubic surfaces) on the other side.

— Wikipedia on Mysterious duality

2009.12.26 Saturday ACHK

Quantum foam is the source of quantum randomness.

— Me@2009.09.06

2009.12.25 Friday (c) ACHK

The Hubbard-Stratonovich (HS) transformation is an exact mathematical transformation invented by Russian physicist Ruslan L. Stratonovich and popularized by British physicist John Hubbard.

— Wikipedia on Hubbard-Stratonovich transformation

2009.12.21 Monday ACHK

It is used to convert a particle theory into its respective field theory by linearizing the density operator in the many-body interaction term of the Hamiltonian and introducing a scalar auxiliary field. It is defined as (Baeurle 2002, Baeurle 2003)

where the real constant a > 0. The basic idea of the HS transformation is to reformulate a system of particles interacting through two-body potentials into a system of independent particles interacting with a fluctuating field.

— Wikipedia on Hubbard-Stratonovich transformation

2009.12.20 Sunday ACHK

邏輯建基於對邏輯概念進行語理分析.

— 哲道行者 p.179

Logic is based on the linguistic-conceptual analysis of basic logic concepts.

The basic logic concepts are “and”, “or”, “implies / if…then”, “not”.

— Translation by Me@2009.12.19

2009.12.19 Saturday (c) ACHK

Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.

Light is made up of particles called photons and hence inherently is “grainy” (quantized). Quantum optics is the study of the nature and effects of light as quantized photons.

Research into quantum optics that aims to bring photons into use for information transfer and computation is now often called photonics to emphasize the claim that photons and photonics will take the role that electrons and electronics now have.

— Wikipedia on Quantum optics

2009.12.17 Thursday ACHK

Coherent states in quantum optics

In quantum mechanics a coherent state is a specific kind of quantum state, applicable to the quantum harmonic oscillator, the electromagnetic field, etc. that describe a maximal kind of coherence and a classical kind of behavior.

— Wikipedia on Coherent state

2009.12.16 Wednesday ACHK

For example, a classical electromagnetic field can be viewed as a coherent state of photons.

— Quantum Many-Particle Systems, J W Negele and H Orland, Addison-Wesley, 1988

2009.12.15 Tuesday ACHK

Quantum chaos is a branch of physics which studies how chaotic classical systems can be shown to be limits of quantum-mechanical systems.

— Wikipedia on Quantum chaos

2009.12.14 Monday ACHK

Functional differentiation can be reduced to partial differentiation by discretization.

— Me@2009.12.12, based on Professor Renbao Liu

2009.12.13 Sunday (c) ACHK

Complex number method (Phasors) is the frequency response of the Laplace transform.

(Put s = j \omega, where j = \sqrt{-1}.)

— Me@2001

2009.12.12 Saturday (c) ACHK

Accelerator physics deals with the problems of building and operating particle accelerators.

The experiments conducted with particle accelerators are not regarded as part of accelerator physics. These belong (according to the objectives of the experiments) to particle physics, nuclear physics, condensed matter physics, materials physics, etc. as well as to other sciences and technical fields.

— Wikipedia on Accelerator physics

2009.12.11 Friday ACHK

The Fock state (e.g. a single photon) is the most particle-like state; it has a fixed number of particles, and phase is indeterminate.

It should be noted that the notation | \alpha \rangle does not refer to a Fock state. For example, at \alpha = 1, one should not mistake |1 \rangle as a single-photon Fock state — it represents a Poisson distribution of fixed number states with a mean photon number of unity.

— Wikipedia on Coherent state

2009.12.10 Thursday ACHK

A Fock state (also known as a number state), in quantum mechanics, is any state of the Fock space with a well-defined number of particles in each state.

— Wikipedia on Fock state

2009.12.09 Wednesday ACHK

In quantum mechanics, a stationary state is an eigenstate of a Hamiltonian, or in other words, a state of definite energy. It’s called stationary because the corresponding probability density has no time dependence.

As an eigenstate of the Hamiltonian, a stationary state is not subject to change or decay (to a lower energy state). In practice, stationary states are never truly “stationary” for all time. Rather, they refer to the eigenstate of a Hamiltonian where small perturbative effects have been ignored. The language allows one to discuss the eigenstates of the unperturbed Hamiltonian, whereas the perturbation will eventually cause the stationary state to decay. The only true stationary state is the ground state.

— Wikipedia on Stationary state

2009.12.08 Tuesday ACHK

Every two level system can be regarded as a spin.

— Wang Dawei@2009.11.30

2009.12.07 Monday ACHK

The lapses in intuition mostly stemmed from the fact that the limit of an infinite statistical system has many zero-one laws which are absent in finite systems: an infinitesimal change in a parameter can lead to big differences in the statistical behavior, as Democritus expected.

— Wikipedia on Ising Model

2009.12.06 Sunday ACHK

While a magnetic monopole particle has never been observed, there are a number of phenomena in condensed-matter physics where a material, due to the collective behavior of its electrons and ions, can show emergent phenomena that resemble magnetic monopoles in some respect. These should not be confused with actual monopole particles; in particular, the divergence of the microscopic magnetic B-field is zero everywhere in these systems, unlike in the presence of a true magnetic monopole particle. The behavior of these quasiparticles would only become indistinguishable from true magnetic monopoles — and they would truly deserve the name — if the so-called magnetic fluxtubes connecting these would-be monopoles became unobservable which also means that these flux tubes would have to be infinitely thin, obey the Dirac quantization rule, and deserve to be called Dirac strings.

— Wikipedia on “Monopoles” in condensed-matter systems

2009.12.05 Saturday ACHK